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Cómo usar el glosario en español:
1. Busca el término en inglés que desees encontrar.
2. El término en español, junto con la definición,
se encuentran en la columna de la derecha.
Glossary/Glosario
Español
English
A
absolute value (58) The distance a number is from
zero on the number line.
valor absoluto Distancia que un número dista de
cero en la recta numérica.
accuracy (589) The degree of conformity of a
measurement with the true value.
exactitud Grado de conformidad de una medida con
el valor verdadero.
acute angle (449) An angle with a measure greater
than 0° and less than 90°.
ángulo agudo Ángulo con una medida mayor que 0°
y menor que 90°.
acute triangle (454) A triangle that has three acute
angles.
triángulo acutángulo Triángulo que posee tres
ángulos agudos.
adjacent angles (493) Two angles that have the same
vertex, share a common side, and do not overlap.
ángulos adyacentes Dos ángulos que poseen el
mismo vértice, comparten un lado y no se
traslapan.
algebraic expression (17) An expression that is built
out of numbers and variables using one or more
operations.
expresión algebraica Expresión compuesta por
números y variables que usan una o más
operaciones.
algebraic fraction (170) A fraction with one or more
variables in the numerator or denominator.
fracción algebraica Fracción con una o más variables
en el numerador o denominador.
alternate exterior angles (492) Nonadjacent exterior
angles found on opposite sides of the transversal.
In the figure below, 1 and 7, 2 and 8 are
alternate exterior angles.
ángulos alternos externos Ángulos exteriores no
adyacentes que se encuentran en lados opuestos
de una transversal. En la siguiente figura, 1 y
7, 2 y 8 son ángulos alternos externos.
1 2
4 3
1 2
4 3
alternate interior angles (492) Nonadjacent interior
angles found on opposite sides of the transversal.
In the figure above, 4 and 6, 3 and 5 are
alternate interior angles.
ángulos alternos internos Ángulos interiores no
adyacentes que se encuentran en lados opuestos
de una transversal. En la figura anterior, 4 y 6,
3 y 5 son ángulos alternos internos.
altitude (520) A line segment that is perpendicular to
the base of a figure with endpoints on the base
and the side opposite the base.
altura Segmento de recta perpendicular a la base de
una figura y cuyos extremos yacen en la base y en
el lado opuesto de la base.
angle (447) Two rays with a common endpoint form
an angle. The rays and vertex are used to name
an angle. The angle below is ABC.
ángulo Dos rayos con un punto común forman un
ángulo. Los rayos y el vértice se usan para identificar el ángulo. El siguiente ángulo es ABC.
A
A
B
C
area (132) The measure of the surface enclosed by a
geometric figure.
B
C
área Medida de la superficie que encierra una figura
geométrica.
Glossary/Glosario R1
Glossary/Glosario
5 6
8 7
5 6
8 7
arithmetic sequence (249) A sequence in which the
difference between any two consecutive terms is
the same.
sucesión aritmética Sucesión en que la diferencia
entre dos términos consecutivos cualesquiera es
siempre la misma.
average (82) The sum of data divided by the number
of items in the data set, also called the mean.
promedio Suma de los datos dividida entre el
número de elementos en el conjunto de datos.
También llamado media.
B
back-to-back stem-and-leaf plot (607) Used to
compare two sets of data. The leaves for one set
of data are on one side of the stem and the leaves
for the other set of data are on the other side.
diagrama de tallo y hojas consecutivo Se usa para
comparar dos conjuntos de datos. Las hojas de
uno de los conjuntos de datos aparecen en un
lado del tallo y las del otro al otro lado de éste.
bar graph (722) A graphic form using bars to make
comparisons of statistics.
gráfica de barras Tipo de gráfica que usa barras para
comparar estadísticas.
bar notation (201) In repeating decimals the line or
bar placed over the digits that repeat. For
example, 2.6
3 indicates the digits 63 repeat.
notación de barra En decimales periódicos, la línea o
barra que se escribe encima de los dígitos que se
repiten. Por ejemplo, en 2.6
3 la barra encima del
63 indica que los dígitos 63 se repiten.
base (153) In 24, the base is 2. The base is used as a
factor as many times as given by the exponent
(4). That is, 24 2 2 2 2 .
base En 24, la base es 2. La base se usa como factor las
veces que indique el exponente (4). Es decir,
24 2 2 2 2 .
base (288) In a percent proportion, the whole
quantity, or the number to which the part is
being compared.
base En una proporción porcentual, toda la cantidad
o número al que se compara la parte.
parte
por ciento
base
100
Glossary/Glosario
part
percent
base
10 0
base (520, 521, 522) The base of a parallelogram or a
triangle is any side of the figure. The bases of a
trapezoid are the parallel sides.
base La base de un paralelogramo o de un triángulo
es cualquier lado de la figura. Las bases de un
trapecio son los lados paralelos.
base (557) The bases of a prism are any two parallel
congruent faces.
base Las bases de un prisma son cualquier par de
caras paralelas y congruentes.
best-fit line (409) On a scatter plot, a line drawn that
is very close to most of the data points. The line
that best fits the data.
recta de ajuste óptimo En una gráfica de dispersión,
una recta que está muy cercana a la mayoría de
los puntos de datos. La recta que mejor se ajusta a
los datos.
binomial (669) A polynomial with exactly two terms.
binomio Polinomio con exactamente dos términos.
boundary (419) A line that separates a graph into
half planes.
frontera Recta que divide una gráfica en semiplanos.
box-and-whisker plot (617) A diagram that divides a
set of data into four parts using the median and
quartiles. A box is drawn around the quartile
values and whiskers extend from each quartile to
the extreme data points.
diagrama de caja y patillas Diagrama que divide un
conjunto de datos en cuatro partes usando la
mediana y los cuartiles. Se dibuja una caja
alrededor de los cuartiles y se extienden patillas
de cada uno de ellos a los valores extremos.
C
center (533) The given point from which all points on
the circle are the same distance.
R2 Glossary/Glosario
centro Punto dado del cual equidistan todos los
puntos de un círculo.
círculo Conjunto de todos los puntos del plano que
están a la misma distancia de un punto dado del
plano llamado centro.
circle graph (723) A type of statistical graph used to
compare parts of a whole.
gráfica circular Tipo de gráfica estadística que se usa
para comparar las partes de un todo.
circumference (533) The distance around a circle.
circunferencia Longitud del contorno de un círculo.
coefficient (103) The numerical part of a term that
contains a variable.
coeficiente Parte numérica de un término que
contiene una variable.
combination (642) An arrangement or listing in
which order is not important.
combinación Arreglo o lista en que el orden no es
importante.
common difference (249) The difference between
any two consecutive terms in an arithmetic
sequence.
diferencia común Diferencia entre dos términos
consecutivos cualesquiera de una sucesión
aritmética.
common multiples (226) Multiples that are shared
by two or more numbers. For example, some
common multiples of 4 and 6 are 0, 12, and 24.
múltiplos comunes Múltiplos compartidos por dos o
más números. Por ejemplo, algunos múltiplos
comunes de 4 y 6 son 0, 12 y 24.
common ratio (250) The ratio between any two
consecutive terms in a geometric sequence.
razón común Razón entre dos términos consecutivos
cualesquiera de una sucesión geométrica.
compatible numbers (714) Numbers that have been
rounded so when the numbers are divided by
each other, the remainder is zero.
números compatibles Números redondeados de
modo que cuando se dividen, el residuo es cero.
complementary (493) Two angles are complementary
if the sum of their measures is 90°.
complementarios Dos ángulos son complementarios
si la suma de sus medidas es 90°.
composite number (159) A whole number that has
more than two factors.
número compuesto Número entero que posee más
de dos factores.
compound event (650) Two or more simple events.
evento compuesto Dos o más eventos simples.
cone (569) A solid with a circular base lying in one
plane plus a vertex not lying on that plane. The
remaining surface of the cone is formed by
joining the vertex to points on the circle by line
segments.
cono Sólido con una base circular que yace en un
plano, más un vértice que no yace en ese plano.
La superficie restante del cono se forma de la
unión del vértice a puntos en el círculo mediante
segmentos de recta.
congruent (455, 493, 500) Line segments that have the
same length, or angles that have the same measure,
or figures that have the same size and shape.
congruentes Segmentos de recta que tienen la misma
longitud o ángulos que tienen la misma medida o
figuras que poseen la misma forma y tamaño.
conjecture (7) An educated guess.
conjetura Suposición informada.
constant (103) A term without a variable.
constante Término sin variables.
constant of variation (394) The slope, or rate of
change, in the equation y kx, represented by k.
constante de variación La pendiente, o tasa de
cambio, en la ecuación y kx, representada por k.
converse (462) The statement formed by reversing
the phrases after if and then in an if-then
statement.
recíproca Un enunciado que se forma intercambiando los enunciados que vienen a continuación de
si-entonces en un enunciado si-entonces.
Glossary/Glosario
circle (533) The set of all points in a plane that are
the same distance from a given point called the
center.
coordinate (57) A number that corresponds with a
point on a number line.
coordenada Número que corresponde a un punto en
la recta numérica.
coordinate plane (33) Another name for the
coordinate system.
plano de coordenadas Otro nombre para el sistema
de coordenadas.
coordinate system (33) A coordinate system is
formed by the intersection of two number lines
that meet at right angles at their zero points, also
called a coordinate plane.
sistema de coordenadas Un sistema de coordenadas
se forma de la intersección de dos rectas numéricas
perpendiculares que se intersecan en sus puntos
cero. También llamado plano de coordenadas.
corresponding angles (492) Angles that have the
same position on two different parallel lines
cut by a transversal. In the figure, 1 and
5, 2 and 6, 3 and 7, 4 and 8 are
corresponding angles.
ángulos correspondientes Ángulos que tienen la
misma posición en dos rectas paralelas distintas
cortadas por una transversal. En la figura, 1 y
5, 2 y 6, 3 y 7, 4 y 8 son ángulos
correspondientes.
1 2
4 3
1 2
4 3
5 6
8 7
5 6
8 7
corresponding parts (500) Parts of congruent or
similar figures that match.
partes correspondientes Partes de figuras congruentes
o semejantes que se corresponden mutuamente.
cosine (477) If ABC is a right triangle and A is an
acute angle,
coseno Si ABC es un ángulo rectángulo y A es uno
de sus ángulos agudos,
measure of the leg adjacent to A
measure of the hypotenuse
medida del cateto adyacente a A
medida de la hipotenusa
cosine A coseno A counterexample (25) An example that shows a
conjecture is not true.
a
c
contraejemplo Ejemplo que muestra que una
conjetura no es verdadera.
b
d
Glossary/Glosario
a
c
b
d
a
c
cross products (270) If , then ad bc. If
productos cruzados Si , entonces ad bc. Si
b
d
a
c
ad bc, then .
b
d
ad bc, entonces .
cubic function (688) A function that can be
described by an equation of the form
y ax3 bx2 cx d, where a 0.
función cúbica Función que puede describirse
por una ecuación de la forma
y ax3 bx2 cx d, donde a 0.
cylinder (565) A solid with two parallel congruent
circular bases. The third surface of the cylinder
consists of all parallel circles of the same radius
whose centers lie on the segment joining the
centers of the bases.
cilindro Sólido con dos bases circulares congruentes
y paralelas. La tercera superficie del cilindro
consta de todos los círculos paralelos del mismo
radio cuyos centros yacen en el segmento que
une los centros de las bases.
D
deductive reasoning (25) The process of using facts,
properties, or rules to justify reasoning or reach
valid conclusions.
razonamiento deductivo Proceso de usar hechos,
propiedades o reglas para justificar un
razonamiento o para sacar conclusiones válidas.
defining a variable (18) Choosing a variable and a
quantity for the variable to represent in an
equation.
definir una variable Seleccionar una variable y una
cantidad para la variable psts representst en una
ecuación.
degree (448) The most common unit of measure for
angles.
grado La unidad de medida angular más común.
degree (670) The sum of the exponents of the
variables of a monomial.
grado Suma de los exponentes de las variables de un
monomio.
dependent events (651) Two or more events in which
the outcome of one event does affect the outcome
of the other event(s).
eventos dependientes Dos o más eventos en que el
resultado de uno de ellos afecta el resultado del
otro o de los otros eventos.
diagonal (528) A line segment that joins two
nonconsecutive vertices of a polygon.
diagonal Segmento de recta que une dos vértices no
consecutivos de un polígono.
diameter (533) The distance across a circle through
its center.
diámetro Distancia de un lado a otro de un círculo
medida a través de su centro.
dilation (512) A transformation that alters the size of
a figure but not its shape.
dilatación Transformación que altera el tamaño de
una figura, pero no su forma.
dimensional analysis (212) The process of including
units of measurement when computing.
análisis dimensional Proceso que incorpora las
unidades de medida al hacer cálculos.
direct variation (394) A special type of linear
equation that describes rate of change. A
relationship such that as x increases in value,
y increases or decreases at a constant rate.
variación directa Tipo especial de ecuación lineal que
describe tasas de cambio. Relación en que a
medida que x aumenta de valor, y aumenta o
disminuye a una tasa constante .
discount (299) The amount by which the regular
price of an item is reduced.
descuento Cantidad por la que se reduce el precio
normal de un artículo.
Distance Formula (466) The distance between two
points, with coordinates (x1, y1) and (x2, y2), is
Fórmula de la distancia La distancia entre dos
puntos, con coordenadas (x1, y1) y (x2, y2), se
given by d (x2 x1)2 (y2 y1)2.
calcula con d (x2 x1)2 (y2 y1)2.
divisible Un número es divisible entre otro si, al
dividirlos, el residuo es cero.
domain (35) The domain of a relation is the set of all
x-coordinates from each pair.
dominio El dominio de una relación es el conjunto
de coordenadas x de todos los pares .
E
edge (556) Where two planes intersect in a line.
arista Recta en donde se intersecan dos planos.
empty set (336) A set with no elements shown by the
symbol { } or .
conjunto vacío Conjunto que carece de elementos y
que se denota con el símbolo { } o .
equation (28) A mathematical sentence that contains
an equals sign ().
ecuación Enunciado matemático que contiene el
signo de igualdad ().
equilateral triangle (455) A triangle with all sides
congruent.
triángulo equilátero Un triángulo cuyos lados son
todos congruentes.
equivalent equations (111) Two or more equations
with the same solution. For example, x 4 7
and x 3 are equivalent equations.
ecuaciones equivalentes Dos o más ecuaciones con
las mismas soluciones. Por ejemplo, x 4 7 y
x 3 son ecuaciones equivalentes.
Glossary/Glosario
divisible (148) A number is divisible by another if,
upon division, the remainder is zero.
equivalent expressions (98) Expressions that have
the same value.
expresiones equivalentes Expresiones que tienen el
mismo valor.
evaluate (12) Find the numerical value of an
expression.
evaluar Calcular el valor numérico de una expresión.
expanded form (154) A number expressed using
place value to write the value of each digit in the
number.
forma desarrollada Número que se escribe usando el
valor de posición para indicar el valor de cada
dígito de un número.
experimental probability (311) What actually occurs
when repeating a probability experiment many
times.
probabilidad experimental Lo que en realidad
ocurre al repetir muchas veces un experimento de
probabilidad.
exponent (153) In 24, the exponent is 4. The exponent
tells how many times the base, 2, is used as a
factor. So, 24 2 2 2 2.
exponente En 24, el exponente es 4. El exponente
indica cuántas veces se usa la base, 2, como
factor. Así, 24 2 2 2 2.
exterior angles (492, 531) Four of the angles formed
by the transversal and two parallel lines. Exterior
angles lie outside the two parallel lines.
ángulos exteriores Cuatro de los ángulos formados
por una transversal y dos rectas paralelas. Los
ángulos exteriores yacen fuera de las dos rectas
paralelas.
Glossary/Glosario
F
face (556) A flat surface, the side or base of a prism.
cara Superficie plana, el lado o la base de un prisma.
factorial (642) The expression n factorial (n!) is the
product of all counting numbers beginning with
n and counting backward to 1.
factorial La expresión n factorial (n!) es el producto de
todos los números naturales, comenzando con n y
contando al revés hasta llegar al 1.
factors (148) Two or more numbers that are
multiplied to form a product.
factores Dos o más números que se multiplican para
formar un producto.
factor tree (160) A way to find the prime
factorization of a number. The factors branch out
from the previous factors until all the factors are
prime numbers.
árbol de factores Forma de encontrar la factorización
prima de un número. Los factores se ramifican de
los factores anteriores hasta que todos los factores
son números primos.
formula (131) An equation that shows a relationship
among certain quantities.
fórmula Ecuación que muestra la relación entre
ciertas cantidades.
frequency table (623) A chart that indicates the
number of values in each interval.
tabla de frecuencias Tabla que indica el número de
valores en cada intervalo.
function (369) A function is a special relation in
which each element of the domain is paired with
exactly one element in the range.
función Una función es una relación especial en que
a cada elemento del dominio le corresponde un
único elemento del rango.
Fundamental Counting Principle (636) If event M
can occur in m ways and is followed by event N
that can occur in n ways, then the event M
followed by event N can occur in m n ways.
Principio fundamental de contar Si el evento M
puede ocurrir de m maneras y lo sigue un evento
N que puede ocurrir de n maneras, entonces el
evento M seguido del evento N puede ocurrir de
m n maneras.
G
geometric sequence (250) A sequence in which the
ratio between any two consecutive terms is the
same.
sucesión geométrica Sucesión en que la razón entre
dos términos consecutivos cualesquiera es
siempre la misma.
graph (34) A dot at the point that corresponds to an
ordered pair on a coordinate plane.
gráfica Marca puntual en el punto que corresponde a
un par ordenado en un plano de coordenadas.
greatest common factor (GCF) (164) The greatest
number that is a factor of two or more numbers.
máximo común divisor (MCD) El número mayor
que es factor de dos o más números.
greatest possible error (594) One-half the precision
unit, used to describe the actual measure.
error máximo posible La mitad de la unidad de
precisión. Se usa para describir la medida exacta.
H
half plane (419) The region that contains the solution
for an inequality.
semiplano Región que contiene la solución de una
desigualdad.
histogram (623) A histogram uses bars to display
numerical data that have been organized into
equal intervals.
histograma Un histograma usa barras para exhibir
datos numéricos que han sido organizados en
intervalos iguales.
hypotenuse (460) The side opposite the right angle in
a right triangle.
hipotenusa Lado opuesto al ángulo recto en un
triángulo rectángulo.
hypotenuse
hipotenusa
I
identidad Ecuación que es verdadera para cada valor
de la variable.
independent events (650) Two or more events in
which the outcome of one event does not
influence the outcome of the other event(s).
eventos independientes Dos o más eventos en que el
resultado de uno de ellos no afecta el resultado
del otro o de los otros eventos .
indirect measurement (472) Using the properties of
similar triangles to find measurements that are
difficult to measure directly.
medición indirecta Uso de las propiedades de
triángulos semejantes para hacer mediciones que
son difíciles de realizar directamente.
inductive reasoning (7) Reasoning based on a
pattern of examples or past events.
razonamiento inductivo Rezonamiento basada en un
patrón de ejemplos o de sucesos pasados.
inequality (57, 340) A mathematical sentence that
contains , , , , or .
desigualdad Enunciado matemático que contiene
, , , o .
integers (56) The whole numbers and their opposites.
. . . , 3, 2, 1, 0, 1, 2, 3, . . .
enteros Los números enteros y sus opuestos.
. . . , 3, 2, 1, 0, 1, 2, 3, . . .
interior angles (492, 528) Four of the angles
formed by the transversal and two parallel
lines. Interior angles lie between the two
parallel lines.
ángulos interiores Cuatro de los ángulos formados
por una transversal y dos rectas paralelas. Los
ángulos interiores yacen entre las dos rectas
paralelas.
interquartile range (613) The range of the middle
half of a set of data. It is the difference between
the upper quartile and the lower quartile.
amplitud intercuartílica Amplitud de la mitad
central de un conjunto de datos. Es la diferencia
entre el cuartil superior y el inferior.
inverse operations (110) Operations that undo each
other, such as addition and subtraction.
operaciones inversas Operaciones que se anulan
mutuamente, como la adición y la sustracción.
irrational number (441) A number that cannot be
a
expressed as , where a and b are integers and b
b
does not equal 0.
número irracional Número que no puede escribirse
a
como , donde a y b son enteros y b
b
no es igual a 0.
Glossary/Glosario
identity (336) An equation that is true for every
value of the variable.
isosceles triangle (455) A triangle that has at least
two congruent sides.
triángulo isósceles Triángulo que posee por lo
menos dos lados congruentes.
Glossary/Glosario
L
lateral area (578) The sum of the areas of the lateral
faces of a solid.
área lateral Suma de las àreas de las caras laterales
de un sólido.
lateral faces (578) The lateral faces of a prism,
cylinder, pyramid, or cone are all the surface of
the figure except the base or bases.
caras laterales Las caras laterales de un prisma,
cilindro, pirámide o cono son todas las superficies
de la figura, excluyendo la base o las bases.
least common denominator (LCD) (227) The least
common multiple of the denominators of two or
more fractions.
mínimo común denominador (mcd) El mínimo
común múltiplo de los denominadores de dos o
más fracciones.
least common multiple (LCM) (226) The least of
the nonzero common multiples of two or more
numbers. The LCM of 4 and 6 is 12.
mínimo común múltiplo (mcm) El menor de los
múltiplos comunes no nulos de dos o más
números. El MCM de 4 y 6 es 12.
leaves (606) In a stem-and-leaf plot, the next greatest
place value of the data after the stem forms the
leaves.
hojas En un diagrama de tallo y hojas, las hojas las
forma el segundo valor de posición mayor
después del tallo.
legs (460) The sides that are adjacent to the right
angle of a right triangle.
catetos Lados adyacentes al ángulo recto de un
triángulo rectángulo.
legs
catetos
like terms (103, 674) Expressions that contain the
same variables to the same power, such as 2n and
5n or 6xy2 and 4xy2.
términos semejantes Expresiones que tienen las
mismas variables elevadas a los mismos
exponentes, como 2n y 5n ó 6xy2 y 4xy2.
line (447) A never-ending straight path.
recta Trayectoria rectilínea interminable.
line graph (722) A type of statistical graph used to
show how values change over a period of time.
gráfica lineal Tipo de gráfica estadística que se usa
para mostrar cómo cambian los valores durante
un período de tiempo.
line of symmetry (506) Each half of a figure is a
mirror image of the other half when a line of
symmetry is drawn.
eje de simetría Cuando se traza un eje de simetría,
cada mitad de una figura es una imagen
especular de la otra mitad.
line segment (453) Part of a line containing two
endpoints and all the points between them.
segmento de recta Parte de una recta que contiene
dos extremos y todos los puntos entre éstos.
linear equation (375) An equation in which the
variables appear in separate terms and neither
variable contains an exponent other than 1. The
graph of a linear equation is a straight line.
ecuación lineal Ecuación en que las variables aparecen en términos separados y en la cual ninguna
de ellas tiene un exponente distinto de 1. La
gráfica de una ecuación lineal es una recta.
lower quartile (613) The median of the lower half of
a set of data, indicated by LQ.
cuartil inferior Mediana de la mitad inferior de un
conjunto de datos, se denota con CI.
M
mean (82, 238) The sum of data divided by the
number of items in the data set, also called the
average.
media Suma de los datos dividida entre el número
de elementos en el conjunto de datos. También
llamada promedio.
measures of central tendency (238) For a list of
numerical data, numbers that can represent the
whole set of data.
medidas de tendencia central Números que pueden
representar todo el conjunto de datos en una lista
de datos numéricos.
measures of variation (612) Used to describe the
distribution of statistical data.
medidas de variación Se usan para describir la
distribución de datos estadísticos.
median (238) In a set of data, the middle number of
the ordered data, or the mean of the two middle
numbers.
mediana En un conjunto de datos, el número central
de los datos ordenados numéricamente o la
media de los dos números centrales.
midpoint (468) On a line segment, the point that is
halfway between the endpoints.
punto medio En un segmento de recta, el punto que
equidista de ambos extremos.
Midpoint Formula (468) On a coordinate plane, the
coordinates of the midpoint of a segment whose
endpoints have coordinates at (x1, y1) and (x2, y2)
Fórmula del punto medio En el plano de coordenadas, el punto medio de un segmento cuyos
extremos son (x1, y1) y (x2, y2) se calcula con la
mixed number (200) The indicated sum of a whole
1
number and a fraction. For example, 3.
número mixto Suma de un entero y una fracción.
1
Por ejemplo, 3.
mode (238) The number or numbers that occurs most
often in a set of data.
moda Número o números de un conjunto de datos
que aparecen más frecuentemente.
monomial (150) An expression that is a number,
a variable, or a product of numbers and/or
variables.
monomio Expresión que es un número, una variable
y/o un producto de números y variables.
multiple (226) The product of a number and a whole
number.
múltiplo Producto de un número por un número
entero.
mutually exclusive events (652) Two or more events
that cannot happen at the same time.
eventos mutuamente exclusivos Dos o más eventos
que no pueden ocurrir simultáneamente.
x x
2
x x
2
y y
2
y y
2
1
2
1
2
fórmula ,
.
1
2
1
2
are given by ,
.
2
2
número negativo Número menor que cero.
nonlinear function (687) A function with a graph
that is not a straight line.
función no lineal Función cuya gráfica no es una
recta.
null set (336) A set with no elements shown by the
symbol { } or .
conjunto vacío Conjunto que carece de elementos y
que se denota con el símbolo { } o .
numerical expression (12) A combination of
numbers and operations such as addition,
subtraction, multiplication, and division.
expresión numérica Combinación de números y
operaciones, como adición, sustracción,
multiplicación y división.
O
obtuse angle (449) An angle with a measure greater
than 90° but less than 180°.
ángulo obtuso Ángulo que mide más de 90°, pero
menos de 180°.
Glossary/Glosario
N
negative number (56) A number less than zero.
obtuse triangle (454) A triangle with one obtuse
angle.
triángulo obtusángulo Triángulo que posee un
ángulo obtuso.
Glossary/Glosario
obtuse
angle
triángulo
obtusángulo
odds (646) A way to describe the chance of an event
occurring.
posibilidades Una manera de describir la
oportunidad de que ocurra un evento.
open sentence (28) An equation that contains a
variable.
enunciado abierto Ecuación que contiene una
variable.
opposites (66) Two numbers with the same absolute
value but different signs.
opuestos Dos números que tienen el mismo valor
absoluto, pero que tienen distintos signos.
ordered pair (33) A pair of numbers used to locate
any point on a coordinate plane.
par ordenado Par de números que se usa para ubicar
cualquier punto en un plano de coordenadas.
order of operations (12)
1. Simplify the expressions inside grouping
symbols.
2. Evaluate all powers.
3. Do all multiplications and/or divisions from
left to right.
4. Do all additions and/or subtractions from left
to right.
orden de las operaciones
1. Reduce las expresiones dentro de símbolos de
agrupamiento.
2. Evalúa todas las potencias.
3. Ejecuta todas las multiplicaciones y/o
divisiones de izquierda a derecha.
4. Ejecuta todas las adiciones y/o sustracciones
de izquierda a derecha.
origin (33) The point at which the number lines
intersect in a coordinate system.
origen Punto de intersección de las rectas numéricas
de un sistema de coordenadas.
outcomes (310) Possible results of a probability
event.
resultado Resultados posibles de un experimento
probabilístico.
outliers (621) Data that are more than 1.5 times the
interquartile range from the quartiles.
valores atípicos Datos que distan de los cuartiles
más de 1.5 veces la amplitud intercuartílica.
P
parallel lines (492) Two lines in the same plane that
do not intersect.
rectas paralelas Dos rectas en el mismo plano que no
se intersecan.
parallelogram (514) A quadrilateral with opposite
sides parallel and congruent.
paralelogramo Cuadrilátero con lados opuestos
congruentes y paralelos.
part (288) In a percent proportion, the number being
compared to the whole quantity.
parte En una proporción porcentual, el número que
se compara con la cantidad total.
percent (281) A ratio that compares a number to 100.
por ciento Razón que compara un número con 100.
percent equation (298) An equivalent form of
percent proportion, where % is written as a
decimal.
Part Percent Base
ecuación porcentual Forma equivalente a la proporción porcentual en que el % se escribe como
decimal.
Parte Por ciento Base
percent of change (304) The ratio of the increase or
decrease of an amount to the original amount.
porcentaje de cambio Razón del aumento o disminución de una cantidad a la cantidad original.
percent of decrease (306) The ratio of an amount of
decrease to the previous amount, expressed as a
percent. A negative percent of change.
porcentaje de disminución Razón de la cantidad de
disminución a la cantidad original, escrita como
por ciento. Un por ciento de cambio negativo.
percent of increase (305) The ratio of an amount of
increase to the original amount, expressed as a
percent.
porcentaje de aumento Razón de la cantidad de
aumento a la cantidad original, escrita como por
ciento.
percent proportion (288)
proporción porcentual
p
per cent
a
part
or b
base
100
100
p
parte
por c iento
a
o base
100
b
100
cuadrados perfectos Números racionales cuyas
raíces cuadradas son números racionales. 25 es
un cuadrado perfecto porque 25 5.
perimeter (132) The distance around a geometric
figure.
perímetro Longitud alrededor de una figura
geométrica.
period (201) In a repeating decimal, the digit or
digits that repeats. The period of 0.6
is 6.
período En un decimal periódico, el dígito o dígitos
que se repiten. El período de 0.6
es 6.
permutation (641) An arrangement or listing in
which order is important.
permutación Arreglo o lista en que el orden es
importante.
perpendicular lines (494) Lines that intersect to form
a right angle.
rectas perpendiculares Rectas que se intersecan
formando un ángulo recto.
pi, (533) The ratio of the circumference of a circle
to the diameter of the circle. Approximations for
22
are 3.14 and .
pi, Razón de la circunferencia de un círculo al
22
diámetro del mismo. 3.14 y son
7
aproximaciones de .
plane (556) A two-dimensional flat surface that
extends in all directions and contains at least
three noncollinear points.
plano Superficie plana bidimensional que se extiende
en todas direcciones y que contiene por lo menos
tres puntos no colineales.
point (447) A specific location in space with no size
or shape.
punto Ubicación específica en el espacio sin tamaño
o forma.
polygon (527) A simple closed figure in a plane
formed by three or more line segments.
polígono Figura simple y cerrada en el plano
formada por tres o más segmentos de recta.
polyhedron (556) A solid with flat surfaces that are
polygons.
poliedro Sólido con superficies planas que son
polígonos.
polynomial (669) An algebraic expression that
contains the sums and/or products of one or
more monomials.
polinomio Expresión algebraica que contiene sumas
y/o productos de uno o más monomios.
power (153) A number that is expressed using an
exponent.
potencia Número que puede escribirse usando un
exponente.
precision (590) The exactness to which a
measurement is made.
precisión Exactitud con que se realiza una medida.
prime factorization (160) A composite number
expressed as a product of prime factors. For
example, the prime factorization of 63 is 3 3 7.
factorización prima Número compuesto escrito
como producto de factores primos. Por ejemplo,
la factorización prima de 63 es 3 3 7.
7
Glossary/Glosario
perfect squares (436) Rational numbers whose
square roots are whole numbers. 25 is a perfect
square because 25 5.
prime number (159) A whole number that has
exactly two factors, 1 and itself.
número primo Número entero que sólo tiene dos
factores, 1 y sí mismo.
principle (300) The amount of money in an account.
capital Cantidad de dinero en una cuenta.
prism (557) A solid with two congruent parallel
polygonal bases. The remaining edges join
corresponding vertices of the bases so that the
remaining faces are rectangles.
prisma Sólido con dos bases poligonales paralelas y
congruentes. Las aristas restantes unen los
vértices correspondientes de las bases de modo
que las caras restantes son rectángulos.
rectangular prism
triangular prism
prisma rectangular
probabilidad Si los resultados son equiprobables, la
razón del número de maneras en que puede
ocurrir el evento al número de resultados posibles.
probability (310) If outcomes are equally likely, the
ratio of the number of ways a certain event can
occur to the number of possible outcomes.
número de resultados favorables
P(evento) number of favorable outcomes
P(event) número de resultados posibles
number of possible outcomes
Glossary/Glosario
prisma triangular
proportion (270) A statement of equality of two or
more ratios.
proporción Enunciado de la igualdad de dos o más
razones.
protractor (448) An instrument used to measure
angles.
transportador Instrumento que se usa para medir
ángulos.
pyramid (557) A solid with a polygonal base lying
in one plane plus one additional vertex not lying
on that plane. The remaining edges of the
pyramid join the additional vertex to the
vertices of the base.
pirámide Sólido con una base que es un polígono
que yace en un plano, más un vértice adicional
que no yace en ese plano. Las aristas restantes de
la pirámide juntan los vértices adicionales a los
vértices de la base.
Pythagorean Theorem (460) If a triangle is a right
triangle, then the square of the length of the
hypotenuse is equal to the sum of the squares of
the lengths of the legs or c2 a2 b2.
Teorema de Pitágoras Si un triángulo es rectángulo,
entonces el cuadrado de la longitud de la
hipotenusa es igual a la suma de los cuadrados
de las longitudes de los catetos, o c2 a2 b2.
a
c
a
b
c
b
Q
quadrants (86) The four regions into which the
x-axis and y-axis separate the coordinate plane.
cuadrantes Las cuatro regiones en que los ejes x y y
dividen el plano de coordenadas.
quadratic function (688) A function that can
be described by an equation of the form
y ax2 bx c, where a 0.
función cuadrática Función que puede describirse
por una ecuación de la forma
y ax2 bx c, donde a 0.
quadrilateral (513) A closed figure with four sides
and four vertices, including squares, rectangles,
and trapezoids.
cuadrilátero Figura cerrada de cuatro lados y cuatro
vértices, incluyendo cuadrados, rectángulos y
trapecios.
quartiles (613) The values that divide a set of data
into four equal parts.
cuartiles Valores que dividen un conjunto de datos
en cuatro partes iguales.
radical sign (436) The symbol used to indicate
a positive square root of a number.
R
signo radical El símbolo que se usa para
indicar la raíz cuadrada positiva de un número.
radius (533) The distance from the center to any
point on the circle.
radio Distancia del centro a cualquier punto de un
círculo.
range (35) The range of a relation is the set of all
y-coordinates from each ordered pair.
rango El rango de una relación es el conjunto de
coordenadas y de todos los pares.
range (612) A measure of variation that is the
difference between the least and greatest values
in a set of data.
amplitud Medida de variación que es la diferencia
entre los valores máximo y mínimo de un
conjunto de datos.
rate (265) A ratio of two measurements having
different units.
tasa Razón de dos medidas que tienen unidades
distintas.
rate of change (393) A change in one quantity with
respect to another quantity.
tasa de cambio Cambio de una cantidad con respecto
a otra.
ratio (264) A comparison of two numbers or
quantities. The ratio of 2 to 4 can be stated as 2 out
2
of 4, 2 to 4, 2:4, or .
razón Comparación de dos números o cantidades. La
razón de 2 a 4 se puede expresar como,
2
2 de 4, 2:4, ó .
rational number (205) A number that can be
a
written as a fraction in the form , where a and b
b
are integers and b 0.
número racional Número que puede escribirse como
a
una fracción de la forma donde a y b son
b
enteros y b 0.
ray (447) A part of a line that extends indefinitely in
one direction.
rayo Parte de una recta que se extiende
indefinidamente en una dirección.
real numbers (441) The set of rational numbers
together with the set of irrational numbers.
números reales El conjunto de los números racionales junto con el de números irracionales.
reciprocal (215) Another name for a multiplicative
inverse.
recíproco Otro nombre del inverso multiplicativo.
rectangle (514) A parallelogram with four right angles.
rectángulo Paralelogramo con cuatro ángulos rectos.
reflection (506) A transformation where a figure is
flipped over a line. Also called a flip.
reflexión Transformación en que una figura se voltea
a través de una recta.
regular polygon (529) A polygon having all sides
congruent and all angles congruent.
polígono regular Polígono cuyos lados son todos
congruentes y cuyos ángulos son también todos
congruentes.
relation (35) A set of ordered pairs.
relación Conjunto de pares ordenados.
repeating decimal (201) A decimal whose digits
repeat in groups of one or more. Examples are
0.181818… and 0.8333… .
decimal periódico Decimal cuyos dígitos se repiten
en grupos de uno o más. 0.181818… y 0.8333…
son ejemplos de este tipo de decimales.
rhombus (514) A parallelogram with four congruent
sides.
rombo Paralelogramo con cuatro lados congruentes.
4
4
Glossary/Glosario
right angle (449) An angle that measures 90°.
ángulo recto Ángulo que mide 90°.
right triangle (454) A triangle with one right angle.
triángulo rectángulo Triángulo que tiene un ángulo
recto.
rotation (506) A transformation where a figure is
turned around a fixed point. Also called a turn.
rotación Transformación en que una figura se hace
girar alrededor de un punto fijo. También se
llama vuelta.
Glossary/Glosario
S
sample (309) A subgroup or subset of a population
used to represent the whole population.
muestra Subgrupo o subconjunto de una población
que se usa para representarla.
sample space (311) The set of all possible outcomes.
espacio muestral Conjunto de todos los resultados
posibles.
scale (276) The relationship between the
measurements on a drawing or model and the
measurements of the real object.
escala Relación entre las medidas de un dibujo o
modelo y las medidas de la figura verdadera.
scale drawing (276) A drawing that is used to
represent an object that is too large or too small to
be drawn at actual size.
dibujo a escala Dibujo que se usa para representar
una figura que es demasiado grande o pequeña
como para ser dibujada de tamaño natural.
scale factor (277) The ratio of a length on a scale
drawing or model to the corresponding length on
the real object.
factor de escala Razón de la longitud en un dibujo a
escala o modelo a la longitud correspondiente en
la figura verdadera.
scale model (276) A model used to represent an
object that is too large or too small to be built at
actual size.
modelo a escala Modelo que se usa para representar
una figura que es demasiado grande o pequeña
como para ser construida de tamaño natural.
scalene triangle (455) A triangle with no congruent
sides.
triángulo escaleno Triángulo que no tiene lados
congruentes.
scatter plot (40) A graph that shows the relationship
between two sets of data.
gráfica de dispersión Gráfica en que se muestra la
relación entre dos conjuntos de datos.
scientific notation (186) A number in scientific
notation is expressed as a 10n, where
1 a 10 and n is an integer. For example,
5,000,000 5.0 106.
notación científica Un número en notación
científica se escribe como a 10n, donde
1 a 10 y n es un entero. Por ejemplo,
5,000,000 5.0 106.
sequence (249) An ordered list of numbers, such as,
0, 1, 2, 3, or 2, 4, 6, 8.
sucesión Lista ordenada de números, como
0, 1, 2, 3 ó 2, 4, 6, 8.
sides (447) The two rays that make up an angle.
lados Los dos rayos que forman un ángulo.
significant digits (590) The digits recorded from
measurement, indicating the precision of the
measurement.
dígitos significativos Los dígitos de una medición
que indican la precisión de la medición.
similar solids (584) Solids that have the same shape
but not necessarily the same size.
sólidos semejantes Sólidos que tienen la misma
forma, pero no necesariamente el mismo tamaño.
similar triangles (471) Triangles that have the same
shape but not necessarily the same size.
triángulos semejantes Triángulos que tienen la
misma forma, pero no necesariamente el mismo
tamaño.
simple event (310) One outcome or a collection of
outcomes.
evento simple Resultado o colección de resultados.
simple interest (300) The amount of money paid or
earned for the use of money.
interés simple Cantidad que se paga o que se gana
por usar el dinero.
I prt
(Interest principal rate time)
I crt (Interés capital rédito tiempo)
simplest form (104) An algebraic expression in
simplest form has no like terms and no
parentheses.
forma reducida Una expresión algebraica reducida
no tiene ni términos semejantes ni paréntesis.
simplest form (169) A fraction is in simplest form
when the GCF of the numerator and the
denominator is 1.
forma reducida Una fracción está reducida si el
MCD de su numerador y denominador es 1.
simplify (25) To write an expression in a simpler
form.
reducir Escribir una expresión en forma más simple.
simulation (656) The process of acting out a situation
to see possible outcomes.
simulación Proceso de representación de una
situación para averiguar los resultados posibles.
sine (477) If ABC is a right triangle and A is an
acute angle,
seno Si ABC es un triángulo rectángulo y A es un
ángulo agudo,
measure of the leg opposite A
measure of the hypotenuse
sine A .
medida del cateto opuesto a A
medida de la hipotenusa
seno A .
skew lines (558) Lines that are neither intersecting
nor parallel. Skew lines lie in different planes.
rectas alabeadas Rectas que no se intersecan y que
no son paralelas. Las rectas alabeadas yacen en
distintos planos.
slant height (578) The length of the altitude of a
lateral face of a regular pyramid.
altura oblicua En una pirámide regular, la longitud
de la altura de una cara lateral.
slope (387) The ratio of the rise, or vertical change, to
the run, or horizontal change. The slope describes
the steepness of a line.
pendiente Razón de la elevación o cambio vertical al
desplazamiento o cambio horizontal. La
pendiente describe la inclinación de una recta.
rise
run
slope elevación
desplazamiento
pendiente forma pendiente-intersección Una ecuación lineal de
la forma y mx b, donde m es la pendiente y b
es la intersección y.
solution (28) A value for the variable that makes an
equation true. For x 7 19, the solution is 12.
solución Valosss y que posee cuatro ángulos rectos.
solving the equation (28) The process of finding a
solution to an equation.
resolver la ecuación (28) Proceso de hallar una
solución a una ecuación.
solving a right triangle (461) Using the Pythagorean
Theorem to find the length of the third side of a
right triangle, if the lengths of the other two sides
are known.
resolver un triángulo rectángulo Uso del Teorema
de Pitágoras para hallar la longitud de un tercer
lado de un triángulo rectángulo, si se conocen las
longitudes de los otros dos lados.
square (514) A parallelogram with all sides
congruent and four right angles.
cuadrado Paralelogramo cuyos lados son todos
congruentes y que posee cuatro ángulos rectos.
square root (436) One of the two equal factors of a
number. The square root of 25 is 5 since 52 25.
raíz cuadrada Uno de los dos factores iguales de un
número. Una raíz cuadrada de 25 es 5 porque
52 25.
standard form (154) A number is in standard form
when it does not contain exponents. The standard
form for seven hundred thirty-nine is 739.
forma estándar Un número está en forma estándar si
no contiene exponentes. Por ejemplo, la forma
estándar de setecientos treinta y nueve es 739.
Glossary/Glosario
slope-intercept form (398) A linear equation in the
form y mx b, where m is the slope and b is
the y-intercept.
stem-and-leaf plot (606) A system used to condense
a set of data where the greatest place value of the
data forms the stem and the next greatest place
value forms the leaves.
diagrama de tallo y hojas Sistema que se usa para
condensar un conjunto de datos, en que el valor
de posición máximo de los datos forma el tallo y
el segundo valor de posición máximo forma las
hojas.
stems (606) The greatest place value common to all
the data values is used for the stem of a stemand-leaf plot.
tallos Máximo valor de posición común a todos los
datos que se usa como el tallo en un diagrama de
tallo y hojas.
straight angle (449) An angle with a measure equal
to 180°.
ángulo llano Ángulo que mide 180°.
supplementary (494) Two angles are supplementary
if the sum of their measures is 180°.
suplementarios Dos ángulos son suplementarios si
sus medidas suman 180°.
surface area (573) The sum of the areas of all the
surfaces (faces) of a 3-dimensional figure.
área de superficie Suma de las áreas de todas las
superficies (caras) de una figura tridimensional.
system of equations (414) A set of equations with the
same variables. The solution of the system is the
ordered pair that is a solution for all of the
equations.
sistema de ecuaciones Conjunto de ecuaciones con
las mismas variables. La solución del sistema es
el par ordenado que resuelve ambas ecuaciones.
T
tangent (477) If ABC is a right triangle and A is an
acute angle,
measure of the leg opposite A
tangent A measure of the leg adjacent to A
term (103) When plus or minus signs separate an
algebraic expression into parts, each part is a
term.
Glossary/Glosario
term (249) Each number within a sequence is called a
term.
terminating decimal (200) A decimal whose digits
end. Every terminating decimal can be written as
a fraction with a denominator of 10, 100, 1000,
and so on.
theoretical probability (311) What should occur in a
probability experiment.
transformation (506) A movement of a geometric
figure.
translation (506) A transformation where a figure is
slid from one position to another without being
turned. Also called a slide.
transversal (492) A line that intersects two parallel
lines to form eight angles.
tangente Si ABC es un triángulo rectángulo y A es
un ángulo agudo,
medida del cateto opuesto al A
medida del cateto adyacente a A
tangente A término Cada una de las partes de una expresión
algebraica separadas por los signos de adición o
sustracción.
término Cada número de una sucesión se llama
término.
decimal terminal Decimal cuyos dígitos terminan.
Todo decimal terminal puede escribirse como una
fracción con un denominador de 10, 100, 1000, etc.
probabilidad teórica Lo que debería ocurrir en un
experimento probabilístico.
transformación Desplazamiento de una figura
geométrica.
translación Transformación en que una figura se
desliza sin girar, de una posición a otra. También
se llama deslizamiento.
transversal Recta que interseca dos rectas paralelas
formando ocho ángulos.
trapezoid (514) A quadrilateral with exactly one pair
of parallel sides.
trapecio Cuadrilátero con sólo un par de lados
paralelos.
tree diagram (635) A diagram used to show the total
number of possible outcomes.
diagrama de árbol Diagrama que se usa para
mostrar el número total de resultados posibles.
triangle (453) A polygon having three sides.
triángulo Polígono de tres lados.
trigonometric ratio (477) A ratio of the lengths of
two sides of a right triangle. The tangent, sine,
and cosine ratios are three trigonometric ratios.
razón trigonométrica Razón de las longitudes de dos
lados de un triángulo rectángulo. La tangente, el
seno y el coseno son tres razones trigonométricas.
trigonometry (477) The study of the properties of
triangles. Trigonometry means angle measurement.
trigonometría Estudio de las propiedades de los
triángulos. La palabra significa medida de ángulos.
trinomial (669) A polynomial with three terms.
trinomio Polinomio de tres términos.
two-step equation (120) An equation that contains
two operations.
ecuación de dos pasos Ecuación que contiene dos
operaciones.
U
unit rate (265) A rate simplified so that it has a
denominator of 1.
tasa unitaria Tasa reducida que tiene denominador
igual a 1.
upper quartile (613) The median of the upper half of
a set of data, indicated by UQ.
cuartil superior Mediana de la mitad superior de un
conjunto de datos, denotada por CS.
V
variable Marcador de posición para cualquier valor.
Venn diagram (164) A diagram that is used to
show the relationships among sets of numbers
or objects by using overlapping circles in a
rectangle.
diagrama de Venn Diagrama que se usa para
mostrar las relaciones entre conjuntos de
números o elementos mediante círculos, que
pueden traslaparse, dentro de un rectángulo.
vertex (447) The common endpoint of the rays
forming an angle.
vértice Extremo común de los dos rayos que forman
un ángulo.
vertex (453) A vertex of a polygon is a point where
two sides of the polygon intersect.
vértice El vértice de un polígono es un punto en que
se intersecan dos lados del mismo.
vertex (556) Where three or more planes intersect in a
point.
vértice Punto en que se intersecan tres o más planos.
vertical angles (493) Two pairs of opposite angles
formed by two intersecting lines. The angles
formed are congruent. In the figure, the vertical
angles are 1 and 3, 2 and 4.
ángulos opuestos por el vértice Dos pares de ángulos opuestos formados por dos rectas que se
intersecan. Los ángulos que resultan son
congruentes. En la figura, los ángulos opuestos
por el vértice son 1 y 3, 2 y 4.
4
1
3
2
4
1
3
2
vertical line test (370) If any vertical line drawn on
the graph of a relation passes through no more
than one point on the graph for each value of x in
the domain, then the relation is a function.
prueba de la recta vertical Si todas las rectas verticales trazadas en la gráfica de una relación no
pasan por más un punto para cada valor de x en
el dominio, entonces la relación es una función.
volume (563) The measure of space occupied by a
solid region.
volumen Medida del espacio que ocupa un
sólido.
X
x-axis (33) The horizontal number line which helps to
form the coordinate system.
eje x Recta numérica horizontal que forma parte de
un sistema de coordenadas.
Glossary/Glosario
variable (17) A placeholder for any value.
x-coordinate (33) The first number of an ordered
pair.
coordenada x El primer número de un par
ordenado.
x-intercept (381) The x-coordinate of a point where a
graph crosses the x-axis.
intersección x La coordenada x de un punto en que
una gráfica interseca el eje x.
Y
eje y Recta numérica vertical que forma parte de un
sistema de coordenadas.
y-coordinate (33) The second number of an ordered
pair.
coordenada y El segundo número en un par
ordenado.
y-intercept (381) The y-coordinate of a point where a
graph crosses the y-axis.
intersección y La coordenada y de un punto en que
una gráfica interseca el eje y.
Glossary/Glosario
y-axis (33) The vertical number line which helps to
form the coordinate system.
Selected Answers
Chapter 1 The Tools of Algebra
Page 5
Chapter 1 Getting Started
1. 14.8 3. 3.1 5. 2.95 7. 3.55 9. 7.88 11. Sample
answer: 1200 13. Sample answer: 120 15. Sample answer:
20,000 17. Sample answer: 220 19. Sample answer: 14
21. Sample answer: $5 23. Sample answer: 120
25. Sample answer: 4 27. Sample answer: 10
Pages 9–10
Lesson 1-1
1. when an exact answer is not needed 3. 1:33 P.M. 5. 17
7. 3072 9. 178 beats per min 11. 17 13. 25 15. 34 17. 27
19.
21. Since $68 $15 $20 $16 $119, Ryan does not have
enough money for the ski trip. 23. about 5 h 25. Sample
answer: about 21,800 transplants 27a. There are more
even products. Since any even number multiplied by any
number is even, and only an odd number multiplied by an
odd number is odd, there are more even products in the
table. There are about 3 times as many evens as odds.
27b. Yes; in the addition table, there is only one more even
number than odd. 29. B 31. 3 33. 35 35. 109
Pages 14–16
Lesson 1-2
Pages 19–21
1. 14
Practice Quiz 1
3. 79
Pages 26–27
Lesson 1-5
1. Sample answer: b 7 12 and 8 h 3 3. 6 5. 5
7. 6 9. Symmetric 11. Let n the number; n 8 23; 15
13. C 15. 11 17. 12 19. 5 21. 15 23. 9 25. always
27. 15 29. 0 31. 15 33. 17 35. 11 37. 9 39. 3 41. 4
43. Let h the number; h 10 27; 37 45. Let w the
number; 9 w 36; 27 47. Let x the number; 3x 45;
15 49. $8 51. Symmetric Property of Equality
53. Symmetric Property of Equality 55. 3 57. Sample
answer: Once the variable(s) are replaced in the open
sentence, the order of operations is used to find the value of
the expression. Answers should include the following.
• To evaluate an expression, replace the variable(s) with
the given values, and then find the value of the
expression.
• To solve an open sentence, find the value of the variable
that makes the sentence true.
59. B 61. 23 d 63. 10 n 65. 11 67. 42 69. 18
71. 50 73. 90
Lesson 1-3
1. Sample answer: 7n and 3x 1; 2 3 and 3 8
3. Sample answer: 4 c d 5. 6 7. 17 9. g 5
11. 7 n 8 13. 11 15. 38 17. 2 19. 9 21. 27 23. 56
25. 53 27. 44 29. 32 31. 71°F 33. s $200 35. h 6
37. 5q 4 39. n 6 9 41. 17 4w 43. 10 45. x 3
47. p 4 49. s c m d 51. 1 53. D 55. 7 57. 9
59. 36 61. 22
Page 21
Pages 30–32
Page 32
Practice Quiz 2
1. Identity () 3. 24h
Pages 36–38
5. 8
Lesson 1-6
1. Sample answer: (3, 5); the x-coordinate is 3 and the
y-coordinate is 5. 3. The domain of a relation is the set of
x-coordinates. The range is the set of y-coordinates.
5.
7. (6, 5)
y
5. 22
Lesson 1-4
1. Sample answer: 3 · 4 4 · 3 3. Kimberly; the
Associative Property only holds true if all numbers are
added or all numbers are multiplied, not a combination of
the two. 5. Additive Identity 7. 28 9. 45 11. n 13
13. $42; To find the total cost, add the three costs together.
D
O
x
Selected Answers R19
Selected Answers
1. Sample answer: (8 3) 2 3. Emily; she followed the
order of operations and divided first. 5. ; 20 7. ; 66
9. ; 15 11. 12 9 13. 4 15. 25 17. 38 19. 2 21. 55
23. 24 25. 64 27. 180 29. 50 31. 6 3 33. 9 5
35. 24 6 37. 3 $6 39. (4 2) (2 13)
41. (3 57) (2 12) 43. 61 (15 3) 43
45. 56 (2 6) 4 3
47. (50 25) (7 24) (4 22) (3 16)
49. 0-07-825200-8 51. Sample answer:
111 (1 1 1) (11 1) 53. C 55. 64 57. 28
59. $275 61. Sample answer: about 26 compact cars
63. 126 65. 563
Since the order in which the costs are added does not
matter, the Commutative Property of Addition holds true
and makes the addition easier. By adding 4 and 26, the
result is 30, and 30 12 is 42. 15. Multiplicative
Identity 17. Commutative Property of Multiplication
19. Associative Property of Addition 21. Additive
Identity 23. Associative Property of Multiplication
25. Commutative Property of Addition 27. 55 29. 40
31. 990 33. 0 35. false; (100 10) 2 100 (10 2)
37. false; 9 3 3 9 39. m 12 41. a 27 43. 12y
45. 48c 47. 75s
49. There are many real-life situations in which the order in
which things are completed does not matter. Answers
should include the following.
• Reading the sports page and then the comics, or reading
the comics and then the sports page. No matter the
order, both parts of the newspaper will be read.
• When washing clothes, you would add the detergent and
then wash the clothes, not wash the clothes and then add
the detergent. Order matters.
51. B 53. 36 55. w 12 57. 35 59. 15, 21 61. 296
63. 1050 65. 7493
y
y
1
6
6
4
0
2
3
1
29. Science Experiment
100
90
80
domain {1, 6, 0, 3};
range {6, 4, 2, 1}
x
O
x
Height (cm)
9.
70
60
50
40
30
20
11.
y
10
24
21
0
18
Cost
15
12
9
31.
y
x
y
6
4
5
3
5
2
1
6
0
1 2 3 4 5 6 7 8 x
Number of Tickets
13.
y
1 2 3 4 5
Bounce
domain {4, 5, 1};
range {5, 2, 6}
15.
x
O
y
D
33.
y
X
x
O
17.
O
x
19. (7, 3) 21. (6, 6)
23. (3, 4) 25. on the x-axis;
on the y-axis
y
35.
y
N
x
O
27.
Speed of a House Mouse
O
x
y
7
0
3
2
4
4
5
1
domain {7, 3, 4, 5};
range {0, 2, 4, 1}
x
y
0
1
0
3
0
5
2
0
domain {0, 2};
range {1, 3, 5, 0}
80
70
Distance (ft)
Selected Answers
x
O
x
60
50
40
30
20
10
0
1 2
3 4 5 6 7 8
Time (sec)
R20 Selected Answers
37. (0, 14.7), (1, 10.2), (2, 6.4), (3, 4.3), (4, 2.7), (5, 1.6)
39. domain {0, 1, 2, 3, 4, 5}; range {14.7, 10.2, 6.4, 4.3,
2.7, 1.6} 41. {(0, 100), (1, 95), (2, 90), (3, 85), (4, 80), (5, 75)}
43. about 93°C; about 96°C 45. Ordered pairs can be used
to graph real-life data by expressing the data as ordered
pairs and then graphing the ordered pairs. Answers should
include the following.
• The x- and y-coordinate of an ordered pair specifies the
point on the graph.
• longitude and latitude lines.
47. D 49a.
49b. triangle
49c. (4, 2), (4, 8),
(10, 2)
49d. triangle
49e. The figures
have the same
shape but not the
same size.
y
51. 6 53. Multiplicative Identity
61. 28 63. 7 65. 9
55. 7
57. 10 · 30
Field Goal Attempts
3
6
1
7
5
x
O
59. 12
35. Positive; as the height increases, the circumference
increases.
Lesson 1-7
1. Sample answer: make predictions, draw conclusions,
spot trends 3. negative, positive, and none 5. No; hair
color is not related to height. 7. Since the points appear to
be random, there is no relationship. 9. The number of
songs on a CD usually does not affect the cost of the CD;
no. 11. As speed increases, distance traveled increases;
positive. 13. The size of a television screen and the
number of channels it receives are not related; no. 15. The
number decreases.
17.
Player Statistics
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
2
27. 10
domain: {2, 6, 7};
range: {3, 1, 5}
x
O
Pages 42–44
Addition 25. Multiplicative Property of Zero
29. 17 31. 6
y
33.
x y
Chapter 2 Integers
Page 55
1. 22
3. 42
5. 8
Pages 59–61
7. 4
9. T 11. V 13. Q
Lesson 2-1
1. Draw a number line. Draw a dot at 4. 3. The absolute
value of a number is its distance from 0 on a number line.
5. 15
8 9 10 11 12 13 14 15 16
7. 4 2; 2 4 9. 11. 13. 10 15. 21 17. 3
19. 54, 52, 45, 37, 36, 34, 27, 27, 2
21. 6
⫺8 ⫺7⫺6⫺5⫺4 ⫺3 ⫺2⫺1 0
23. 9
5 6 7 8 9 10 11 12 13
25. 5
⫺8⫺7⫺6⫺5⫺4 ⫺3⫺2⫺1 0
27.
200 600 1000 1400 1800 2200 2600 3000
400 800 1200 1600 2000 2400 2800
Minutes Played
y
y
M
O
O
29. (0, 4) 31. domain {0, 4, 2, 6}; range {9, 8, 3, 1}
33. 7 35. b 18 37. 31
Pages 47–50
Chapter 1 Study Guide and Review
1. d 3. e 5. c 7. 20 9. 22 11. 22 13. 16 15. 12
17. 14 19. 10 21. 25 23. Commutative Property of
⫺8 ⫺6⫺4⫺2 0 2 4 6 8
31. 5 10; 10 5 33. 248 425; 425 248
35. 212 32; 32 212 37. 39. 41. 43. 45. {15, 4, 2, 1} 47. {60, 57, 38, 98, 188} 49. 46
51. 5 53. 7 55. 2 57. 9 59. –20 61. 4 63. 40 65. 3
67.
⫺54
⫺90 ⫺70 ⫺50 ⫺30 ⫺10
69. 54 70 71. 7 73. Sometimes; if A and B are both
positive, both negative, or one is 0, it is true. If one number
is negative and the other is positive, it is false. 75. B
77. Positive; as height increases, so does arm length.
79. x y {(3, 2), (3, 4), (2, 1), (2, 4)}
K
x
29.
x
3
2
3
4
2
1
2
4
81. Commutative Property of Multiplication
83. Commutative Property of Multiplication
87. 17 89. 1049
85. 388
Selected Answers
19. about 800 21. Sample answer: Yes; as more emphasis is
placed on standardized tests, students will become more
comfortable taking the tests, and the scores will increase.
23. C
25.
27.
⫺3⫺2 ⫺1 0 1 2 3 4 5
Pages 67–68
Lesson 2-2
Pages 87–89
1a. Negative; both addends are negative. 1b. Positive;
12 2. 1c. Negative; 11 9. 1d. Positive;
both addends are positive. 3. 6 5. 5 7. 3 9. 4
11. 4 (5) 1 13. 7 15. 11 17. 16 19. 21
21. 66 23. 2 25. 2 27. 6 29. 26 31. 21 33. 2
35. 6 37. 3 39. 0 41. 5 43. 8 45. 40
47. 107,680
49. To add integers on a number line, start at 0. Move right
to show positive integers and left to show negative
integers. Answers should include the following.
3
• Sample answer:
5
23–34.
R (3, 5)
1
y
A (4, 5)
E (0,3)
21 0 1 2 3 4 5 6
• Sample answer:
Lesson 2-6
1. Sample answer: (3, 6) represents a point 3 units to the
right and 6 units up from the origin. (6, 3) represents a
point 6 units to the right and 3 units up from the origin.
3. Keisha; a point in Quadrant I has two positive
coordinates. Interchanging the coordinates will still result
in two positive coordinates, and the point will be in
Quadrant I. 5. (1, 3) 7. (5, 4) 9. II 11. III 13. (2, 4)
15. (4, 2) 17. (2, 2) 19. (0, 2) 21. (3, 5)
K (5, 1)
4
D (0, 0) G (5, 0)
x
F (4, 0) O
6543 21 0 1 2
H (0, 3)
B (5, 5)
51. D 53. {12, 9, 8, 0, 3, 14} 55. no relationship
57. 6 59. 20 61. 25 63. 42 65. 65
Pages 72–74
5
Page 74
b
69. 20
1. 80, 70, 69
Selected Answers
71. 75
3. 6
5. 7
7. 32
9. 9
Lesson 2-5
1. Sample answer: 16 4 4 3. 11 5. 3 7. 10
9. 13 11. 0 13. 9 15. 8 17. 10 19. 50 21. 11
23. 11 25. 19 27. 12 29. 13 31. 16 33. 49 points
35. 61 37. Sample answer: x 144; y 12; z 12
39. When the signs of the integers are the same, both a
product and a quotient are positive; when the signs are
different, the product and quotient are negative. Answers
• Sample answer: 4 (6) 24 and 24 4 6;
3 2 6 and 6 (3) 2
• Sample answers: same sign: 30 (5) 6, 30 5 6;
different signs: 24 8 3, 24 (8) 3
41. B 43. 39 45. 50cd 47. B 49. D
Page 84
1. 84
27. IV
29. none
Practice Quiz 2
3. 126
5. 31
7. 25
9. 20xy
31. none
33. none
35. Sample answer:
y
x
x
O
Lesson 2-4
1. 3(5) 15 3. Sample answer: (4)(9)(2) 5. 40
7. 28 9. 540 11. 21y 13. 120 15. A 17. 42
19. 72 21. 70 23. 128 25. 45 27. 130 29. 308
31. 528 33. 1344 35. 56°F 37. 96y 39. 55b
41. 108mn 43. 135xy 45. 88bc 47. –90jk 49. 99
51. 80 53. 216 55. 248 ft 57a. True; 3(5) 5(3)
57b. True; 2(3 5) (2 3)(5) 59. B 61. 16 63. 4
65. 10 67. 126°F 69. 14 71. (6, 2) 73. (1, 5) 75. (5, 5)
77. 480 79. 550 81. 6 83. 15 85. 4
Pages 83–84
23. I 25. IV
73. 120
Practice Quiz 1
Pages 77–79
S (2, 5)
Lesson 2-3
1. Sample answer: 5, 5; 9, 9 3. 3 5. 9 7. 2 9. 20
11. 21 13. Utah, Washington, Wisconsin, or Wyoming
15. 1 17. 3 19. 9 21. 12 23. 10 25. 12 27. 3
29. 9 31. 14 33. 28 35. 239 37. 1300 39. 14,776 ft
41. 24 43. 36 45. 9 47. 20 49. 23 51. 17
53. 10,822 55a. False; 3 4 4 3 55b. False;
(5 2) 1 5 (2 1) 57. A 59. 2450 61. 3 63. 7
x
86
65. 67. C (6, 1)
M (4, 2)
The points are
along a line
slanting down to
the right,
crossing the
y-axis at 5 and
the x-axis at 5.
y
1
4
2
3
3
2
4
1
5
0
6
1
37. Sample answer:
y
x
O
x
y
2
4
1
2
0
0
1
2
2
4
3
6
The points are
along a line
slanting up,
through the
origin.
39. Sample answer:
y
O
x
x
y
3
1
2
0
1
1
0
2
1
3
2
4
The points are
along a line
slanting up,
crossing the
y-axis at 2 and
the x-axis
at 2.
41. 5-point star
y
40–43.
A, F
K (1, 3)
D
C
x
O
41. III 43. None
y
A (4, 3)
O
x
R (3, 0)
J (2, 4)
E
B
43. Sample answer:
y
The graph can include any
integer pairs where x 3 or
x 3.
x
O
47. The new triangle is
translated right 2 units and
up 2 units; it is the same
size as the original triangle.
y
C'
B'
C
A'
B
A'
A
B'
x
B
x
O
51. Sample answer:
x
O
53. D 55. 3
67. 0
57. 8
59. 96
61. 13°F 63. 24h
65. 45b
1. negative number 3. coordinate 5. integers
7. inequality 9. 11. 13. 25 15. 22 17. 5 19. 4
21. 10 23. 8 25. 5 27. 4 29. 9 31. 66 33. 48
35. 7 37. 4 39. 2
Lesson 3-1
1. Sample answer: 2(3 4) 2 3 2 4 3. 5 7 5 8,
75 5. 2 6 4 6, 36 7. 3n 6 9. 6x 30 11. $56.25
13. 5 7 5 3, 50 15. 4 3 3 3, 21 17. 8 2 8 2, 32
19. 6 8 6(5), 18 21. 3 9 (3)(2), 21
23. 10(5) 3(5), 35 25. 12($15 $10 $8),
12($15) 12($10) 12($8); $396 27. 5y 30 29. 7y 56
31. 10y 20 33. 10 5x 35. 9m 18 37. 15s 45
39. 12x 36 41. 2w 20 43. 5a 50 45. 5w 40
47. 5a 30 49. 3a 3b 51. $9918 53. No;
3 (4 5) 23, (3 4)(3 5) 56 55. C
57. 8(20 3) 184 59. 16(10 1) 176
61. 9(100 3) 927 63. 12(1000 4) 12,048 65. 6
67. 4 69. 21, 25, 29 71. 80, 160, 320 73. 8 (4)
75. 3 (9) 77. 7 (10)
Lesson 3-2
1. terms that contain the same variable or are constants
3. Koko; 5x x 6x, not 5x. 5. terms: 2m, 1n, 6m; like
terms: 2m, 6m; coefficients: 2, 1, 6: constant: none 7. 8a
9. 7c 12 11. 9y 13. 3y 16 15. 4x 12y 17. terms:
3, 7x, 3x, x; like terms: 7x, 3x, x; coefficients: 7, 3, 1;
constant: 3 19. terms 2a, 5c, 1a, 6a; like terms: 2a, 1a, 6a;
coefficients: 2, 5, 1, 6; constant: none 21. terms: 6m, 2n,
7; like terms: none; coefficients: 6, 2; constant: 7 23. 7x
25. 11y 27. 7a 3 29. 7y 9 31. 2x 33. y
35. 4x 8 37. 8y 39. x 12 41. 5b 6 43. 4a 6
45. 8 47. 16m 2n 49. 9c 2d 51. 3s 80
53. 5d 2 55. 6x 2 57a. Distributive Property
57b. Commutative Property 57c. Substitution Property of
Equality 57d. Distributive Property 59. C 61. 2y 16
63. III 65. 17 67. 2 69. 11 71. 5 73. 13
Page 107
Practice Quiz 1
1. 6x 12
3. 7y 4
Pages 113–114
5. 2m 15
Lesson 3-3
1. Addition Property of Equality 3. 11
9.
3 2 1
Pages 90–92
11. 0
0
1
2
3
5. 4
7. 55
4
11. C 13. 13 15. 8 17. 15 19. 1 21. 15 23. 24
25. 36 27. 4 29. 31 31. 118 33. n 9 2; 11
35. n 3 6; 3
37.
6 5 4 3 2 1
0
1
Selected Answers
The points lie outside a
rhombus defined by (0, 4),
(4, 0), (0, 4), and (4, 0).
y
1. 6 3. 10 5. 5 (7) 7. 5 (9) 9. 3
13. 5 2n 15. n 3
Pages 105–107
A
O
Page 97
Pages 100–102
45. The new triangle is
twice the size of the original
triangle, and is moved to
the right and up.
y
C'
C
Chapter 3 Equations
39.
5
6
7
8
9
⫺4 ⫺3 ⫺2 ⫺1
0
10 11 12
41.
1
2
3
43. 12 x 20; 32 47. 17 million 49. When you solve an
equation, you perform the same operation on each side so
that the two sides remain equal. Answers should include
the following.
• In an equation, both sides are equal. In a balance scale,
the weight of the items on both sides are equal.
• The Addition and Subtraction Properties of Equality
allow you to add or subtract the same number from each
side of an equation. The two sides of the equation remain
equal.
51. C 53. 3t 12 55. 4z 4 57. 4m 1
59. Additive Inverse Property 61. 84 63. 25 65. 9
67. 4
Pages 117–119
with a certain amount and increase or decrease at a certain
rate. Answers should include the following.
• You’ve been running 15 minutes each day as part of a
fitness program. You plan to increase your time by 5
minutes each week. After how many weeks do you plan
to run 30 minutes each day? (5w 15 30, 3 weeks)
• You are three years older than your sister is. Together the
sum of your ages is 21. How old is your sister?
(2x 3 21, 9 years old)
29. D 31. 4 33. 5 35. 11 37. 4 39. 5 41. 6
Page 130
1. 13
Practice Quiz 2
3. 18
Pages 133–136
5. 3n 20 32, 4
Lesson 3-7
1. d rt 3. Sample answer:
5 in.
4 in.
Lesson 3-4
1. Multiplication Property of Equality 3. Sample
answer: 5x 20 5. 5 7. 27 9. 66 11. 7 13. 8
15. 8 17. 24 19. 14 21. 33 23. 9 25. 43 27. 135
29. 130 31. 29 33. 168 35. 6x 42; 7
x
37. 8; 32
4
5. 34 km, 30 km2 7. 4 in. 9. 8 h 11. 15 mph 13. 54 cm,
162 cm2 15. 136 in., 900 in2 17. 48 m, 144 m2 19. 20 m,
25 m2 21. 11 yd 23. 5 m 25. 39 ft 27. 19 yd 29. 390 yd,
9000 yd2 31. d 2r 33. 4300 ft2 35. 23.5 mph
4 ft
4 cm
37.
39.
39.
⫺9 ⫺8 ⫺7 ⫺6 ⫺5 ⫺4 ⫺3 ⫺2
3 ft
4 cm
41.
⫺3 ⫺2 ⫺1
0
1
2
3
4
43.
30 31 32 33 34 35 36 37
45. 12,000 5x; 2400 mi2 47. 6p 24, 4 painters
49a. True; one pyramid balances two cubes, so this is the
same as adding one cube to each side. 49b. True; one
pyramid and one cube balance three cubes, which balance
one cylinder. 49c. False; one cylinder and one pyramid
balance five cubes. 51. B 53. 13 55. 28 57. 7y 6
59. 36 61. 10 63. 2 65. 2 67. 19 69. 27
Selected Answers
Pages 122–124
Lesson 3-5
1. You undo the operations in reverse order. 3. 8 5. 2
7. 40 9. 4 11. 10 13. 2 15. 4 17. 8 19. 13 21. 3
23. 28 25. 64 27. 65 29. 21 31. 11 33. 30 35. 33
37. 13 39. 5 41. 5 43. –2 45. 10 47. 3 h 49. 131 bikes
51. 5x 2 8 53. C 55. 7 57. 2 59. 2
61. 5y 15 63. 9y 36 65. 8r 40 67. (2, 3)
69. (3, 4) 71. x 15 73. 2x 10
Pages 128–130
Lesson 3-6
1. is, equals, is equal to 3. Ben; Three less than means that
three is subtracted from a number. 5. 2n 4 2, 1
7. 2x 5 37, 21 yr 9. 3n 20 4, 8
11. 10n 8 82, 9
n
13. 8 42, 136
4
15. 3n 8 2, 2 17. 17 2n 5, 6
19. 4n 3n 5 47, 6 21. 8 5x 7, 3 h 23. 2x 2 12. 5 million people 25. Sample answer: By 2020, Texas is
expected to have 10 thousand more people age 85 or older
than New York will have. Together, they are expected to
have 846 thousand people age 85 or older. Find the
expected number of people age 85 or older in New York by
2020. 27. Two-step equations can be used when you start
41. Sometimes; a 3-inch by 4-inch rectangle has a perimeter
of 14 inches and an area of 12 square inches; a 6-inch by
8-inch rectangle has a perimeter of 28 inches and an area of
48 square inches. 43. Formulas are important in math and
science because they summarize the relationships among
quantities. Answers should include the following.
• Sample answer: The formula to find acceleration is
vf vi
a where vf is the final velocity and vi is the
t
initial velocity.
• You can find the acceleration of an automobile with this
formula.
45. C 47. 9 49. 8 51. 4x 9 53a. {(1870, 14),
(1881, 600), (1910, 1000), (2000, 1500)} 53b. domain:
{1870, 1881, 1910, 2000}, range: {14, 600, 1000, 1500}
Pages 138–140
1. like terms 3. Multiplication Property of Equality
5. Distributive Property 7. coordinate 9. constant
11. 3h 18 13. 5k 5 15. 9t 45 17. 2b 8
19. 9a 21. 2n 8 23. 3 25. 5 27. 8 29. 18
31. 1 33. 6 35. 2n 3 53; 25 37. 34 ft, 72 ft2
Chapter 4 Factors and Fractions
Page 147
1. 2x 2 3. 2k 16 5. 12c 24 7. 7a 7b 9. 14
11. 28 13. 63 15. 30 17. 45 19. 78 21. 0.39 23. 0.005
Pages 150–152
Lesson 4-1
1. Use the rules for divisibility to determine whether 18,450
is divisible by both 2 and 3. If it is, then the number is also
divisible by 6 and there is no remainder. 3a. Sample
answer: 102 3b. Sample answer: 1035 3c. Sample answer:
343 5. 2 7. 2, 5, 10 9. 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
11. yes; a number 13. No; two terms are added. 15. 2000,
2004, and 2032 are leap years. 17. 3, 5 19. 2, 3, 5, 6, 10
21. 2 23. 5 25. 2, 3, 6 27. 2, 5, 10 29. 1, 2, 3, 6, 19, 38,
57, 114 31. 1, 5, 13, 65 33. 1, 2, 4, 31, 62, 124 35. 1, 3, 5, 9,
15, 27, 45, 135 37. yes; a number 39. No; one term is
subtracted from another term. 41. No; two terms are
added. 43. No; one term is subtracted from another term.
45. yes; the product of a number and a variable 47. yes;
the product of numbers and variables 49. 6 ways; 1 72,
2 36, 3 24, 4 18, 6 12, 8 9 51. Alternating rows
of a flag contain 6 stars and 5 stars, respectively. Fifty is not
divisible by a number that would make the arrangement of
stars in an appropriate-sized rectangle. 53. Never; a
number that has 10 as a factor is divisible by 2 5, so it is
always divisible by 5. 55a. 24 cases 55b. 36 bags
55c. Sample answer: 12 cases, 18 bags; 14 cases, 15 bags;
16 cases, 12 bags 57. The side lengths or dimensions of a
rectangle are factors of the number that is the area of the
rectangle. Answers should include the following.
• A rectangle with dimensions and area labeled; for
example, a 4 5 rectangle would have length 5 units,
width 4 units, and area 20 square units.
• Factors are numbers that are multiplied to form a
product. The dimensions of a rectangle are factor pairs of
the area since they are multiplied to form the area.
59. C 61. 34 in., 60 in2 63. 5n 2 3; 1 65. 2 67. 64
69. 27 71. 2304
Pages 155–157 Lesson 4-2
1. A prime number has exactly two factors: 1 and itself. A
composite number has more than two factors.
3. Francisca; 4 is not prime. 5. prime 7. 2 32 9. 2 52
11. 5 a a b 13. 3 and 5, 5 and 7, 11 and 13, 17 and 19, 29
and 31, 41 and 43 15. composite 17. composite
19. composite 21. prime 23. 34 25. 32 7 27. 22 52
Page 163
Practice Quiz 1
1. 3, 5 3. none
Pages 166–168
5. 37
7. 7 11 x
9. 1 23 n n n
Lesson 4-4
1. Sample answer: Find the prime factorization of each
number. Multiply the factors that are common to both.
3. Jack; the common prime factors of the expressions are 2
and 11, so the GCF is 2 11 or 22. 5. 3 7. 14 9. 36
11. 14n 13. 3(n 3) 15. 5(3 4x) 17. 4 19. 8 21. 10
23. 9 25. 8 27. 5 29. 4 31. 3 33. 4 35. 4x 37. 2s
39. 14b 41. 4n 43. Sample answer: 2x, 6x2 45. 3(r 4)
47. 3(2 y) 49. 7(2 3c) 51. 4(y 4)
53a. 7; Sample answer:
7 14 21 28 35
↓ ↓ ↓ ↓ ↓
7(1) 7(2) 7(3) 7(4) 7(5)
The terms increase by a factor of 7.
53b. 42, 49 55a. 6-in. squares 55b. 20 tiles 57. Yes; the
GCF of 2 and 8 is 2. 59. D 61. yes 63. no 65. yes
67. 3 3 n 69. 1 5 j k 71. 92 73. 6 75. 10
77. 36 79. 24 81. 1000
Pages 171–173
Lesson 4-5
1
7
1. The GCF of the numerator and denominator is 1. 3. 16
17
5. simplified 7. a
2
5
6
9. 11. simplified 13. B 15. 9
5
1
19
21. simplified 23. 25. 27. 22
12
3
20
y2
1
20
7z2
2
31. or y 33. 35. 37. 39. simplified
8t
21
4
1
24
330
3
294
43. 45a. yes; 45b. No; cannot
25
440
4
349
7
264
1
31
be simplified. 45c. yes; 47. 49. 10
528
2
50
2
9
3
29. 92
gh
41. 3
17. 19. 51. Fractions represent parts of a whole. So, measurements
that contain parts of units can be represented using
fractions. Answers should include the following.
• Measurements can be given as parts of a whole because
smaller units make up larger units. For example, inches
make up feet.
3
• Twelve inches equals 1 foot. So, 3 inches equals or
12
1
foot.
4
53. A 55. 2 57. 5 59. composite
65. (6 7)(k3) 67. (3 5)(x4 x2)
61. prime
63. 27
Selected Answers
1. Sample answer: 25, x5 3. When n is even,
1n (1)n 1. When n is odd, 1n 1 and (1)n 1.
5. 72 7. (2 103) (6 102) (9 101) (5 100)
9. 11 11. 132 13. 61 15. (8)4 17. (t)3 19. m4
21. 2x2y2 23. 9(p 1)2 25. (8 102) (0 101) (3 100)
27. (2 104) (3 103) (7 102) (8 101) (1 100)
29. 1000 31. 32 33. 81 35. 54 37. 13 39. 9 41. 243
43. 64 82 or 43 or 26, 49 72 45. (8)3;
(8)(8)(8); 512 47. Always; the product of two
negative numbers is always positive. 49. 21, 22, 23, 24, 25
51. After 10 folds, the noodles are 5(210) 5(1024) or 5120
feet long, which is slightly less than a mile. So, after 11
folds the length of the noodles will be greater than a mile.
53. 55. 6 32 cm2 57. No; the surface area is multiplied
by 4. The volume is multiplied by 8.
59. As the capacity of computer memory increases, the
factors of 2 in the number of megabytes increases. Answers
• Computer data are measured in small units that are
based on factors of 2.
• In describing the amount of memory in modern
computers, it would be impractical to list all the factors
of 2. Using exponents is a more efficient way to describe
and compare computer data.
61. B 63. 2, 5, 10 65. 150 mph 67. 4 69. 3y 8 71. 1, 5
73. 1, 2, 4, 8, 16 75. 1, 5, 7, 35
29. 2 5 11 31. 3 3 t t 33. 1 5 5 z z z
35. 1 2 19 m n p 37. 3 7 g h h h
39. 2 2 2 2 2 2 n n n
41. 1 2 2 2 3 5 r r s t t t 43. Sample
answer: 25x
45. The number of rectangles that can be modeled to
represent a number indicate whether the number is prime
or composite. Answers should include the following.
• If a number is prime, then only one rectangle can be
drawn to represent the number. If a number is
composite, then more than one rectangle can be drawn to
represent the number.
• If a model has a length or width of 1, then the number
may be prime or composite. If a model does not have a
length or width of 1, then the number must be
composite.
47. C 49. (5)3h2k 51. yes 53. no 55. 9 57. 28
59. 5x 35 61. 10a 60 63. 72 8y
Pages 177–179
Lesson 4-6
Pages 191–194
1. Neither; the factors have different bases. 3. Sample
answer: 5 52 53 5. a6 7. 12x5 9. 102 11. a4 13. 35
15. d10 17. n9 19. 99 21. 18y5 23. 8a3b10 25. 53 27. b3
29. m12 31. (2)1 or 2 33. n6 35. k2m 37. 97 39. 79
41. 102 or 100 times 43. 3 45. 2 times 47. 8 49. 5
51. Each level on the Richter scale is 10 times greater than
the previous level. So, powers of 10 can be used to compare
earthquake magnitudes. Answers should include the
following.
• On the Richter scale, each whole-number increase
represents a 10-fold increase in the magnitude of seismic
waves.
• An earthquake of magnitude 7 is 105 times greater than
an earthquake of magnitude 2 because 107 102 107 2
or 105.
3x
2y
53. B 55. simplified 57. 59. 2
61. a 63. Positive; as
the high temperature increases, the amount of electricity
1
10
1
20
Pages 183–185
1
64
67. that is used also increases. 65. 69. Lesson 4-7
1. To get each successive power, divide the previous power
by 3. Therefore, 30 3 3 or 1.
1
5
1
t
3. 2 5. 6 7. 34
1
21. 10
a
1
1
1
13. 103 15. 3 17. 3 19.
32
5
(3)
1
1
23. 4 25. x2 27. 4 ; 0.0016 29. 55
q
5
33.
35.
9. 72 11. 92
24
or
42
1
41. 128
1
43. 729
a3
51. a3b2 or 2
b
37.
102
or
1001
39.
59. 0.0029
51.
1
53. 2
7
r2
1
55. 4
b
45. simplified
1
57. 3
(4)
63. 8.0 103 65. 4.571 107
61. 70,450
Chapter 5 Rational Numbers
Page 199
1. 0.6 3. 34 5. 0.2 7. 75
17. 13 19. 15 21. 9
Pages 202–204
9. 1.7
3
5
18
25
11. 13. 15. 6
Lesson 5-1
1. Sample answer: write the fractions as decimals and then
compare. 3. Sample answer: 0.14 5. 2.08 7. 0.26 9. 11. 13. 0.2 15. 0.32 17. 7.3 19. 5.125 21. 0.1
23. 0.4
5
25. 0.16
27. 0.3125
29. 0.83
7
9
7
8
31. , 0.8, 33. 35. 37. 39. 41. 43. 45. Sample
8
9
45. 128 times 47. x5 49. x3
47. This is greater
than those who chose English in the survey because
1
0.14, and 0.14 0.13.
7
105
49. All coins were made with a
fraction of silver that was contained in a silver dollar.
Answers should include the following.
• A quarter had one-fourth the amount of silver as a silver
dollar, a dime had one-tenth the amount, and a nickel
had one-twentieth the amount.
• It is easier to perform arithmetic operations using
decimals rather than using fractions.
(x2)3 (x2)(x2)(x2)
51. D 53. 7.7 102 55. 9.25 105
1
or 6
x
55. C 57. 9 101 59. (1 101) (7 102) (3 103) 61. 37 63. 53 65. 8y 48 67. 5n 15 69. 720
71. 40.5 73. 0.0005
Selected Answers
49.
c4
both greater than 0.16 and less than 0.8.
132
1
(x )
1
1
or x3 x3
x6
5c2
47. 8b
10
17
39. 2(15 2n) 41. 43. 1
6
53. Yes; (x3)2 32
x6
3
5
37. 2(t 10)
answer: 0.7 and 0.7; 0.16
and 0.8
; 0.7 and 0.7
are
1
4
10
31.
1. true 3. true 5. true 7. true 9. 3 11. 5 13. 2, 3, 6
15. 2, 5, 10 17. 27 19. 25 21. 90 23. 112 25. 32 5
27. 22 17 29. 7 7 k 31. 2 13 p p p 33. 6 35. n
61. 29
63. 32
65. 56
Pages 207–209
1
13
67. 1
1
59. 3
(2)
y
4
1
71. 73. 7
8
57. 7
2
3
69. Lesson 5-2
1. any number that can be written as a fraction
4
5
7
9
39
1,000,000
11
7
2
25. 5
3
60
1
25
27. 2
99
Page 185
5. 7. 9. I, Q
1. 5
9
1
17
1
21. 8 23. 100
250
25
3
3
59
4
29. 31. 33. 35. I, Q 37. N, W, I, Q 39. Q
50
200
25
19
1
41. not rational 43. 200 45. Sometimes; and 2 are
100
2
1
both rational numbers, but only 2 is an integer. 47. in.
1250
3
49. Yes; 2 2.375 and 2.375 2.37. 51. The set of rational
8
Practice Quiz 2
1
2
3. 2a 5. 7. 2n7 9. 6
b
5
Pages 188–190
17. 19. 1
Lesson 4-8
1. Sample answer: Numbers that are greater than 1 can be
expressed as the product of a factor and a positive power of
10. So, these numbers are written in scientific notation
using positive exponents. Numbers between 0 and 1 cannot
be expressed as the product of a factor and a whole number
power of 10, so they are written in scientific notation using
negative exponents. 3. 0.000308 5. 849,500 7. 6.97 105
9. 1.0 103 11. Mars, Venus, Earth 13. 57,200
15. 0.005689 17. 0.0901 19. 2505 21. 2.0 106
23. 6.0 103 25. 5.0 107 27. 5.894 106
29. 4.25 104 31. 6.25 106 33. 7.53 107
35. 37. 39. Arctic, Indian, Atlantic, Pacific 41. 6.1 105, 0.0061, 6.1 102, 6100, 6.1 104
43. 48,396 45. 2.52 105; 252,000 47. Bezymianny; Santa
Maria; Agung; Mount St. Helens tied with Hekla 1947;
Hekla, 1970; Ngauruhoe
57. 15a4 59. c $2.50
49. 3.14
1
81
51. B 53. 1
49
55. 11. 13. 7
3
3. 15. numbers includes the set of natural numbers, whole
numbers, and integers. In the same way, natural numbers
are part of the set of whole numbers and the set of whole
numbers is part of the set of integers. Answers should
• The number 5 belongs to the set of natural numbers,
whole numbers integers, and rational numbers.
1
• The number belongs only to the set of rational
2
numbers.
53. C 55. 7.8 57. 2.5
59. 3,050,000 61. 0.01681
63. (4 102) (8 101) (3 100) 65. 24 cm; 27 cm2
67. 8 2 1 2 69. 7x 28 71. Sample answer:
5 4 20 73. Sample answer: 7 2 14 75. Sample
answer: 16 2 32
3
1 1
5
13
6
8
1. Sample answer: , 3. 5. 7. 9. 11. 20
2 3
9
22
7
t
1
8
12
1
1
3
1
13. 15. 17. 19. 21. 23. 25. 1
40
45
49
3
4
8
6
1
2
4
27. 3 29. 14 31. 10 33. 4 35. 6 37. 27 39. 27
3
3
9
8c
9
11
xz2
41. 43. 45. 47. 49. 12.7 51. 10.257
11
25
60
3
8
3
3
5
53a. Sample answer: 53b. Sample answer: 4
5
4
6
5
13
1
7
55. A 57. 59. 61. 63. 65. 0.16 67. 4.875
8
32
5
9
69. 8n 71. 2t 73. 9
1. Dividing by a fraction is the same as multiplying by its
reciprocal.
8
25
5
4
3. 5. 7
15
4
5
7. 9. 1
29
36
11. 1
3a
2
13. 5
8
1
9
15. 6 boards 17. or 5 19. 21. 23. 1
9
24
29
15
15
1
1
25. 27. 29. 1 31. 1 33. 10 35. 1 37. 2
22
16
2
3
5
81
1
4
16
39. 6 41. 43. 45. 5 47. 6 ribbons 49. 6r
256
4
3
t
51. 8 days 53. Dividing by a fraction is the same as
multiplying by its reciprocal. Answers should include the
following.
• For example, a model of two circles, each divided into
1
4
four sections, represents 2 . Since there are 8 sections,
1
4
2 8.
• Division of fractions and multiplication of fractions are
1
4
inverse operations. So, 2 equals 2 4 or 8.
55. C
5
24
10
61. Q 63. not rational
21
2
2
71. 3 73. 1
3
3
59. 57. 1
7
1
4
67. 1 69. 6
65. 7
2
7
4
7
8r
1
3
1
3
15. 11
3x
4
2
5
2
1
1
2
4
1
3
17. 19. 21. 1 23. 25. 11 27. 9 29. 3
2
2
9
5
3
4
3
6
1
3
1
5x
3
31. 4 33. 8 35. 2 37. 39. 41. 43. 2c
m
7
8
5
5
8
7
3
45. 5 in. 47. 38 ft 49. When you use a ruler or a tape
8
4
7
5. 7. 9. 8 11. 13. measure, measurements are usually a fraction of an inch.
1
16
1
8
• The marks on a ruler represent of an inch, of an
1
2
inch, of an inch, and of an inch.
• Fractional measures are used in sewing and construction.
7
8
3
10
51. A 53. 1 55. 61. 52 7
Pages 228–230
5
12
9. Lesson 5-6
1. The LCM involves the common multiples of a set of
numbers; the LCD is the LCM of the denominators of two
or more fractions. 3. 24 5. 70 7. 48 9. 8 11. 100x
13. 15. front gear: 5; back gear: 13 17. 60 19. 48
21. 84 23. 100 25. 96 27. 84 29. 630 31. 112a2b
33. 75n4 35. 15 37. 35 39. 24 41. 16c2d 43. 60 s 45. 47. 49. 51. 53. amphibians 55. 12 and 18
57. Never; sample answer: 5 and 6 do not contain any
factors in common, and the LCM of 5 and 6 is 30. 59a. If
two numbers are relatively prime, then their LCM is the
product of the two numbers. For example, the LCM of 4
and 5 is 22 5 or 20; the LCM of 6 and 25 is 2 3 52 or 150.
59b. Always; the LCM contains all of the factors of both
numbers. Therefore, it must contain any common factors.
1
2
1
7
ad
5
69. 71. 7 2n 11; 2
61. B 63. 65. 1 67. 3
73. 20 75. Sample answer: 0 1 1 77. Sample
answer: 1 2 3 79. Sample answer: 8 7 15
Pages 234–236
Lesson 5-7
1. Find the least common denominator. 3. José; he finds a
common denominator by multiplying the denominators.
Daniel incorrectly adds the numerators and the
2
5
1
9
6
4
9
5
1
1
1
1
5
11.
13.
15. 1
17.
19. 21. 1
23. 7
10
28
16
15
8
8
9
11
7
5
3
3
25. 11
27. 14
29. 3
31. 5 lb 33. 8 in.
36
9
8
5
4
1
1
35. Sample answer: Fill the -cup. From the -cup, fill the
2
2
1
1
1
1
1
1
-cup. cup will be left in the -cup because .
3
6
2
2
3
6
denominators of unlike fractions.
5. 7. 9. 4
37. Find the LCM of the denominators. Then rename the
fractions as like fractions with the LCM as the
denominators. Answers should include the following.
• For example, the LCM of 4 and 6 is 12. So,
1
3
57. 1 59. 42 cm; 90 cm2
63. 22 3 n 65. 2 3 7 a2 b
4
5
4
5
49. 2 51. 1 53. 27
Pages 241–242
2
55. 9
10
2
Lesson 5-8
1. Mean; when an extreme value is added to the other data,
it can raise or lower the sum, and therefore the mean.
3. 12.4; 8; none 5. 3.6; 3.5; 4 7. Sample answer: 13 could
be an extreme value because it is 12 less than the next
value. It lowers the mean by 2.1. 9. 98 11. 8.9; 8; 8
13. 7.6; 7.5; 7.1 and 7.4 15. 4.3; 4.2; 4.1 and 4.2 17. Sample
answer: the median, 95, or the modes, 95 and 97, because
most students scored higher than mean, which is 91.
19. Sample answer: The median home price would be
useful because it is not affected by the cost of the very
expensive homes. The cost of half the homes in the county
would be greater than the median cost and half would
be less.
33. 7.9
21. C
5
6
7
8
23. 9 25. 3 27. 29. 18
31. 5
35. 3
Selected Answers
3. Kayla; Ethan incorrectly left out the negative sign on the
1
4
Practice Quiz 1
3
2
5. 7. 25
27
3. 3.125
• Writing the prime factorization of the denominators is
the first step in finding the LCM of the denominators,
which is the LCD. Then the fractions can be added or
subtracted.
1
1
1
39. B 41. Sample answer: 43. 36 45. 6n3 47. 9
6
7
first term.
1. 0.16
3
1
1
5
10
13
or 1.
12
12
4
6
12
12
1.
Page 224
Pages 246–248
5
9
1
3
2
65. 1
3
4
57. 120 59. 21c2 61. 3x
11
1
69. 1 71. 3 73. 6.0; 6.5; 3.6
15
6
1
77. 2 79. G; 3; 81, 243, 729
2
3
5
5
67. 2
6
49. 51. 1 53. 2 55. Lesson 5-9
1. Subtraction Property of Equality 3. Ling; dividing 0.3
by 3 does not isolate the variable on one side. 5. 18.7
63. 1
9. 2 11. –90 13. 29.15 in. 15. 2.4 17. 12.24
12
2
3
31
7
19. 5.9 21. 23. 6 25. 27. 2 29. 4
15
10
36
9
1
3
7
1
31. 5 33. 32 35. 1 37. 5 39. 2 41. 13 in. by
4
4
8
2
1
1
21 in. 43. $16.66 45. 2 ft 47. Equations with fractions
2
4
13
7. 1
30
can be written to represent the number of vibrations per
second for different notes. To solve, multiply each side of
the equation by the reciprocal of the fraction. Answers
• For example, if n vibrations per second produce middle
5
4
and 7.2 75. 3.25
81. neither
Chapter 6 Ratio, Proportion, and
Percent
Page 263
1. 24 3. 10,560 5. 480 7. 4000 9. 6 11. 580
13. 50 15. 15,000 17. 48.8 19. 13.44 21. 0.18
1
3
3
4
25. 27. simplified 29. simplified 31. 23. 3.04
C, then n vibrations per second produce the note E
Pages 266–268
above middle C.
1. Sample answer:
5
3
Lesson 6-1
• The equation n 440 represents the number of
vibrations per second to produce middle C. To solve,
5
8
49. D 51. 13; 12; 11 and 12
17
24
55. 53. 70.8; 66; 60
17
36
57. 11
3
1
61. 63. 6 65. 6 67. 5 69. 15
8
3
Page 248 Practice Quiz 2
13
2
1. 72 3. 10 5. 7. 1 9. 32.4; 30.5; 29
16
3
9. 0.75 inch/hour 11. 24.2 miles/gallon 13. 576
15. No; the ratio will be 2 to 3.
2
5
9
32,000
3
7
17. 19. 21. 59. 7
23. 1. Arithmetic sequences have a common difference and the
terms can be found by adding or subtracting. Geometric
sequences have a common ratio and the terms can be found
by multiplying or dividing. 3. A; 4; 19, 23, 27
31. 4.5 m/sec 33. 7.8 ft/h 35. 39 pages/week 37. The
6-pack of soda costs $0.37 per can. The 12-pack of soda
costs $0.35 per can. So, the 12-pack is less expensive.
39. 26.4 41. 19.2 43. 45. 47. about 579 mi/h 49.
$9 51. C 53b. The ratios should be close in value. 53c.
Sample answer: Pyramid of Khufu in Giza,
Egypt; The Taj Mahal in India; The Lincoln Memorial in
Washington, D.C. 55. arithmetic; 0.3; 13.3, 13.6, 13.9
1 5 4
3 3 3
5. neither 7. A; ; , , 1
49, 60
9. $11,027.36
1
1
125 625
1
5
1
3125
11. A; 11; 38,
1 2 5
6 3 6
2 2
1 2
25. G; ; , , 27 81
3 9
2.5, 2, 1.5
23. neither
19. A; ; , , 1
21. A; 0.5,
1
1 1 1
2 32 64 128
27. G; ; , , 29a. Arithmetic; the common
difference is $3. 29b. $48 31. Find the pattern, continue
the sequence, and use the new values to make predictions.
• The difference between any two consecutive terms in an
arithmetic sequence is the common difference. To find
the next value in such a sequence, add the common
difference to the last term. The ratio of any two
consecutive terms in a geometric sequence is the
common ratio. So, to find the next value in such a
sequence, multiply the last term by the common ratio.
• Sequences occurring in nature include geysers spouting
every few minutes, the arrangement of geese in
migration patterns, and ocean tides.
33. A 35. 56 37. 5.28 39. 10 41. 3.3; 3.3; 3.6
7
45. b3 47. 6 49. 15
8
Pages 254–258 Chapter 5 Study Guide and Review
43. 102 in.
1. rational
3. algebraic fraction 5. LCD
7. reciprocal
3
1
5
8
11
4
7
5
7
2
1
21. 4 23. 25. 1 27. 3 29. 31. 6 33. 1
25
11
27
9
9
5
3
4
4
3
1
35. 3 37. 9 39. x 41. 6 43. 3 45. 4 47. 21x
9
4
5
9. arithmetic
11. 0.45
13. 0.46
15. 6.36
17
118
1760
1
13. G; 3; 162, 486, 1458 15. A; 3; 13, 10, 7
17. G; ; , , Selected Answers
1
3
3. Sample answer: $12 per person 5. 7. 5 3
3 5
multiply each side by the reciprocal of , .
1
12
1
3
57. 67. 40
3
1
25. 27. 29. 0.10 cents/pencil
59. 13 61. 5.2 107
63. 3.8 102 65. 30
69. 13
Pages 272–274
Lesson 6-2
1. A statement of equality of two ratios. 3. Yes 5. 15
7. 4.2 9. yes 11. no 13. yes 15. 4 17. 20 19. 15
21. 1.4 23. 7.5 25. 0.94 27. 0.8 29. 15 31. 26
12
3
5
6.25
72
m
33. ; 18
39. $22.47
a
c
d
8.75
35. ; 7
1
2
41. chocolate pieces: 3 c; peanuts: 1 c
b b
c
d
d
d a
a
c
b
4
51. 53. 102 55. 6.5
7y
43. , , or 45. C
49. 4
Pages 278–280
1. 1 unit
7.
37. about 360.8 ft
Lesson 6-3
3 units
10 ft
5. 1 in. 5 ft
3. 40 mi
9. 12 ft
15 ft
17. 19. 47. 57.3 mph
11. 24.6 ft 13. 11.4 ft
1
15. 49 ft
2
2
3
17. 19. 1 cm 0.25 cm
0.5 in. ⫽ 10 ft
21. A scale factor less than 1 means that the drawing or
model is drawn smaller than actual size. A scale factor of 1
means that the drawing or model is drawn actual size. A
scale factor greater than 1 means the drawing or model is
1
2
1
4
23. B 25a. 25b. drawn larger than actual size.
25c. The perimeter of a 3-inch by 5-inch rectangle is
16 inches. The area is 15 square inches. For a 6-inch by
10-inch rectangle, the perimeter should be double the
3-inch by 5-inch rectangle. That is, 16 2 or 32 inches. The
area should be 4 times the area of the 3-inch by 5-inch
rectangle. That is, 4 15 or 60 square inches. Since the
perimeter of the 6-inch by 10-inch rectangle is 32 and its
1
area is 60, the conjecture is true. 27. 3.5 29. 21.6 31. 6
12
33.
4m3
35. 3
18t5
1
37. 20
2
39. 5
39
41. 50
41
43. 50
3
10
11. 0.8%
3. , 0.3
1
4
5. 1, 1.25
7
20
7. 1, 1.35
7
8
53
10,000
27. , 0.0053
37. 175%
61
100
1
2
21. 3, 3.5
22
25
39. 1.7%
2
3
47. 61%, , 0.69
31. 270%
37
1000
41. 49. 0.4
23
100
23. , 0.61
29. 9%
9. 45%
17. , 0.88
13. 133.3% 15. daily newspaper
19. , 0.875
21
50
29. 1
5
25. 2, 2.23
33. 0.06% 35. 22.5%
43. 0.45
1
4
Page 292
41. 25
Practice Quiz 1
1. $0.14 per can
3. 1 ft 3069 ft
Pages 295–297
Lesson 6-6
1
5
5. 19.5
1
5
5. Sample answer: 13
7. Sample answer: 72 9. Sample answer: 8; fraction
1
3
method: 24 or 8
11. Sample answer: 21; meaning of
percent method: 152% means about 150 for every 100 or
about 15 for every 10. 14 has 1 tens. 1 15 15. So, 152%
of 14 is about 21. 13. Sample answer: 14 15. Sample
answer: 33 17. Sample answer: 49 19. Sample answer: 4
21. Sample answer: 90 23. Sample answer: 375
1
4
25. Sample answer: 8 or 2 billion 27. Sample answer:
3
10
27; fraction method: 90 or 27 29. Sample answer: 36;
1
4
2
5
1
4
8 or 2. 33. Sample answer: 78; meaning of percent: 127%
means about 130 for every 100 or about 13 for every 10.
64 has 6 tens. 6 13 78. So, 127% of 64 is about 78.
35. Sample answer: 450; meaning of percent: 295% means
about 300 for every 100 or about 30 for every 10. 145 has
one 100 and about 5 tens. (300 1) (30 5) 300 150
or 450. 37. Sample answer: Pluto and Mars, or Neptune
and Jupiter
1
3
39. Sample answer: 90,000 or 30,000 miles
41. about 10% 43. 7 to 8 45. C 47. 21 49. Maine:
31,813 sq mi; New Hampshire: 8238 sq mi; West Virginia:
18,779 sq mi; Vermont: 7279 sq mi; Alabama: 35,071 sq mi
51. 160% 53. 0.77 55. 4.21 57. 8.9 59. 21 61. 0.5
63. 0.25 65. 0.07
30%
40%
65%
3
10
2
5
• 25% 0.25; 30% 0.3; 40% 0.4;
1
11
3
55. A 57. 59. 61. 1
12
21
13
65. composite 67. 800 69. 0.94 71. 320
5. 104
7. 60%
9. 45%
11. 50 13. 77 15. 36% 17. 112 19. 0.2% 21. 16%
23. about 70% 25. 26.8 lbs
27. In real-world situations, percents are important because
they show how something compares to the whole. Answers
Lesson 6-7
1. Use the percent equation in any situation where the rate
and base are known. 3. I interest; p principal;
r annual interest rate; t time in years 5. 50 7. 3%
9. $1680 11. 1.5 years 13. 95% 15. 50 17. 63 19. 37.5%
21. 14.52 23. 218% 25. 0.9% 27. 13.2 29. $25.49
31. $17 33. $18.50 35. $1113.75 37. $244.76 39. 16
41. $1.20 43. If you know two of the three values, you can
use the percent proportion to solve for the missing value.
• To find the amount of tax on an item, you can use the
percent proportion or the percent equation.
• For example, the following methods can be used to find
6% tax on $24.99.
Method 1: Percent Proportion
x
6
24.99
100
Method 2: Percent Equation
n 0.06(24.99)
Using either method, x 1.50. The amount of tax is $1.50.
45. B 47. Sample answer: 250; meaning of percent method:
126% means about 125 for every 100 and 12.5 for every 10.
Selected Answers
Pages 300–302
%
number correct
1. 3. 40%
100
50
39. 6
method: Since 1% of 806 is about 8, % of 806 is about of
53. Percents are related to fractions and decimals because
they can be expressed as them. Answers should include the
following.
•
63. composite
1
2
2
5
possibilities that satisfy the conditions, and .
1
4
13
65% 0.65
20
1
fraction method: 90 or 36 31. Sample answer: 2; 1%
45. 19%
51. There are only two
25%
7
9
31. 1 33. 35. 3 37. 8
So, 18% of 216 is about 44.
1. Sample answer: write an equivalent fraction with a
denominator of 100 or express the fraction as a decimal and
then express the decimal as a percent. A fraction is greater
than 100% if it is greater than 1. It is less than 1% if it is less
1
100
3
copper, nickel). The outer layer is or 75% copper and 4
4
or 25% nickel.
1. 18% is about 20% or . 216 is about 220. of 220 is 44.
than .
• For example, the outer layer of the new state quarters is
an alloy of 3 parts copper to 1 part nickel.
• Thus, there are 4 parts to the outer layer (copper, copper,
198 has about 2 one-hundreds. 125 2 250. So, 126% of
198 is about 250. 49. 121 51. 41 53. 38 cm 55. 8w 24
57. 89% 59. 156% 61. 22.4%
Pages 306–308
Lesson 6-8
1. If the amount increases, it is a percent of increase. If the
amount decreases, it is a percent of decrease. 3. Mark; he
divided the difference of the new amount and the original
amount by the original amount. 5. 60%; D 7. 10.1%; I
9. A 11. 170%; I 13. 12%; D 15. 5.4%; D 17. 164%; I
19. 10.1% 21. 14.3% 23. 150%
25. The amount by which a rectangle is increased or
decreased can be represented by a percent. Answers should
• If the size of the new rectangle is greater than the size of
the original rectangle, the percent of increase is greater
than 100%.
• Original Rectangle
Less than 100%
12
100
9
8
6
100
100
100
4
3
or 6%; D, L, S, U: or 4%; G: or 3%; B, C, F, H, M,
100
100
2
1
P, V, W, Y, blank: or 2%; J, K, Q, X, Z: or 1%
100
100
18n2
41. 146.9% 43. 23.9 45. 2x5 47. 7
• E: or 12%; A, I: or 9%; O: or 8%; N, R, T: Pages 316–320
1. proportion
3
4
3. scale factor 5. experimental probability
1
4
20
9
7. 9. 11. 2
25
21. ; 0.08
31. 40%
13. 30
1
5
23. 1; 1.2
33. 7.5%
15. 0.9
17. 45.6 ft
5
8
25. ; 0.625
35. 40%
27. 24%
37. 25
39. 50
7
20
19. ; 0.35
29. 45.2%
41. 43
43. 9
1
45. 8 47. Sample answer: 16; fraction method: 32 or 16
2
1
49. Sample answer: 10; fraction method: 50 or 10
5
51. Sample answer: 1; 1% method: Since 1% of 304 is about
1
3
1
3
3, % of 304 is about of 3 or 1.
57. 200
59. D; 70%
53. 48%
61. I; 86.2%
1
63. 3
55. 94.5
2
3
65. 67. 0
Chapter 7 Equations and Inequalities
Page 327
Greater than 100%
1. 4 3. 24 5. 44 7. 11 9. 17
15. 15 17. 72 19. 5 21. 1
Pages 332–333
11. 16
Lesson 7-1
1. Subtraction Property of Equality 3. 8
9. 75 miles
27. D 29. $149.85
31. $13.46
33. Sample answer: 63;
9
fraction method: 70 or 63 35. integer, rational
10
1
37. rational 39. 20% 41. 83%
3
Page 308
Practice Quiz 2
2
5
1. Sample answer: 28; fraction method: 70 or 28
3. $14.50 5. 158%
Selected Answers
Pages 312–314
Lesson 6-9
1. The event will not happen.
3. Sample answer: Spinning
the spinner shown and
having it land on 4.
1
2
1
2
4
3
2
5
1
4
5. ; 50% 7. ; 40% 9. 1; 100% 11. 75
13. ; 25%
1
7
15. ; 50% 17. 0; 0% 19. ; 87.5% 21.
2
8
11
1
1
23. ; 61.1% 25. ; 33% 27. 1; 100%
18
3
3
1
33. 35. 0.05; 5% 37. 1140
4
2
; 22.2%
9
1
1
29. 31. 16
6
39. Once the probability or likeliness of something
happening is known, then you can use the probability to
make a prediction. For example, in football, if you know the
number of field goals a player has made in the past, you
can use the information to predict the number of field goals
he/she will make in upcoming games. Answers should
13. 14
11. 13
13. 7
15. 0.5
5. 3
17. 6
7. 0.3
4
19. 3
21. 3 23. 4.2 25. 0.3 27. 3.4 29. 3y 14 y; 7 31. 16
33. 72 35. 70 min 37. 29 39. A 41. 40° 43. 12.5%
45. 6.48
47. 70
Pages 336–338
49. 6a 27
51. 2.4c 28
1
2
9
2
53. n Lesson 7-2
1. Multiply 4 times (x 1). Subtract 2x from each side. Add
4 to each side. Divide each side by 2. 3. 11 5. 13 7. 9. 7 ft; w 3 ft; A 21 ft2 11. 6 13. 2.5 15. 18 17. 3
19. 35 21. 23. all numbers 25. 6 27. all numbers
29. 0 31. 70 yd by 150 yd 33. w: 3 ft; : 13 ft; A: 39 ft2
35. triangle: 7, 8, 9; rectangle, 4, 8; perimeter: 24 37. 2 gal
39. Many equations include grouping symbols. You must
use the Distributive Property to correctly solve the
equation. Answers should include the following.
• The Distributive Property states that a(b c) ab ac.
• You use the Distributive Property to remove the
grouping symbols when you are solving equations.
41. D 43. 0.4 45. 40% 47. 0.375 49. 3.24 51. 7
53. 24 55. 8
Page 338
Practice Quiz 1
1. 2x 5x 150; 50
Pages 342–344
3. 3.1
5. all numbers
Lesson 7-3
1. An inequality represents all numbers greater or less than
a given number. A number line graph can represent all
those numbers. 3. n 14 25 5. true
7.
⫺2 ⫺1 0 1 2 3 4 5 6
9.
1 2 3 4 5 6 7 8 9
11. x 20 13. f 18,000
19. false 21. true
15. 86 2w 17. true
Pages 353–354
23.
Lesson 7-5
1. Multiply each side by 12 and reverse the inequality
symbol. 3. Tamika is correct. She divided each side of the
inequality by 9. Since 9 is a positive number, she did not
reverse the inequality symbol.
⫺1 0 1 2 3 4 5 6 7
25.
4 5 6 7 8 9 10 11 12
5. x 2
27.
⫺4 ⫺3⫺2 ⫺1 0 1 2 3 4
6 7 8 9 10 11 12 13 14
7. a 50
29.
⫺2 ⫺1 0 1 2 3 4 5 6
10
31.
9. m 8.4
⫺6 ⫺5⫺4 ⫺3⫺2 ⫺1 0 1 2
33.
11. y 72
⫺8⫺7⫺6 ⫺5⫺4 ⫺3 ⫺2 ⫺1 0
35. x 13 37. x 3 39. x 32 41. m 6.4
43. b 14,600 30,000; b 15,400 45. Symmetric: If
a b, then b a; not true. Sample counterexample: 4 5,
but 5 4. Transitive: If a b and b c, then a c; true.
47. B
49a.
30
⫺9
50
70
90
⫺8.6 ⫺8.2 ⫺7.8 ⫺7.4
⫺80 ⫺76 ⫺72 ⫺68 ⫺64
13. C
15. y 9
5 6 7 8 9 10 11 12 13
17. b 3
⫺4 ⫺3⫺2 ⫺1 0 1 2 3 4
⫺3 ⫺2 ⫺1 0 1 2 3 4 5
19. t 5
49b.
1 2 3 4 5 6 7 8 9
⫺3 ⫺2 ⫺1 0 1 2 3 4 5
51. 5 53. 4n 6 3n 2; 8
59. 7 61. 19.8
55. G: 16, 32, 64
57. 13
1. Use addition to undo subtraction; use subtraction to
undo addition. 3. Sample answer: Joanna works part-time
at a clothing store. Part-time workers must work fewer than
30 hours a week. If Joanna has already worked 8 hours this
week, how many hours can she still work? 5. y 7
7. a 11 9. t 3
11. x 10
7 8 9 10 11 12 13 14 15
15. b 22
25. y 1.4
94
98
102
106
17. y 5
19. r 7
25. w 2
⫺4 ⫺3 ⫺2 ⫺1 0 1 2 3 4
27. r 4
1 2 3 4 5 6 7 8 9
29. k 18
⫺20 ⫺18
21. j 4
1
29. b 3
4
27. f 5.4
1 2 3 4 5 6 7 8 9
⫺16 ⫺14
⫺12
31. t 16
⫺20 ⫺18 ⫺16 ⫺14 ⫺12
1 2 3 4 5 6 7 8 9
Selected Answers
23. w 6
31. n 5
90
23. z 3
13. p 2
21. h 98
33. n 4
33. p 2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
35. x 5
35. y 5.7
5.2
5.4
5.6
5.8
74
78
82
86
37. b 72
37. m 27
23
3
4
25
27
29
31
39. b 1
0
2
3
5
⫺7⫺6 ⫺5 ⫺4 ⫺3⫺2 ⫺1 0 1
1
2
1
1
12
2
41. s 4
3
4
5
43. 980 lb 45. 42 x 74; x 32; at least 32 mph
47. Always; subtracting x gives 1 0, which is always
true. 49. C 51. F 53. F 55. 3 cm, 9 cm 57. 8 32
59. 5x 17.5 61. 3 63. 15 65. 2 67. 4 69. 48
70
39a. 40m 2000 39b. at least 50 min 41. Inequalities can
be used to compare the weights of objects on different
planets. Answers should include the following.
• Comparing the weight of an astronaut in a space suit on
Mars to the same astronaut on the moon: 113 50.
• If you multiply or divide the astronaut’s weight by the
same number, the inequality comparing the weights on
different planets would still be true.
43. 40 45. c 20
55. 9 57. 32
47. 2n 14
5
21
2a
c
49. 51. 53. 4
Page 354
Practice Quiz 2
Pages 360–362
1.
⫺4 ⫺3 ⫺2 ⫺1 0 1 2 3 4
3. a 40
5. n 124
Pages 357–359
7. r 225
9. g 7
Lesson 7-6
1. Check the solution by replacing the variable with a
number in the solution. If the inequality is true, the solution
checks. 3. Jerome is correct. By the Distributive Property
2(2y 3) 4y 6 not 4y 3.
1. true 3. false; identity 5. false; inequality 7. true
9. false; is greater than or equal to 11. 3 13. 4 15. 1
17. 1 19. 1.2 21. 9 23. 16 25. all numbers 27. true
29. b 17
1
31. t 3
2
14
16
18
20
22
24
0
1
2
3
4
5
33. k 5.1
⫺1 0 1 2 3 4 5 6 7 8 9
5. n 2
35. y 7
1 2 3 4 5 6 7 8 9
⫺12 ⫺10
7. c 1
2
37. a 2
5
⫺4 ⫺3⫺2 ⫺1 0 1 2 3 4
9. x 8
39. n 4
1 2 3 4 5 6 7 8 9
1
2
⫺4
⫺2
41. t 12
⫺8
⫺6
⫺4
0
2
4
6
1
4
43. b 4
Chapter 8 Functions and Graphing
11. d 9
⫺10
⫺9
⫺8
⫺7
⫺6
Page 367
1.
13. x 8
1 2 3 4 5 6 7 8 9
15. c 4
⫺4 ⫺3 ⫺2 ⫺1 0 1 2 3 4
3.
17. x 3
⫺4 ⫺3 ⫺2 ⫺1 0 1 2 3 4
19. k 5
⫺7⫺6⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0 1
5.
21. n 5
⫺7 ⫺6 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0 1
x
0
y
4
3
3
x
6
y
8
7
10
8
12
domain {0, 3}; range {4, 3}
domain {6, 7, 8}; range {8, 10, 12}
x
8
y
5
7
1
6
1
1
2
domain {8, 7, 6, 1}; range {5, 1, 1, 2}
23. b 2
⫺4 ⫺3 ⫺2 ⫺1 0 1 2 3 4
Pages 371–373
25. y 30
Selected Answers
7. E 9. A 11. F 13. true 15. true 17. true
10
30
50
70
90
⫺10
⫺8
⫺6
⫺4
⫺2
27. c 4
29. n 7
31. n 4.5
1 2 3 4 5 6 7 8 9
Lesson 8-1
1. Sample answer: a set of ordered pairs: {(1, 2), (4, 3),
(2, 1), (3, 3)}
a table:
a graph:
y
x
1
y
2
4
3
2
1
3
3
(⫺3, 3)
(4, 3)
(1, 2)
x
O
(⫺2, ⫺1)
33. t 1
⫺4⫺3 ⫺2 ⫺1 0 1 2 3 4
35. c 4
⫺10
⫺8
⫺6
⫺4
⫺2
37. 0.55c 0.35 2; 3 candy bars 39. 2s 10 40,
15 subscriptions 41. x 200; Sample explanation: The
inequality finds at what mileage Able’s charge is greater
than Baker’s charge. 43. more than 100 minutes 45. k 3
and k 3, or k {2, 1, 0, 1, 2} 47. D 49. 5 x 1
51. y 37 53. n 5 55. a 18.6 57. 0.5%
59. 16.6
mpg 61. $1.25 an issue 63. 6 m
3. Sample answer:
This graph does not
represent a function
because when x equals 1,
there are two y values, 0
and 2.
y
O
x
5. Yes; each x value is paired with only one y value. 7. No;
5 is paired with 4 and 14. 9. Yes; any vertical line passes
through no more than one point of the graph. 11. As wind
speed increases, the windchill temperature decreases.
13. Yes; each x value is paired with only one y value.
15. No; 5 in the domain is paired with 4 and 1 in the
range. 17. No; 2 in the domain is paired with 5 and 1 in
the range. 19. Yes; each x value is paired with only one
y value. 21. No; a vertical line passes through more than
one point. 23. Yes; any vertical line passes through no
more than one point of the graph. 25. Generally, as the
years progress, the number of farms decreases. An
exception is in the year 2000. 27. Generally, as the years
progress, the size of farms increases. An exception is in the
year 2000. 29. Generally, as foot length increases, height
increases. 31. Sometimes; a relation that has a member of
the domain paired with more than one member in the
range is not a function.
33. For a given wind speed, there is only one windchill
temperature for each actual temperature. So, the
relationship between actual temperatures and windchill
temperatures is a function. Answers should include the
following.
• For a given wind speed, as the actual temperature
increases, the windchill temperature increases.
• Since the relationship between actual temperatures and
windchill temperatures is a function, there cannot be two
different windchill temperatures for the same actual
temperature when the wind speed remains the same.
35. A 37. a 21 39. x 6 41. 43. 18 45. 75
47. 13 49. 5 51. 0
15. Sample answer: (1, 8), (0, 7), (1, 6), (2, 5)
17. Sample answer: (1, 5), (0, 0), (1, 5), (2, 10)
19. Sample answer: (1, 2), (0, 1), (1, 4), (2, 7)
21. Sample answer: (1, 5), (0, 6), (1, 7), (2, 8)
23. Sample answer: (1, 13), (0, 10), (1, 7), (2, 4)
25. Sample answer: (1, 0), (1, 1), (1, 2), (1, 3)
27. 6.2 mi 29. Quadrant I; a person cannot have a
negative age or heart rate.
31.
33.
y
y
O
x
yx5
y x 6
x
O
35.
37.
y
y
x
O
x
O
y 3x 4
x y 6
39.
41.
y
y
1. Sample answer: Infinitely many values can be substituted
for x, or the domain.
3. x
(3, 2), (1, 4),
x5 y
3
3 5
1
1 5
4
0
05
5
1
15
6
2
y 3
x
3x y 7
x
O
2
2(0) 6
6
2
2(2) 6
10
4
2(4) 6
14
14
12
10
8
6
4
2
0
11. Sample answer: (1, 186,000) means that light travels
186,000 miles in 1 second. (2, 372,000) means that light
travels 372,000 miles in 2 seconds.
13. x
(4, 2), (0, 6),
2x 6
y
0
43. P
(2, 10), (4, 14)
Selected Answers
7. Sample
y 2x 1
2(4) 6
O
(0, 5), (1, 6)
5. Sample answer: (1, 4), (0, 0), (1, 4), (2, 8)
answer: (1, 1), (0, 6), (1, 11), (2, 16)
9.
y
4
x
O
(3, 12)
(2, 8)
(1, 4)
1 2 3 4 5 6 7s
45. Yes; the points lie on a straight line. 47. Yes; the points
lie on a straight line. 49. No; the exponent of x is not 1.
51. Sample answer: In the first table, as the x values
increase by 1, the y values increase by 2. In the second
table, as the x values increase by 1, the y values do not
change by a constant amount. 53. B 55. Yes; each x value
is paired with only one y value. 57. No; 11 in the domain
is paired with 8 and 21 in the range.
59. x 4;
1
6
61. 63. 3
7
2
3
4
5
6
7
65. 4
Lesson 8-3
1. To find the x-intercept, let y 0 and solve for x. To find
the y-intercept, let x 0 and solve for y. 3. 1; 3
5. 4; 4 7. 3; 2
9.
35.
Money ($)
Pages 384–385
y
(6, 0)
x
O
x 2y 6
(0, 3)
11.
y
18
16
14
12
10
8
6
4
2
y 18 3x
0
(0, 3)
(0.5, 0)
x
O
y
39. B 41. Sample answer:
(1, 5), (0, 7), (1, 9), (2, 11)
43. Sample answer: (1, 1),
(0, 5), (1, 9), (2, 13) 45. no
47. n 12 49. 2.8%
51. 16 53. 25
y 6x 3
(1, 2)
y 2x
15. none; 5
13. 1; 1
23. 5; 4
17. 5; 5
25.
19. none; 4
x
The x-intercept 6 represents the number of books that she
can buy with no money left over. The y-intercept 18
represents the money she has before she buys any books.
37. The x- and y-intercept are both 0. Therefore, the line
passes through the origin. Since two points are needed to
graph a line, y 2x cannot be graphed using only the
intercepts.
The y-intercept 3
represents the base
fee of $3.
y
1 2 3 4 5 6 7 8 9
Number of Books
21. 8; 4
(1, 2)
x
O
27.
y
y
(0, 4)
(0, 2)
(2, 0)
Pages 389–391
xy4
x
O
x
(4, 0)
O
Lesson 8-4
1. Sample answer: horizontals do not rise, so
0
rise
slope or 0.
run
3. Mike; Chloe should have
run
subtracted 2 from 11 in the denominator.
yx2
9. 0
11. B 13. 4
3
4
15. 17. 0
19. 1
2
3
5. 7. 2
3
2
21. 3
4
23. undefined 25. 27. It decreased; negative slope.
Selected Answers
29.
31.
y
y
(0, 4)
y 2x 4
O
x
(0, 2)
(2, 0)
y 2
x
O
29. Slope can be used to describe the steepness of roller
coaster hills. Answers should include the following.
• Slope is the steepness of a line or incline. It is the ratio of
the rise to the run.
• An increase in rise with no change in run makes a roller
coaster hill steeper. An increase in run with no change in
rise makes a roller coaster less steep.
31. A 33. 2; 6 35. Sample answer: (1, 3), (0, 5), (1, 7),
(2, 9) 37. Sample answer: (1, 8), (0, 7), (1, 6), (2, 5)
39. y 2x
33.
1
3
41. y x
y
(0, 3)
Pages 395–397
3x 6y 18
x
O
(6, 0)
Lesson 8-5
1. The slope is 60, the rate of change is 60 units for every
1 unit, and the constant of variation is 60. 3. Justin; any
linear function, including direct variations, has a rate of
change. 5. increase of $12 per hour 7. y 6x 9. increase
of 12 in./ft 11. decrease of 2°F/min
13. Sample answer: The population of wild condors
decreased from 1966 to 1990. Then the population increased
from 1990 to 1996. The population of condors in captivity
increased slowly from 1966 to 1982, then increased more
rapidly from 1982 to 1996.
Rate of Change
(number per year)
Interval
1966–1982
Condors in
the Wild
2.25
1982–1990
3
1990–1992
0
7.
9.
y
y
y 1x 1
4
Condors in
Captivity
0.1875
x
O
x 2y 4
4.625
8
1992–1994
1.5
14.5
1994–1996
12.5
3.5
15. y 5x 17. y 0.75x 19. y 2.54x 21. A line
representing the relationship between time and distance
has a slope that is equal to the speed. Answers should
• Sample drawing:
11. The y-intercept 25 represents the charge for a basic cake.
Slope 1.5 represents the cost per additional slice.
13. 2; 4 15. 2; 3 17. 0; 4
19.
21.
y
y
y x 6
y
Distance (mi)
x
O
300
x
O
200
x
O
100
0
1 2 3 4 5 6
x
23.
25.
Time (h)
y
y
xy0
• As speed increases, the slope of the graph becomes
steeper.
23. B 25. 2
27.
y
y 3x 2
4
O
x
O
x
y x 1
(0, 1)
(1, 0)
x
O
27.
29.
y
y
x
O
Page 397
Practice Quiz 1
1. No; 1 is paired with 2 and 3.
3.
y
x
5x y 3
O
31.
x
O
yx4
5. 9; 9
y
7. 5; 4
O
x
y 3
9. 2
1. a 3. Alex; the equation in slope-intercept form is
1
2
y x 4.
5. 1; 0
33. slope 50, the descent in feet per minute;
b
m
y-intercept 300, initial altitude 35. . Replace y with 0
Selected Answers
2x 3y 12
31. y 1 3x
29. 14
in y mx b and solve for x.
37. B 39. y 4x 41. 2
3
43. 4 45. 6x 2x 28; 7 47. 5
49. 29
51. 11
1. Sample answer: Find the y-intercept b and another point
on the line. Use the points to determine the slope m. Then
substitute these values in y mx b and write the
equation.
1
2
3
9. y x 1
4
5. y 2x 3
17. y 2x 3
19. y 2.5
3. y x 1
1
2
7. y x 1
11. y 2x 6
1
3
13. y 5
15. y x 8
1
2
21. y x
23. y x 1
25. y x 27. y 7 29. y 4x 3 31. y 1088x;
The speed of sound is 1088 feet per second.
33a. d 0.5(0.7c 1.06) or d 0.371c 33b. $18.55 35. C
37. 6; 7 39. 3; 2 41. positive
Pages 410–413
11. No, the equation gives a negative value for barometric
pressure, which is not possible. Also, the data in the scatter
plot do not appear to be linear. 13. Sample answer: 238 in.
15. As latitude increases, temperature decreases.
17. Sample answer: 61.3°F 19. The data describing the life
expectancy for past generations can be displayed using a
scatter plot. Then a line is drawn as close to as many of the
points as possible. Then the line can be extended and used
to predict the life expectancy for future generations.
• A best-fit line is a line drawn as close to as many of the
data points as possible.
• Although the points may not be exactly linear, a best-fit
line can be used to approximate the data set.
21. A 23. y 2x 2 25. y 4
27.
y
y x 3
Lesson 8-8
Number of Households
(millions)
1. Sample answer: Use a ruler to extend the line so that it
passes through the x value for which you want to predict.
Locate the x value on the line and determine the
corresponding y value. Or, write an equation for the best-fit
line and substitute the desired value of x to find the
corresponding value of y.
y
3. Sample answer:
40
35
30
29. n 7
41. 2
25
20
15
10
5
’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02
Year
Selected Answers
Attendance (millions)
y
1500
1450
1400
x
35. 4.5
37. 3
39. 1
Lesson 8-9
1. Sample answer: A group of two or more equations form a
system of equations. The solution is the ordered pair that
satisfies all the equations in the system. If the equations are
graphed, the solution is the coordinates of the point where
the graphs intersect. The system has infinitely many
solutions if the equations are the same and the graphs
coincide. 3. (5, 4)
5. no solution
y
xy4
xy2
1350
1300
1250
1200
x
O
1150
0
’93 ’94 ’95 ’96 ’97 ’98 ’99
Year
9. Sample answer:
x
7. (2, 6)
Barometric Pressure
(in. mercury)
y
35
9. (3, 2) 11. infinitely many
13. (3, 3)
30
25
20
15
y
15. infinitely many
y
x y 6
y 2x
3
yx
10
5
0
3
2
31. d 33. 2
Pages 416–418
0
5. y 20x 320
7. Sample answer:
x
O
(3, 3)
10 20 30 40 50 60 70
Altitude
(1000s ft)
O
x
O
x
2x 3y 0
x
17. (2, 4)
5.
y
7.
y
y 2x
y 1x 3
2
y
y 3x 2
y x1
(2, 4)
x
O
x
O
9.
0
40
35
27b. Sample answer:
The line representing
runner B has a
steeper slope than
the line representing
runner A. The
intersection point
represents the time
and distance at
which runner B
catches up to
runner A.
y
Children
25
20
10
5
25x 15y 630
5 10 15 20 25 30 35 x
Adults
0
B
A
75
Distance (m)
30
15
x
1 2 3 4 5 6 7
Time (s)
Sample answer:
5 adults, 30 children;
10 adults, 22 children;
15 adults, 15 children
y
45
Distance (m)
19. (2, 0) 21. (4, 10) 23. (3, 6) 25. (6, 11); an order of
6 pounds will cost the same, $11.00, for both sites.
27a. Sample answer:
y
A
No; since slope
75
represents rate,
the slopes of the
B
graphs are the
50
same. Therefore,
the runners will
25
never meet.
11.
13.
y
y
50
25
x
O
0
29. C 31. positive slope
39. yes
1 2 3 4 5 6 7
Time (s)
33. y 3x
35. yes
x
y 3
37. no
15.
17.
y
y
y0
y
Age
30
29
28
27
26
25
24
23
0
x
O
y x4
O
x
19.
21.
y
x
’84 ’88 ’92 ’96 ’00 ’04 ’08
Year
x
O
9. (0, 5)
y
y 13 x 1
O
x
y 2x 4
1. y x 3 3a. Sample answer: (0, 1), (1, 0), (2, 1)
3b. Sample answer: (0, 0), (1, 1), (2, 2)
Selected Answers
Practice Quiz 2
1
3. ; 3 5. y 1
2
7. Sample answer:
x
O
y x
Page 418
1. 1; 8
x
O
23.
19.
y
y x 3000
6000
Sales ($)
21.
y
y
5000
4000
xy 4
y 3x 2
3000
x
O
2000
1000
25. No; the number of sales and the costs cannot be
negative. 27. 10x 25y 1440 29. Sample answer:
25 small, 45 large; 50 small, 30 large; 100 small, 10 large
31.
y
23.
25.
y
y
(0, 2)
y x 2
(2, 0)
Econo Rafts
(3, 0)
O
x
O
30
x
O
x
3000
6000
Costs ($)
0
100x 40y 1500
x
y x 3
(0, 3)
20
10
27.
5
0
29.
x
10
15
Super Rafts
y
y
x y 2
x 4
(4, 0)
3
2
33a. y x 1, y x 2
x
O
(2, 0)
33b. Sample answers: (0, 2), (1, 2), (3, 2) 35. C
x
O
(0, 2)
39. (2, 5)
37. (0, 3)
yx 3
y
y
(0, 3)
O
x
O
x
y 2x 1
31. 1
7
33. 35. undefined 37. increase of 8 m/s
8
39.
y x 3
41.
y
y
(2, 5)
x
y x4
O
41. 0.4
43. 0.5
Pages 424–428
y 1x 2
x
O
3
1. d 3. h 5. a 7. f 9. c 11. Yes; each x value is paired
with only one y value. 13. Yes; each x value is paired with
only one y value.
15.
43. y x 3
45. Sample answer:
17.
y
y
y x 4
y x
O
y
Attendance
Selected Answers
x0
x
3000
2900
2800
2700
2600
2500
2400
O
x
0
x
2000 2001 2002 2003
Year
47. (3, 3)
65.
y
67. (5, 7)
y
( 3, 3)
y3
2
71. 3
49. no solution
73. 9 75. It can
be written as a fraction.
yx
x
O
69. (4, 3)
3
4
6
79. It can be written as .
1
77. It can be written as .
x
O
y
y 3x 5
Pages 443–445
Lesson 9-2
1. Whereas rational numbers can be expressed in the form
a
, where a and b are integers and b does not equal 0,
b
x
O
irrational numbers cannot. 3. N, W, Z, Q
10
9. ,
3
3x y 1
3
3,
5
5. Q 7. , 3.7 11. 8.6, 8.6 13. N, W, Z, Q 15. Q
13
17. Q 19. I 21. I 23. Z, Q 25. Q 27. Z, Q 29. always
1
2
41. 10, 105
, 10, 1.05
51. (4, 4)
53.
55.
y
y
y x 4
x
x
O
O
1
4
43. Sample answer: 4
and 49
45. 7, 7 47. 4.7, 4.7 49. 12, 12 51. 11.3,
11.3 53. 1.3, 1.3 55. 1.9, 1.9 57. 12 or –12
59. 4 or –4 61. 36
63. If a square has an area that is not a perfect square, the
lengths of the sides will be irrational. Answers should
•
Area y 3x 1
Area 56 in 2
64 in 2
65. B 67. 2621.2 ft2 69. 7 71. 3 73. Sample answer:
(0, 5), (1, 6), (6, 2) 75. x 5 77. $0.53/cupcake
Chapter 9 Real Numbers and
Right Triangles
Page 435
6
5
33. 35. 37. 39. , 4, 2.1, 5
31. always
79.
81.
83.
1. 3. 5. 7. 9. 8
19. 34 21. 97
11. 60
13. 9
15. 11
17. 8
3:00
1.69
Pages 449–451
55˚
10 9 8 7 6 5 4 3 2 1
5. 8a 7. 3.9 9. 8 11. 44.9 mi 13. 6 15. 5a 17. not
possible 19. 14y 21. 18, 18 23. 1.5 25. 7.5 27. 9.3
29. 15.8 31. 1.7 33. 70.7 35. 9 37. 7 39. 14
41. 17 43. 2 45. 6 47. 14.8 mi 49. 9; Since
64 65 81, 64 65 81. Thus it follows that
8 65 9. So, 9 is greater than 65. 51a. 10.4 in.;
41.6 in. 51b. 14.2 cm; 56.8 cm 51c. 8.4 m; 33.6 m
53. 10 55. 2 57. Sample answer: A number that has a
rational square root will have an ending digit of 0, 1, 4, 5, 6,
or 9. The last digit is the ending digit in one of the squares
from 1–100. There are just six ending digits. 59. D
61. Sample answer: addition and subtraction 63. a
Lesson 9-3
, NP
; 1, MNP, PNM, N 3. 20°; acute
1. N; NM
5. 70°; acute 7. acute
9. straight angle
11. 15°; acute 13. 85°; acute
17. 60°; acute 19. 90°
15. 135°; obtuse
21.
23.
acute
40˚
25.
acute
65˚
obtuse
27.
155˚
obtuse
95˚
Selected Answers
1. A positive number squared results in a positive number,
and a negative number squared results in a positive
number. 3. Sample answer: 1.69
7:45
10:00
31a. obtuse 31b. right 31c. acute
33. better self-image: about 95°;
better health: about 101°; more alert:
38˚
about 79°; more relaxed: about 56°;
other: about 29° 35. 24
37. C 39. Z, Q 41. I 43. 4 45. x 7 22 47. 99
49. 60 51. 18
29.
acute
Page 451
1. 6
Page 470
Practice Quiz 2
3. Yes; 342 302 162 5. (1, 5)
1. obtuse isosceles
Pages 473–475
Lesson 9-7
1. Sample answer:
A
corresponding sides:
X
AB
BC
AC
XY
YZ
XZ
Practice Quiz 2
3. 8.2, 8.2
Pages 455–457
5. obtuse
Y
B
Lesson 9-4
1. Whereas an isosceles triangle has at least two sides
congruent, an equilateral triangle has three sides congruent.
3. Sample answer:
30
˚
120˚
Z
C
x
6
5. 6 km 7.
15
9
7
x
11. ; 5 13. always
4.2
3
3. ; 10
15. 68 yd
4
5. 90; right 7. right isosceles 9. acute isosceles
11. 27; right 13. 112; obtuse 15. 90; right 17. 20°, 60°, 100°
19. acute equilateral 21. right scalene 23. acute scalene
25. always 27. obtuse 29. acute 31. not possible
33. not possible 35. 45°; 50°; 85° 37. 10, 15, 21 39. B
41. 180°; straight 43. 145°; obtuse 45. 9, 9 47. 9.2, 9.2
49. 144 51. 324 53. 729
Lesson 9-5
1. Sample answer: 8, 15, 17 3. 25 5. 15 7. no 9. B
11. 26 13. 12.5 15. 18.9 17. 23 in. 19. 12 21. 12.1
23. 37.3 25. 28 27. 33.5 29. yes 31. no 33. no
35. 32 in.
37. There is enough information to find the lengths of the
legs. Since the right triangle is an isosceles right triangle,
we know that the lengths of the legs are equal. So, in the
Pythagorean Theorem, we can say that a b. In addition,
we know that c 8.
c2 a2 b2 Pythagorean Theorem
82 a2 a2 a b and c 8
82 2a2
Add a2 and a2.
64 2a2
Evaluate 82.
Selected Answers
64
2a2
2
2
32 a2
Simplify.
Take the square root of each side.
39. D 41. 17 units 45. 90; right 49. n 9 51. 5
a
32
Pages 479–481
Lesson 9-6
1. the point halfway between two endpoints
3. Sample answer:
; The coordinates of the
y
1
midpoint of AB
are , 0.
2
Midpoint
1, 0
2
(
A
O
2
Lesson 9-8
1. The sine ratio compares the measure of the leg opposite
the angle to the measure of the hypotenuse. The cosine
ratio compares the measure of the leg adjacent to the angle
to the measure of the hypotenuse. The tangent ratio
compares the measure of the leg opposite the angle to the
measure of the leg adjacent to the angle. 3. 0.8824
5. 1.875 7. 0.9455 9. 25.6 11. 7.8 13. 0.9231 15. 0.7241
17. 2.4 19. 0.8944; 0.4472; 2.0 21. 0.1045 23. 0.8572
25. 0.2126 27. 6.8 29. 24.9 31. 97.6 33. about 21 m
35. about 44 m 37. 24.0 39. 40.4 41. sin 45° cos 45°;
sin 60° cos 30°; sin 30° cos 60° 43. To find heights of
buildings. Answers should include the following.
• If two of the three measures of the sides of a right triangle
are known, you can use the Pythagorean Theorem to find
the measure of the third side. If the measure of an acute
angle and the length of one side of a right triangle are
known, trigonometric ratios can be used to find the
missing measures.
x
•
sin 6° 19
19(sin 6°) x
2.0 x
19 ft
6˚
x ft
The height of the ramp is about 2 feet.
45. C
47. 1, 49. (3, 4) 51. a 6
1 1
2 2
Pages 483–486
(3, 1)
17. 6 ft
Divide each side by 2.
Pages 468–470
)
B
(2, 1)
5. 11.2 7. (2, 5) 9. 9.2
11. 10.2 13. 16.6 15. 4.8
17.
19.2 19. (1, 3) 21. (4, 2)
x
23. (2, 2) 25. (3, 4)
27. 11, 5
1
2
1. real numbers 3. obtuse 5. hypotenuse
7. trigonometric ratio 9. 6 11. –9 13. not possible
15. 9, 9 17. 1.2, 1.2 19. 90°; right 21. 35°; acute
23. obtuse isosceles 25. 13.7 27. 15.9 29. 9.4 31. (3, 5)
AB
HJ
BC
JK
33. (0, 2) 35. ; 10
Chapter 10
Page 491
1. 44
3. 51
15. 10.7
37. 1.3333
Two-Dimensional Figures
5. 28
1
6
7. 39
9. 44
7
8
11. 71.8
3
8
13. 12.5
2
9
17. 10 19. 3 21. 5 23. 6
Pages 495–497
29. Yes; PM
and M
N
have equal measures. 31. (2, 3)
33. C 35. 9.2 37. 35.1 39. 2, 1 41. –4, 6 43. 28
45. 21 47. 59
20
15
9. ; 24
19. No, triangles ABC and DEF are not similar since the
corresponding sides are not proportional. 21. A 23. 3.6
1
1
25. 7.1 27. 77.4 29. 31. 1 33. 0.7143 35. 0.225
30˚
Pages 462–464
x
18
x
10
; 8
4
5
Lesson 10-1
1. Complementary angles have a sum of 90° and
supplementary angles have a sum of 180°. 3. 56° 5. 124°
7. 28 9. D 11. 127° 13. 53° 15. 127° 17. 148 19. 175
21. 9 23. 41° 25. 73° 27. 112° 29. 5 31. 9 33. They
are supplementary. 35. A 37. Sample answer: Both
graphs intersect to form right angles. 39. Sample answer:
The slopes of the graphs of perpendicular lines are negative
reciprocals of each other. 41. 0.8910 43. 7.5 45. 9m
47.
49.
11. R(4, 3), S(0, 3),
T(4, 1);
y
R
N
Q O
Q'
O
P
P' x
O'
T'
45˚
x
O
T
1. They have the same size and shape. 3. J C,
K B, M G, KM
BG
GC
BC
, M
J , K
J ; BGC
5. M 7. M
N
9. 15 ft 11. K N, J P,
M M, K
NP
PM
NM
J , JM
, K
M
; NPM
13. Z S, W T, Y R, ZW
ST
TR
, W
Y
,
Z
SR
Y
; STR 15. sometimes 17. 30° 19. F 21. A
23. H
F
25. D
C
27. 20 29. 6 31. Sample answer: ZQN
33. Sample answer: WQO 35. Congruent triangles can
be found on objects in nature like leaves and animals.
• Congruent triangles are triangles with the same angle
measures and the same side lengths.
• Sample answer: A bird’s wings when extended are an
example of congruent angles. Another example of
congruent angles would be the wings of a butterfly.
37. D 39. 0.1219 41. 1.1585 43. 6
45–49.
y H
A
J
D
y
S
M
145˚
O
13. M(1, 2), N(4, 4),
O(3, 2), P(3, 0),
Q(0, 0);
x
M'
S'
R'
N'
15.
y
17.
C'
B'
A'
y
D'
E'
B
x
O A
B
E'
C
C
B'
D'
D
E
x
A' O A
C'
E
D
19. translation
21. Sample answer:
; The image of the figures
reflection is the same as the
image of its translation to the
right 6 units.
y
x
O
T
W
O
U
x
T
x
O
A'
C
T'
U'
23. reflection 25. Since many of the movements used in
recreational activities involve rotating, sliding, and flipping,
they are examples of transformations. Answers should
• a translation is a slide, a reflection is a mirror-image, and
a rotation is a turn.
• sample answer: the swing represents a rotation, the
scooter represents a translation, and the skateboard
represents reflection.
27. C 29. DF
31. 110°
33. x 9.6;
7.0
9. D1, 3, E3, 4,
1
2
7. A(2, 5), B(1, 3),
C(2, 0);
1
2
G1, 1, F3, ;
1
2
1
2
y
y
A'
E'
D'
B'
E
A
D
B
C'
O
x
F' x
O
G'
C
F
G
35. 113 37. 47
Pages 515–517
8.0
9.0
10.0
39. 106
Lesson 10-4
1. Sample answer: A textbook is an example of a
quadrilateral; the tiles in a shuffleboard scoring region are
examples of parallelograms; a “dead end” road sign is an
example of a rhombus; and a floppy disk is an example
of a square. 3. 110; 110° 5. rectangle 7. trapezoids,
parallelograms 9. 102; 102° 11. 60; 60°; 60°; 120° 13. 70;
70°; 80°; 120° 15. Sample answer: A chessboard; it is a
square because it is a parallelogram with 4 congruent sides
and 4 right angles. 17. square 19. parallelogram
21. rhombus 23. always 25. sometimes 27. quadrilateral
Selected Answers
1. The figure is moved 5 units to the right and 2 units down.
y
y
3.
5.
C'
R
B'
B
S
A
R'
S'
19. 2880° 21. Sample answer: hexagon, triangle, decagon,
quadrilateral, and pentagon 23. 140° 25. 135° 27. 150°
29. octagons, squares 31. 180 cm 33. 58.5 in.
35. In tessellations, polygons are fit together to create a
pattern such that there are no gaps or spaces.
• Sample answer:
29a. Yes; a rhombus is equilateral
but may not be equiangular.
29b. Yes; a rectangle is
equiangular but may not
be equilateral.
31. B 33. F
35. M
A
37. 14.4
39. 28.52
y E
D
E'
G
F'
D'
G'
Page 517
37. B 39. 120° 41. 60° 43. 30° 45. 18 cm2
47. quadrilateral 49. 16.4x 51. 33.9 53. 18.1
x
O
Pages 536–538
Practice Quiz 1
1. 35° 3. Q(3, 3), R(5, 6), S(7, 3) 5. 60; 60°; 120°
Pages 523–525
Lesson 10-5
1. Sample answer:
3 in.
Selected Answers
8 in.
3. 8 ft2 5. 60 m2 7. 11 m2 9. 90 cm2 11. 43.99 cm2
13. 28 in2 15. 22.8 yd2 17. 36.75 m2 19. about 95,284 mi2
21. 147 km2 23. 57 ft2 25. 5 bags 27. 16 in. 29. 24.5%
31. The area of a parallelogram is found by multiplying the
base and the height of the parallelogram. The area of a
rectangle is found by multiplying the length and the width
of the rectangle. Since in a parallelogram, the base is the
length of the parallelogram, and the height is the width of
the parallelogram, both areas are found by multiplying the
length and the width. Answers should include the following.
• Parallelograms and rectangles are similar in that they are
quadrilaterals with opposite sides parallel and opposite
sides congruent. They are different in that rectangles
always have 4 right angles.
•
33. B 35. 24; 24°; 96° 37. 30
Pages 529–531
39. 26
41. 900
43. 1260
Lesson 10-6
1.
• Sample answer:
3. The number of triangles is 2 less
than the number of sides. 5. octagon;
regular 7. 128.6° 9. hexagon; regular
11. nonagon; not regular 13. decagon,
not regular 15. 540° 17. 1440°
Lesson 10-7
1. Multiply 2 times times the radius. 3. Mark; since the
diameter of the circle is 7 units, its radius is 3.5 units. Thus,
the area of the circle is · (3.5)2 or 38.5 square units.
5. 50.3 m; 201.1 m2 7. 8.2 km; 5.3 km2 9. about 9.1 mi2
11. 40.8 in.; 132.7 in2 13. 131.9 km; 1385.4 km2 15. 79.8 m;
506.7 m2 17. 22.9 cm; 41.9 cm2 19. 96.6 in; 742.6 in2
21. 1.5 m 23. 13 cm 25. about 3979 mi 27. d 29. a
31. about 26 times 33. are safe: 30.5 in2; are unsafe: 13.3 in2;
unsure: 19.7 in2 35. 4 37. C 39. 125° 41. 235°
43. 125° 45. 62.5° 47. Sample answer: S
S
Q
P
, , R
P
49. 144° 51. 38 m2 53. x 7 55. 150.5
Page 538
Practice Quiz 2
1. 112.86 cm2
3. 32 m2
Pages 541–543
5. 29.5 in.; 69.4 in2
Lesson 10-8
1. Sample answer:
3. 49.5 yd2 5. 2 7. 72 ft2 9. 56.1 cm2 11. 18.3 in2
13. 45 ft2 15. 86.8 yd2 17. 85 units2 19. 6963.5 yd2
21. Sample answer: Separate the area into a rectangle and a
trapezoid. 23. 68,679 mi2 25. You can use polygons to
find the area of an irregular figure by finding the area of
each individual polygon and then finding the total area of
the irregular figure. Answers should include the following.
•
• To find the area of the irregular figure shown above, the
figure can be separated into two rectangles and a triangle.
27. C 29. 44.0 cm, 153.9 cm2 31. 540° 33. 1080°
35. 24xy
Pages 544–548
1. supplementary 3. corresponding angles
7. 109° 9. 71° 11. H 13. R
S
15. G
F
5. equilateral
17.
19. 112; 112° 21. 70; 70°;
70° 23. 11 yd2
25. hexagon; 720°
27. decagon; 1440°
29. 13.2 m; 13.9 m2
31. 118 in2 33. 863.4 cm2
y H'
H
x
O
J
J'
I
I'
Pages 570–572
Chapter 11 Three-Dimensional Figures
Page 553
1. yes; triangle
15. yes
3. no
5. 17
7. 7
9. 155
11. yes
13. yes
1. Five planes form a square pyramid because the solid has
five faces. An edge is formed when two planes intersect; a
vertex is formed when three or four planes intersect.
3. triangular pyramid; any one of the following faces can be
considered a base: RST, QRS, QST, QRT; Q
R
, Q
S
, Q
T
, R
T
,
RS
, S
T
; Q, R, S, T 5. intersecting
7.
top
front
side
4 cm
25. The volume of a pyramid is one-third the volume of a
prism with the same base and height. Answers should
• The height of the pyramid and prism are equal. The
bases of the pyramid and prism are squares with equal
side lengths. Therefore, their base areas are equal.
• The formula for the volume of a pyramid is one-third
times the formula for the volume of a prism.
27. B 29. 904.8 cm3 31. 107.5 mm3 33. 10.1 in3
35. 7.8 37. 36
Page 572
Practice Quiz 1
1. triangular prism
Pages 575–577
37. n 11
3
4
Lesson 11-2
39. y 1 41. 14 in2
Pages 565–567
43. 6.5 cm2
1. Sample answer: Finding how much sand is needed to fill
a child’s rectangular sandbox; measure the length, width,
and height, and then multiply to find the volume.
3. 183.6 cm3 5. 1608.5 ft3 7. 282.7 yd3 9. 198.9 ft
11. 512 cm3 13. 748 in3 15. 88.0 ft3 17. 225 mm3
19. 18.6 m3 21. 6.2 m 23. 1728 25. 1,000,000 27. 11.5 in.
1
2
29. The volume will be greater if the height is 8 inches.
By using the formula for circumference, you can find the
radius and volume of each cylinder. If the height is
1
2
8 inches, the volume is 86.5 in3; if the height is 11 inches,
the volume is 67.7 in3. 31. C 33. Sample answer:
QT
and Y
Z
35. x 8 37. 25 39. 4 41. 28
3. 12.6 cm3 5. 11,545,353 ft3
Lesson 11-4
1. Sample answer: The surface of a solid is twodimensional. Its area is the sum of the face areas, which are
given in square units. 3. 150 ft2 5. 571.8 in2 7. 140.7 mm2
9. 282 in2 11. 264 m2 13. 1885.0 ft2 15. 294 ft2
17. 628.3 in2 19. 264.0 in2 21. 754 ft2 23. The surface
area is 4 times greater. 25. D 27. square or rectangle
29. rectangle
31. 565.5 in3
Pages 580–582
33. 15.21
35. 1.3
1
4
37. 3
Lesson 11-5
1. Slant height is the altitude of a triangular face of a
pyramid; it is the length from the vertex of a cone to the
edge of its base. Height of a pyramid or cone is the altitude
of the whole solid. 3. Sample answer: An architect might
use the formulas to calculate the amount of materials
needed for parts of a structure. 5. 42.9 m2 7. 336 ft2
9. 96.3 in2 11. 62.4 in2 13. 339.3 in2 15. 311.9 m2
17. 506.6 mm2 19. Style 8M has 29 in2 more plastic.
21. 339 ft2; 4 squares 23. Many building materials are
priced and purchased by square footage. Architects use
surface area when designing buildings. Answers should
• Surface area is used in covering building exteriors and in
designing interiors.
• It is important to know surface areas so the amounts and
costs of building materials can be estimated.
25. C 27. 5541.8 mm2 29. 7 ft2 31. 25.1 in3 33. infinitely
many solutions 35. 3 37. 3 39. 3.15
Pages 586–588
Lesson 11-6
1. Sample answer:
The cones are similar
because the ratios
comparing their radii
and slant heights are
2
3
5
7.5
equal: .
5m
7.5 m
2m
3m
Selected Answers
9. rectangular prism; LMNP, QRST or LPTQ, MNSR or
PNST, LMRQ; LMNP, QRST, LPTQ, MNSR, PNST, LMRQ;
L
M
, M
N
, N
P
, P
L
, L
Q
, M
R
, N
S
, P
T
, Q
R
, R
S
, S
T
, T
Q
; L, M, N,
P, Q, R, S, T 11. triangular pyramid; any one of the
following faces can be considered a base: WXY, WYZ,
WZX, XYZ; W
X
, W
Y
, W
Z
, X
Z
, X
Y
, Y
Z
; W, X, Y, Z 13. W
R
15. skew 17. top 19. rectangular and pentagonal prisms
23. Never; only three or more planes can intersect in a
single point. 25. Sometimes; three planes may intersect in
a line. Or, the planes may be parallel and not intersect at all.
27. Two-dimensional figures form three-dimensional
figures. Answers should include the following.
• Two-dimensional figures have length and width and
therefore lie in a single plane. Three-dimensional figures
have length, width, and depth.
• Two-dimensional figures form the faces of threedimensional figures.
29. D 31. 37.7 cm; 113.1 cm2 33. 0.5000 35. c 8
Lesson 11-3
1. The base is a circle.
3. Sample answer:
V 134.0 cm3
5. 37.7 cm3 7. 378 ft3 9. 91,636,272 ft3
11. 412 cm3 13. 150 in3 15. 78.5 m3
8 cm
17. 270.8 cm3 19. 565.5 m3 21. 44.0 m3
23a. 2.4 ft3 23b. 314.4 lb
3. no
1
3
5. x 33 ft
7. 525 m 9. 2,976,750 m3
11. yes
13. yes 15. x 7 m, y 18 m 17. Sometimes; bases must
be the same polygon and the corresponding side lengths
must be proportional. 19. always; same shape, diameters
or radii are proportional 21. 2003 or 8,000,000 times
greater 23. If the ratios of corresponding linear
dimensions are equal, the solids are similar. Answers
• For example, if the ratio comparing the heights of two
cylinders equals the ratio comparing their radii, then the
cylinders are similar.
• A cone and a prism are not similar.
25. C
5
9
29. 65° 31. 33. 19.3
27. 184 ft2
35. 6.0
37. 9.4
Page 588
Practice Quiz 2
1. 166 mm2 3. 9.4 m2 5. Yes; their corresponding
dimensions are proportional.
Pages 592–594
23. 45 in.
1
32
13. in.
25. 2 ft2
15. 3
17. 2
19. 1
21. 4
27. 84.47 m 29. 49.5 cm
31. 26 m2
1
33. b; The precision unit of ruler a is inch. The precision
8
1
unit of ruler b is inch. 35. No, the numbers are
16
estimated to the nearest 0.1 million. 37. 46,700,000; 3
39. Not necessarily, because the actual size of the 2.0 mm
wrench can range from 1.95 mm to 2.05 mm and the actual
size of the 2 mm bolt can range from 1.5 mm to 2.5 mm. So,
the bolts could be larger than the corresponding wrenches.
41. A 43. 0.05 mi; between 132.75 mi and 132.85 mi
45. 26.5 cm2 47. 14.8 m2
Selected Answers
Pages 595–598
1. false; lateral area 3. false; slant height 5. false; cylinder
7. true 9. rectangular prism; QRST, UVWX or QTXU,
RSWV or QRVU, TSWX; QRST, UVWX, QTXU, RSWV,
QRVU, TSWX; Q
R
, R
S
, S
T
, T
Z
, U
V
, V
W
, W
X
, X
U
, Q
U
, T
X
,
SW
, R
V
; Q, R, S, T, U, V, W, X 11. rectangular pyramid;
YNPZ; AYZ, AZP, ANP, ANY, YNPZ; A
Y
, A
Z
, A
P
, A
N
, Y
Z
,
Z
P
, P
N
, N
Y
; A, Y, Z, P, N 13. 0.8 mm3 15. 4 ft3
17. 1721.9 cm3 19. 548.7 mm2 21. 45 in2 23. 37.1 in2
25. yes 27. 19.0 cm 29. 0.9 m 31. 973 ft2
Chapter 12 More Statistics and
Probability
Page 605
1
1
1. 16; 15; none 3. 5.3, 5.8, 6.5 5. 7. 3
2
1
1
1
13. 15. 17. 8
6
6
Pages 608–611
1
2
1
2
9. 11. Lesson 12-1
1. Sample answer: The age of the youngest President at the
time of his inauguration was 42 and the age of the oldest
President to be inaugurated was 69. However, most of the
Presidents were 50 to 59 years old at the time of their
inauguration.
Leaf
0
1
2
3
4
67
255
0
5
0 1 20 20
11. Stem
1
2
3
4
5
6
7
8
15. Stem
Lesson 11-7
1. Josh; the first two 0s are not significant because they are
placeholders for the decimal point. The 0 between 2 and 5
is significant because it is between two significant digits
and shows the actual value in the thousandths place.
3. Sample answer: 0.012 or 2500 5. 3 7. 3 9. 7.1 L
11. 544.5 in2
3. Stem
40
41
42
43
44
45
46
47
48
49
50
51
52.
..
62.
..
76
77
78
Leaf
5. 50, 99 7. Sample answer: The
lowest score was 50. The highest
score was 99. Most of the scores
were in the 70–79 interval.
9. Chicken; whereas chicken
sandwiches have 8–20 grams of
fat, burgers have 10–36 grams of
fat.
13. Stem
3
68
49
0
1
2
3
4
5
23
227
79
4 77 77
Leaf
005
5
06
047
0
0
5
4
9 764 764
Leaf
668
01468
025
27
0 37 37
17. never 19. 73 21. Sample
answer: In this 10-year period,
most of the leaders hit between
40 and 50 home runs. 23. 5
25. The average number of games
won by the teams in the Big East
Conference is less than the
average number of games won
by the teams in the Big Ten
Conference. 29a. Sample
answer: It would be easier to find
the median in a stem-and-leaf
plot because the data are
arranged in order from least to
greatest. 29b. Sample answer: It
would be easier to find the mean
in a table because once you find
the sum, it may be easier to count
the number of items in a table.
29c. Sample answer: It would be easier to find the mode in
a stem-and-leaf plot because the value or values that occur
most often are grouped together. 31. C 33. no
35. 62.8 ft; 314.2 ft2 37. 247% 39. 0.65% 41. 57.1%
43. 1.6% 45. 6 47. 1.1
Pages 614–616
Lesson 12-2
1. The range describes how the entire set of data is
distributed, while the interquartile range describes how the
middle half of the data is distributed. 3. Sample answer:
{8, 9, 13, 25, 26, 26, 26, 27, 28, 30, 35, 40} 5. 27; 6 7. 24 h
9. 77; 39 11. 50; 10 13. 25; 15.5 15. 22 17. Feb.: 13.5;
July: 8 19. National League: 42, 44, 48, 38, 10; American
League: 39, 44, 49, 39, 10 21a. Sample answer: {43, 49, 50,
50, 58, 60, 60, 66, 70, 70, 71, 78} 21b. Sample answer:
{15, 18, 20, 20, 44, 60, 60, 64, 70, 70, 75, 79} 21c. Sample
answer: The first set of data has a smaller interquartile
range, thus the data in the first set are more tightly
clustered around the median and the data in the second are
more spread out over the range. 23. C
25. Stem
0
1
2
3
Leaf
9
2458
17
7 37 $37
27. 461.8 cm3 29. 1.6 ft
31. {0.2, 0.3, 0.6, 0.8, 1.2, 1.4, 1.5}
33. {9.8, 9.9, 10.5, 10.9, 11.2, 11.4}
Pages 625–628
1. lower quartile, least value; upper quartile, greatest value
3. Sample answer: {28, 30, 52, 68, 90, 92}
1. Sample answer: Because the intervals are continuous.
Lesson 12-4
Pet Survey
3.
Number of Participants
5.
14 18 22 26 30 34 38 42 46 50
7. Sample answer: The length of the box-and-whisker plot
shows that the winning times of the men’s marathons are
not concentrated around a certain time. 9. The most fuelefficient SUV and the least fuel-efficient sedan both average
22 miles per gallon.
22
20
18
16
14
12
10
8
6
4
2
0
1–3
11.
70
60
80
90 100 110 120 130
4–6
7–9 10–12 13–15
Number of Pets
5. the number of states that have a certain number of roller
coasters 7. The numbers between 10 and 34 are omitted.
9. 2 or more national monuments
13.
11.
70
90
26.0
28.0
30.0
110
130
150
15.
34.0
36.0
Tampa, FL
0
10 20 30 40 50 60 70 80 90
23. C
1
2
3
4
Leaf
4
147
9
8 24 24
4–6
7–9
10–12 13–15
Time (hr)
Touchdowns in a Season
13.
10
8
6
4
2
0
Number of Touchdowns
25. 4
27. Stem
0–3
1
18
5–
16 64
1
8–
14
7
14
1–
13 0
13
4–
11 3
1
–1
97
6
–9
80
• Sample answer: Tampa has a median temperature of 73
and Caribou has a median temperature of 40.5. Whereas
the highest average temperature for Tampa is 82, the
highest average temperature for Caribou is 66.
• Sample answer: You can easily see how the temperatures
vary.
12
11
10
9
8
7
6
5
4
3
2
1
0
Selected Answers
17. 50% 19. Sample answer: The least number of games
won for NFC is 3 and the least number of games won for
the AFC is 1. The most number of games won for the NFC
is 12 and the most number of games won for the AFC is 13.
In addition, for both conferences, the median number of
games won is about 9. 21. A box-and-whisker plot would
clearly display any upper and lower extreme temperatures
and the median temperature. Answers should include the
following.
•
Caribou, ME
Number of Players
32.0
Weekly Study Time
170
Number of Students
50
29. 14
15. 13 17. 37.5% 19. Dallas 21. true 23. false 25. true
27. A 29. absolute frequency: 2, 9, 17, 12, 7, 2; relative
2 9 17 12 1 2
49 49 49 49 7 49
frequency: , , , , , ; cumulative frequency:
2, 11, 28, 40, 47, 49
area codes in 1999 is about 1.5 times the number of area
codes in 1996. The graph is misleading because the drawing
of the phone for 1999 is about 3 times the size of the phone
for 1996. Also, there is a break in the vertical scale.
7. Graph B 9. Graph B; the vertical scale used makes the
decrease in the unemployment rates appear more drastic.
11a. Sample answer:
Commuter Train
Average Length
of U.S. States
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Passengers
60
55
50
12
00
45
40
35
30
25
20
15
10
–1
49
5
0
9
99
9
9
11
0–
59
89
0–
90
60
9
0–
29
30
1–
Amount (millions)
Number of States
31.
Length (mi)
’96
Source: The World Almanac
’97
’98
’99
Year
33. 44; 15 35. Sample answer: Brand B costs one-third
more than brand C.
Page 628
1. Stem
Commuter Train
Passengers
11b. Sample answer:
Practice Quiz 1
59
58
Leaf
6899
026888
02
023
5
69
57
56
55
Amount (millions)
1
2
3
4
5
6
7
8
55 55
3.
54
53
52
51
50
49
48
47
0 10 20 30 40 50 60 70 80 90 100
45
0
Costs
5.
Frequency
Selected Answers
46
10
9
8
7
’96
’97
’98
’99
Year
13. B
15.
6
5
4
3
2
1
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
17. 20.3 m2
9
–8
80 9
–7
70 9
–6
60 9
–5
50 9
–4
40 9
–3
30 9
–2
20 9
–1
10
9
0–
Cost ($)
Pages 631–633
Lesson 12-5
1. Sample answer: inconsistent vertical scale and break in
vertical scale 3. Graph A has a break in the vertical scale.
5. From the vertical scale, you can see that the number of
1
6
2
3
5
6
1
3
19. or 16% 21. or 83%
5
6
23. or 83.3%
Pages 637–639
Lesson 12-6
1. Sample answer: Both methods find the number of
outcomes. Using the Fundamental Counting Principle is
faster and uses less space; using a tree diagram shows what
each outcome is. 3. First find the number of outcomes
possible. The possible outcomes are taco-chicken, taco-beef,
taco-bean, burrito-chicken, burrito-beef, and burrito-bean,
for a total of 6 outcomes. Two of the outcomes have chicken
2
6
1
16
1
3
filling, so the probability of chicken filling is or .
1
7. 4
5. 9. 9
11.
H
H
T
T
H
H
T
H
H
T
19. 31:5
21. 1:17
3
N
B
T
B
N
T
N
B
1
8192
25. 9:4 27. 23. 5:4
4
5
6
7
8
BN
BT YB
YN
YT WB WN WT
15. 36 outcomes 17. 24 outcomes
5
1
19. 1024 outcomes 21. 23. B
N
T
SB
SN
ST
25. Either; the probability of rolling
either odd or even is one-half.
27. Sample answer: any two letters
followed by any four digits 29. D
31. Sample answer: Vertical scale that
does not start at zero. 33. 11–20
18
35.
10
; y 3
39.
S
12 outcomes
9
T
⫺6 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1
BB
100,000
37.
y
y
0
1
2
1
56
1
3
41. 43. Pages 653–655
Lesson 12-9
1. Independent and dependent events are similar because
both are a connection of two or more simple events and the
probability of the compound event is found by multiplying
the probabilities of each simple event. They are different
because the second event in a dependent event is
influenced by the outcome of the first event. Therefore,
the probability of the second event used in calculating the
probability of the compound event is dependent on the
outcome of the first event. 3. The result of the 1st event
1
12
must be taken into account. 5. 1
91
1
5
10
91
13. 15. O
x
x
1
30
5
8
3
7
19. 21. 23. 25. 1
2
9
27. Pages 643–645 Lesson 12-7
1. Sample answer: How many 3-digit numbers can be made
from the digits 1, 2, 3, and 4 if no digit is repeated?
3. Sarah; five CDs from a collection of 30 is a combination
because order is not important. 5. P; 120 ways 7. C;
84 ways 9. 220 pizzas 11. P; 24 flags 13. C; 105 ways
15. P; 1320 ways 17. C; 364 ways 19. 40,320
21. 39,916,800 23. 36 handshakes 25. 3003 ways
31. When order is not
important, duplicate arrangements are not included in the
number of arrangements. Answers should include the
following.
• When order was not important there were half as many
pairs.
• Order is important when you arrange things in a line;
order is not important when you choose a group of
things.
1
21
2
35. 3
37. 3:10
39. 17,576,000
41. 65° 43. 65°
45. 90° 47. 40.6
49. 16
Pages 658–662
Leaf
1. b 3. c 5. d 7. Stem
4
5
6
7
8
9. 23; 7
11. 22; 10
19. 16 outcomes
27. 1:3
55
0055
00000
555
5 5 75 75¢
13. 80°F 15. 50%
17. Graph A
21. C; 364 ways 23. C; 21 ways 25. 3:5
1
30
29. Chapter 13 Polynomials and
Nonlinear Functions
Page 667
1. 1 3. 2 5. 0 7. 5a 20
13. yes 15. yes
9. 4 32n 11. 27b 27c
Selected Answers
41. 28
27. 10 combinations
5
364
3
4
9. 11. combination of 3, 2, and 4 will have a probability of .
33. B
2
29. 5
17. 3
14
7. 29. 0.16 31a. Sample answer: 3 red, 2 white, and 4 blue
31b. Sample answer: The numerator must be 24. Any
O
39. 15
29. 47:53
31. No; 512 is the total number of possible outcomes, so it
could not be a number in the odds of winning. 33. A
35. 6 ways
37.
;a6
W
Y
Lesson 12-8
1. Write a ratio comparing the ways the event can occur to
the ways the event cannot occur. 3. Hoshi; the probability
of rolling a 2 is 1 out of 6. The odds of rolling a 2 are 1 in 5.
5. 1:2 7. 5:1 9. 1:2 11. 2:1 13. 1:1 15. 1:3 17. 5:7
HHH HHT HTH HTT THH THT TTH TTT
8 outcomes
13.
B
Practice Quiz 2
Pages 648–649
T
T
Page 645
1. Sample answer: Bars are different widths.
3. 256 outcomes 5. 15 segments
T
H
33. C 35. Yes; the vertical axis does not include zero.
37. Q 39. I 41. 1:8 43. 11:2
Pages 670–672
Lesson 13-1
Page 681
1. The degree of a monomial is the sum of the exponents of
its variables. The degree of a polynomial is the same as the
degree of the term with the greatest degree. 3. Tanisha;
the degree of a binomial is the degree of the term with the
greater degree. 5. yes; monomial 7. yes; binomial
9. yes; trinomial 11. 0 13. 1 15. 4 17. 2 19. yes;
binomial 21. yes; monomial 23. no 25. yes; trinomial
27. no 29. yes; trinomial 31. 0 33. 3 35. 5 37. 5 39. 3
41. 5 43. Always; any number is a monomial.
45. 2x 2y z xy 49. Polynomials approximate realworld data by using variables to represent quantities that
are related. Answers should include the following.
• Heat index is found by using a polynomial in which one
variable represents the percent humidity and another
variable represents the temperature.
• Heat index cannot be approximated using a linear
equation because the values do not change at a constant
rate.
2
51. C 53. mutually exclusive; 55. 70 in3
1. 4
Pages 676–677
Lesson 13-2
1. x2 and 2x2; 5x and 4x; 2 and 7 3. Hai; the terms have
the same variables in a different order. 5. 7a2 9a 4
7. 13x 4y 9. 4x2 3x 2 11. 3x 3
13. 11x2 5xy 4y2 15. 4x 14 17. 8y 2r
19. 5x2 xy y 21. 7x2 9x 5 23. 5a 4b; 31
25. 4a 6b c; 14 27. 56 29. 23x 12 31. 42x 22
33. Use algebra tiles to model each polynomial and
combine the tiles that have the same size and shape.
• Algebra tiles that represent like terms have the same size
and shape.
• When adding polynomials, a red tile and a white tile that
have the same size and shape are zero pairs and may be
removed. The result is the sum of the polynomials.
35. B 37. 2
2
13
39. 3
26
41. 43. 15c (26)
45. 1 (2x) 47. (n rt) (r2)
Selected Answers
Pages 680–681
Lesson 13-3
1. Subtracting one polynomial from another is the same as
adding the additive inverse. 3. 4r 5. 5x 2
7. 3x2 3x 8 9. 7x 5 units 11. 2n2 6n
13. y2 7y 10 15. 15w2 2w 10 17. 4x 3
19. 2t 2 21. 3a2 2b2 23. 9n2 n 12
25. 2x2 2xy 3y2 27. x y 68 (x y); 34°F
29. In subtracting polynomials and in subtracting
measurements, like parts are subtracted. Answers should
• To subtract measurements with two or more units,
subtract the like units. To subtract polynomials with two
or more terms, subtract the like terms.
• For example, to subtract 1 foot 5 inches from 3 feet
8 inches, subtract the feet 3 1 and subtract the inches
8 5. The difference is 2 feet 3 inches.
31. B 33. 12x 3y 35. t2 12t 2 37. yes; binomial
39. Stem Leaf
41. 8y2 43. 4m3 45. 10r5
5
6
7
8
9
49
468
0112
59
1 54 54
Practice Quiz 1
5. 2x 2
Pages 684–686
7. 8r 3s 9. 3x 5y
Lesson 13-4
1. False; the order in which numbers or terms are
multiplied does not change the product, by the
Commutative Property of Multiplication;
x(2x 3) 2x2 3x and (2x 3)x 2x2 3x. 3. Sample
answer: 2x(x 1) 2x2 2x 5. a2 4a 7. 12x2 28x
9. 15x2 35x 45 11. 14n 35 13. t2 9t
15. 7a2 6a 17. 40n 8n2 19. 3y3 6y 21. 5x2 5xy
23. 14x2 35x 77 25. 4c4 28c2 40c 27. –1
29. high school, 84 ft by 50 ft; college, 94 ft by 50 ft
a
b
33. D 35. 7x 1
37. 4y2 2y 14
39. 8x 11y
c
d
ac
ad
bc
bd
31.
3
57. (x 2x) 4 59. (6n 3n) (2 5)
61. (s 5s) (t 3t)
3. 3
(a b)(c d) ac ad bc bd
41. Sample answer: The scales are labeled inconsistently
or the bars on a bar graph are different widths.
43. reflection
45. x
0
2x2 3
3
(x, y)
(0, 3)
1
1
(1, 1)
2
5
(2, 5)
3
15
(3, 15)
Pages 689–691
Lesson 13-5
1. Sample answer: Determine whether an equation can be
written in the form y mx b or look for a constant rate of
change in a table of values. 3. Sample answer: population
growth 5. Nonlinear; graph is a curve. 7. Nonlinear;
equation cannot be written as y mx b. 9. Linear; rate
of change is constant. 11. Nonlinear; graph is a curve.
13. Linear; graph is a straight line. 15. Nonlinear; graph is
a curve. 17. Linear; equation can be written as
y 0.9x 0. 19. Linear; equation can be written as
3
4
y x 0.
21. Nonlinear; equation cannot be written as
y mx b. 23. Linear; rate of change is constant.
25. Nonlinear; rate of change is not constant.
27. Nonlinear; the points (year, subscribers) would lie on a
curved line, not on a straight line. Or, the rate of change is
not constant. 29. No, the difference between the years
varies, so the change is not constant. 31. A 33. 4t 9t2
35. a2b 2ab2 37. x 39. acute
41.
43.
y
y
y 1x 3
2
O
x
O
yx4
x
Page 691
Practice Quiz 2
23.
1. 2c3 8c 3. 5a2 a3 2a4 5. Nonlinear; equation
cannot be written as y mx b.
y
y
y 4x 3
5.
7.
y
y x
x
3
x
O
Both equations are functions because every value of x is
paired with a unique value of y.
25. (0, 7)
27.
Similar shape; y 3x2 is
y
more narrow.
y x2
x
O
11.
y
y
y 3x 2
x
O
x
y x2 4
y 3x 2
9.
O
y
O
y 2x 2
x
O
1. Sample answer: The graph of y nx2 has line symmetry
and the graph of y nx3 does not. 3. Sample answer:
y x2 3; make a table of values and plot the points.
29.
Same shape; y 2x2
is y 2x2 reflected over the
x-axis.
y
x
O
y x 3 2
y 2x 2
x
O
y 2x 2
13.
15.
y
y
31. A 50x x2 33. 25 ft by 25 ft
35. V 0.2r2 or V 0.6r2
y 2x 3
O
x
x
O
y x 2
19.
y
y
y 2x 3
O
y x3 1
x
O
x
0
21.
y
1 2
y 2x 1
O
x
V
V 0.6r 2
1 2 3 4 5 6 7r
37. Formulas, tables, and graphs are interchangeable ways
to represent functions. Answers should include the
following.
• To make a graph, use a rule to make a table of values.
Then plot the points and connect them to make a graph.
• To write a rule, find points that lie on a graph and make
a table of values using the coordinates. Look for a
pattern and write a rule that describes the pattern.
39. C 41. Sample answer: 18 units2 43. 10x 20
45. 24y 21y2 47. y 4x 3
Pages 698–700
1. trinomial 3. cubic 5. like terms 7. curve 9. yes;
binomial 11. yes; monomial 13. yes; trinomial 15. no
Selected Answers
17.
11
10
9
8
7
6
5
4
3
2
1
17. 1 19. 3 21. 6 23. 5 25. 8b 3 27. 5y2 2y 4
29. y2 y 1 31. 3x2 4x 7 33. x 1 35. 20t 10
37. 6k2 3k 39. 18a 2a3 41. Linear; graph is a straight
line. 43. Nonlinear; rate of change is not constant.
45.
47.
y
y
y 3x 2
O
y x3 1
x
49.
y
y 2x 2 4
Selected Answers
O
x
O
x
Photo Credits
About the Cover
The Great Bear at Hersheypark in Hershey, Pennsylvania, is an inverted coaster – that is, you ride
below it, not above it. With four inversions, including loops, twists, and rolls, this ride reaches a
speed of almost 60 miles per hour and at one point falls 124 feet. Roller coasters use math in their
design and operation from beginning to end. Their designers want to make the tallest, fastest,
most exciting coasters ever!
Cover Alan Schein/CORBIS Stock Market; ix Tom Pidgeon/
Getty Images, x Roy Ooms/Masterfile; xi David YoungWolff/PhotoEdit; xii Robert Fried/Stock Boston; xiii Kay
Chernush/Getty Images; xiv Tony Demin/ International
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Cole/DUOMO; xvii Adam Jones/ Photo Researchers;
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CORBIS; 4-5 ZSSD/SuperStock; 10 Doug Martin; 15 Tom
Pidgeon/Getty Images, 19 TempSport/CORBIS; 27 Ken
Eward/Photo Researchers; 31 Erik Dreyer/Getty Images;
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Images; 57 Jonathan Daniel/Getty Images; 66 NASA; 73
Doug Martin; 78 Mike Mazzaschi/ Stock Boston; 96–97 Jan
Butchofsky-Houser/CORBIS; 99 AP/Wide World Photos;
105 Kit Kittle/CORBIS; 106 Mary Kate Denny/PhotoEdit;
112 file photo; 116 Stuart Westmorland/CORBIS; 123 Index
Stock/Eric Kamp; 127 David Young-Wolff/PhotoEdit; 129
Dwayne Newton/ PhotoEdit; 131 PhotoDisc; 134
AFP/CORBIS; 144-145 Getty Images, (bkgd) CORBIS;
146–147 Thomas Mangelsen/ Minden Pictures; 149
Elizabeth Whiting & Associates/ CORBIS; 151 Aaron
Haupt; 156 Christophe Loviny/ CORBIS; 165 AP/Wide
World Photos; 172 Geoff Butler; 178 Laura Sifferlin; 180
Latent Image; 182 Ralph A. Clevenger/CORBIS; 184
VCG/Getty Images; 189 Robert Fried/Stock Boston;
198–199 SuperStock; 208 Lester Lefkowitz/CORBIS Stock
Market; 214 JPL/ NASA; 217 Tony Anderson/Getty
Images; 219 David Barnes/CORBIS Stock Market; 220 John
Cancalosi/Stock Boston; 223 Tony Freeman/PhotoEdit; 229
NASA; 231 237 Geoff Butler; 247 Andy Caulfield/Getty
Images; 253 (t)Kay Chernush/Getty Images, (b)Geoff
Butler; 262–263 SuperStock; 267 Chuck Pefley/ Stock
Boston; 272 Louisville Slugger Museum, Louisville, KY; 275
Matt Meadows; 276 (t)Landscape plans provided by
1
8
3
8
252.4 458.2 (100 180 in.)Hirshhorn Museum and
Sculpture Garden, Smithsonian Institution; 537 Charles E.
Rotkin/ CORBIS; 552–553 Rohan/Getty Images; 556
EyeWire, Yann Arthus-Bertrand/CORBIS; 558 Walter
Bibikow/Getty Images; 560 (t)SHOE 8/31/94 ©Tribune
Media Services. All Rights Reserved. Reprinted by
permission, (bl)Roberto Otero/Black Star/PictureQuest,
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575 Bob Mullenix; 578 SuperStock; 579 Bob Daemmrich;
581 (l)John Elk III/ Stock Boston, (r)John Elk III/Stock
Boston; 583 Matt Meadows; 584 Aaron Haupt; 586 NASA;
602-603 Getty Images, (bkgd) Richard Price/Getty Images;
604-605 Mike Dobel/Masterfile; 607 610 CORBIS; 614
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640 Aaron Haupt; 644 Mark Burnett; 649 Aaron Haupt; 651
Matt Meadows; 654 CORBIS; 656 Aaron Haupt; 666–667
(bkgd)Digital Stock, David Madison Sports Images; 670
Raymond Gehman/CORBIS; 675 Antonio M.
Rosario/Getty Images; 683 Dallas & John Heaton/CORBIS;
685 Bettmann/CORBIS; 693 Photri/Tom Sanders/CORBIS
Stock Market; 793 William Floyd Holdman/Index Stock
Imagery.
Photo Credits
R51
Photo Credits
Greenscapes Landscape Architects and Contractors,
Columbus, OH, (bl)Matt Meadows, (br)Ron Kimball/Ron
Kimball Stock; 277 Kunio Owaki/CORBIS Stock Market;
278 Jeff Greenberg/Southern Stock/ PictureQuest; 284
Gary White Photography/StockFood; 288 Geoff Butler; 296
Frans Lanting/Minden Pictures; 299 Tony
Demin/International Stock; 306 Michael Paras/
International Stock; 324-325 Mark Richards/PhotoEdit,
(bkgd) Jon Arnold Images/Alamy; 326–327 Michael
Melford/Getty Images; 331 SW Productions/Index
Stock/Picturequest; 337 Matt Meadows; 344 Bob
Daemmrich/Stock Boston; 347 Bob Daemmrich; 348
Douglas Faulkner/Photo Researchers; 356 SuperStock; 358
Doug Martin; 366-367 Paul J. Sutton/Duomo/CORBIS; 370
Peter/Stef Lamberti/Getty Images; 383 David
Keaton/CORBIS Stock Market; 386 Matt Meadows; 387
Tony Freeman/PhotoEdit; 392 Doug Martin; 395
NASA/JSC; 399 Cris Haigh/Getty Images; 401 DUOMO;
408 Gail Shumway/Getty Images; 412 Michael
Steele/Allsport; 417 Chris Cole/DUOMO; 422 Roy
Ooms/Masterfile; 432-433 Jeff Hunter/Getty Images,
(bkgd) Ken Biggs/Getty Images; 434-435 Richard
Cummins/CORBIS; 438 Kunio Owaki/CORBIS Stock
Market; 444 Kennan Ward/CORBIS Stock Market; 456
Garry Gay/ImageBank; 463 Steven E. Sutton/DUOMO; 472
Geoff Butler; 474 Adam Jones/Photo Researchers; 480
David Young-Wolff/ PhotoEdit; 490–491 J. David
Andrews/Masterfile; 500 SuperStock; 503 Chuck
Szymanski/International Stock; 511 Pete Saloutos/CORBIS
Stock Market; 513 Richard Hamilton Smith/CORBIS; 515
(l)Pat LaCroix/Getty Images, (r)Irene Rica Pereira. Untitled,
1951. Oil on board, 101.5 61 cm (40 24 in.). Solomon R.
Guggenheim Museum, New York, NY. Gift of Jerome B.
Lurie, 1981; 516 Elizabeth Murray. Museum of Modern Art,
New York, NY. Acquired through the Bernhill Fund. Gift of
Agnes Gund; 524 SuperStock; 529 Papilio/CORBIS; 530
Roy Lichtenstein. Modern Painting with Clef, 1967. Oil on
synthetic polymer and pencil on canvas.
Index
A
Index
Absolute frequencies, 627
Absolute value, 58, 59, 61, 63, 64,
65, 66, 91
algebraic expressions, 58
integers, 90
Accuracy, 589
Activity. See Algebra Activity;
Geometry Activity
Acute angles, 449, 450, 451, 457,
484, 745
Acute triangles, 454, 456, 746
Addends, 63, 64, 66
Addition, 11, 16, 726, 734, 735, 756
algebraic fractions, 221
Associative Property, 24, 26, 49,
63, 66, 130, 725
Commutative Property, 23, 26,
32, 49, 63, 66, 107, 114, 725
decimals, 5, 538, 712, 713
fractions, 220, 233, 716
integers, 62–63, 64–66, 74, 82, 84,
91, 97, 107, 199, 327
like fractions, 220–224, 256
measurements, 591–592
mixed numbers, 220, 233, 491,
716
polynomials, 674–677, 699
properties, 672
solving equations, 111–112, 113,
139, 244
solving inequalities, 345–349
unlike fractions, 232–236, 257
Addition expressions, 97, 102, 677
Addition Property of Equality, 111,
360
Addition table, 63
Additive identity, 24, 48, 49, 66
Additive inverse, 66, 67, 70, 71, 72,
91, 112, 114, 677, 679, 681, 699
Adjacent angles, 476, 493, 495
Algebra Activity
Analyzing Data, 237
Area and Geoboards, 518–519
Base 2, 158
Capture-recapture, 275
Constructions, 498–499
Dilations, 512
Equations with Variables on Each
Side, 328–329
R52 Index
Fibonacci Sequence, 253
Graphing Irrational Numbers,
465
Half-Life Simulation, 180
Input and Output, 367
It’s All Downhill, 386
Juniper Green, 231
Modeling Multiplication, 682
Modeling Polynomials with
Algebra Tiles, 673
Probability and Pascal’s Triangle,
640
Pythagorean Theorem, 458–459
Ratios in Right Triangles, 476
Scatter Plots, 39
Simulations, 656–657
Slope and Rate of Change, 392
Solving Equations using Algebra
Tiles, 108–109
Symmetry, 505
Taking a Survey, 309
Tessellation, 532
Using a Percent Model, 286–287
Algebra Connection, 25, 35, 58, 77,
150, 161, 166, 170, 176, 181, 211,
217, 221, 227
Algebraic equations, solving, 30,
31, 118, 130, 136, 152, 157, 163,
219, 230, 235, 242, 246, 248, 252,
328–329, 330–333, 338, 344, 349,
443, 444, 457, 484, 685
Algebraic expressions, 17, 19, 69,
99, 667
absolute value, 58
evaluating, 17, 19, 20, 27, 32, 38,
44, 48, 51, 55, 59, 60, 68, 72, 73,
74, 77, 78, 79, 82, 83, 84, 89, 93,
118, 147, 155, 156, 168, 170, 182,
185, 190, 213, 218, 222, 223, 235,
338, 373
factoring, 166, 167, 193
finding value, 27, 32, 48, 74, 457
identify parts, 104
simplifying, 25, 26, 27, 32, 44, 48,
51, 77, 78, 84, 89, 100, 103–107,
118, 139, 147, 157, 213, 224, 439
translating verbal phrases into,
18, 19, 20, 32, 74, 105, 724
writing, 20, 97, 124, 125
Algebraic fractions, 211
addition, 221
division, 217
lowest common denominator, 227
multiplication, 211
simplifying, 169–173, 185, 193
Algebraic relationships, graphing,
87
Algebra tiles. See also Modeling
adding integers, 62–63
algebraic expressions, 103, 106
Distributive Property, 99
equations with variables on each
side, 328–329
multiplication, 682
multiplication, polynomials by
monomial, 683
polynomials, 673, 674, 677
properties of equality, 120, 123
representing expressions, 103
solving equations, 108–109
solving two-step equations, 120
Alternate exterior angles, 492, 493
Alternate interior angles, 492, 493
Altitude, 520
Angles, 447–451, 484
acute, 449, 450, 451, 457, 484, 745
adjacent, 476, 493, 495
alternate exterior, 492, 493
alternate interior, 492, 493
central, 452, 538
complementary, 493, 494, 495,
496, 517, 544
congruent, 493
corresponding, 474, 492, 493, 500,
544
of elevation, 480
exterior, 492, 531
inscribed, 538
interior, 492, 528, 530, 538, 543
measurement, 447, 448
measures, 448, 454
obtuse, 449, 450, 451, 457, 484,
745
quadrilateral, 514
right, 449, 450, 451, 457, 484, 745
straight, 447, 449, 450, 451, 457,
484, 745
supplementary, 494, 495, 496
vertical, 493, 495
Applications. See also CrossCurriculum Connections;
More About
accounting, 67
aerospace, 759
ages, 128
aircraft, 172
air pressure, 37
animals, 172, 184, 229, 266, 306,
619, 639
economics, 761, 769
education, 618
elections, 113
electricity, 761
employment, 758, 762
energy, 83, 179
engineering, 566
entertainment, 36, 141, 391, 411,
415, 421, 760, 769
environment, 289
farming, 372
fast food, 763
fencing, 760
ferris wheel, 763
finance, 677, 765
fish, 291
fitness, 450
flags, 523
floods, 78
flooring, 444
flowers, 644
food, 21, 48, 219, 284, 296, 301,
608, 626, 643, 758, 762
food costs, 397
food service, 129, 637
football, 64, 67
forestry, 297
fuel, 765
fund-raising, 358, 581
furniture, 762
games, 516, 638, 653, 726, 759
gardening, 15, 213, 223, 429
gardens, 279
golf, 67
grilling, 235
grocery shopping, 764
handshakes, 644
health, 9, 248, 610, 762, 763
height, 31, 141
highway maintenance, 570
hiking, 358
hobbies, 312
home improvement, 540
home repair, 252, 390
homework, 343, 769
hourly pay, 240
houses, 234
insects, 279
interior design, 761
Internet, 764, 770
kites, 765
landmarks, 473
landscape design, 540
landscaping, 135, 502, 672
lawn care, 524
license plates, 644
light bulbs, 136
literature, 163
lunchtime, 761
machinery, 209
magazines, 267
maintenance, 766
manufacturing, 208, 767, 768, 770
maps, 88, 292, 472, 473, 759
masonry, 592
measurement, 118, 171, 172, 183,
189, 207, 213, 222, 372, 378, 593,
762
measurement error, 593
media, 283
medicine, 10, 122, 184, 671
metals, 566
meteorology, 128, 157, 246, 759
microwaves, 567
military, 133
mining, 572
mirrors, 511
models, 768
money, 9, 10, 51, 100, 105, 152,
173, 295, 296, 357, 385, 409,
754, 759, 762, 763
monuments, 537, 768
movies, 101, 632
moving, 767
music, 151, 536
Native Americans, 129
newspapers, 758
nutrition, 239, 341, 762, 763, 765
oceanography, 74
oil production, 762
olympics, 128, 273, 619, 624
online service, 762
paint, 274
painting, 118
parades, 167
parks, 474
patterns, 758, 761
pet care, 768
pets, 73, 763
phone calling cards, 123
phone services, 358
photography, 272, 273
picnics, 407
pools, 123, 577, 684
population, 68, 114, 129, 302, 307,
735, 770
postal service, 7, 724
presents, 768
presidents, 629
pressure, 411
production, 770
public safety, 767
publishing, 15, 235, 246, 762
purchasing, 760
quilts, 504
racing, 449
reading, 631
real estate, 301, 525
recreation, 479, 766
remodeling, 762
rides, 475
roller coasters, 279, 439, 625
Index R53
Index
aquariums, 576
architecture, 277, 479, 558, 579,
580, 581, 587, 626, 769, 770
art, 463, 509, 515, 516, 530
astronauts, 606
astronomy, 759, 761
auto racing, 229
aviation, 765, 766
baking, 768
ballooning, 134
banking, 300, 301
baseball, 450, 615–616, 766
baseball cards, 739
basketball, 83, 241, 337, 761
batteries, 567
bicycles, 536
bicycling, 135
birds, 291, 758
birthdays, 106
blood types, 655
books, 291, 766
boxes, 685
brand names, 763
breakfast, 202
bridges, 767
buildings, 480, 559
business, 16, 21, 73, 123, 190, 247,
301, 307, 384, 399, 400, 421, 760,
761, 763, 765, 769
calculators, 301
calendars, 151
camping, 768
candy, 10, 358, 763
carpentry, 167, 218, 390
car rental, 332, 358, 765
cars, 251
car sales, 764
catering, 385
celebrations, 290, 291
census, 764
city planning, 767
codes, 761
college, 762
comics, 560
communication, 10, 185, 631
community service, 134
computers, 177, 203, 638
construction, 589, 695, 766, 770
consumerism, 769
cooking, 218, 247, 516, 763
crafts, 421, 576
cruises, 107
currency, 273
cycling, 228
decorating, 768
design, 277, 279–280, 321
driving, 313
earnings, 353
earthquakes, 177, 761
ecology, 670
Index
running, 135
safety, 343, 480, 495, 496
sailing, 766
salaries, 242
sales, 21, 121, 135, 358, 363, 418,
758
savings, 303, 347
school, 42, 107, 185, 203, 213, 307,
358, 413, 420, 537, 608, 631, 764
school colors, 642
school concert, 765
school supplies, 106
sewing, 218, 223, 235, 259
shadows, 473, 480
shapes, 767
shipping, 679, 768
shipping rates, 765
shoes, 283
shopping, 26, 101, 106, 265, 267,
300, 363, 376, 760, 763, 764
signs, 767
skyscrapers, 438
snacks, 274
soccer, 353
sound, 155
space, 187, 188, 189, 296, 758
space exploration, 758
space shuttle, 16, 19
space travel, 212
spending, 411
sports, 93, 101, 238, 301, 515, 542,
759, 760, 764
statistics, 83, 686, 764
statues, 279
submarines, 759
surveying, 766
surveys, 243
swimming, 410, 641
technology, 393, 411, 744
telecommunications, 690
telephone rates, 251
telephones, 229
television, 463, 769
temperature, 78
tennis, 685
tepees, 768
tessellations, 529
tests, 241
test scores, 40
time, 9, 449
towers, 502
toys, 117
traffic laws, 614
trains, 247
transportation, 10, 14, 204, 348,
760, 761, 767
travel, 8, 15, 16, 134, 156, 212,
219, 259, 267, 594, 620, 630, 632,
760, 766
trees, 534, 758
trucks, 202
R54 Index
utilities, 766
vacations, 241, 625
volleyball, 753, 758, 769
voting, 235
walkways, 542
water parks, 623
weather, 59, 60, 71, 72, 73, 83, 89,
93, 113, 248, 307, 333, 348, 371,
608, 615–616
weather records, 79
white house, 208
wildlife, 129
working, 760
world cultures, 769
write a problem, 130
Approximations, 594, 672
Area, 132, 137, 518–519. See also
Surface area
circles, 533–538, 548, 749
irregular figures, 539–543, 548
parallelograms, 520, 547
rectangles, 132, 133, 134, 135, 140,
141, 152, 214, 224, 349, 671, 730,
767
square, 523
trapezoids, 521, 522–523, 547
triangles, 521, 522, 523, 547
Arithmetic sequences, 249–252, 258,
259, 268, 344, 736
Assessment
Extended Response, 53, 95, 143,
197, 261, 323, 365, 431, 489, 551,
601, 665, 703
Multiple Choice, 52, 94, 142, 196,
260, 322, 364, 430, 488, 550, 600,
664, 702
Open Ended, See Extended
Response
Practice Chapter Test, 51, 93, 141,
195, 259, 321, 363, 429, 487, 549,
599, 663, 701
Practice Quiz, 21, 32, 74, 84, 107,
130, 163, 185, 224, 248, 292, 308,
338, 354, 397, 418, 451, 470, 517,
538, 572, 588, 628, 645, 681, 691
Prerequisite Skills, 5, 10, 16, 21,
27, 32, 38, 55, 61, 68, 74, 79, 84,
97, 102, 107, 114, 119, 124, 130,
147, 152, 157, 163, 168, 173, 179,
185, 199, 204, 209, 213, 219, 224,
230, 236, 242, 248, 263, 268, 274,
280, 285, 292, 297, 302, 308, 327,
333, 338, 344, 349, 354, 367, 373,
379, 385, 391, 397, 401, 408, 413,
418, 435, 440, 445, 451, 457, 464,
470, 475, 491, 497, 504, 511, 517,
525, 531, 538, 553, 561, 567, 572,
577, 582, 588, 605, 611, 616, 621,
628, 633, 639, 645, 649, 667, 672,
677, 681, 686, 691, 706–723
Short Response/Grid In, 53, 95,
124, 143, 197, 261, 323, 354, 365,
431, 489, 517, 531, 537, 551, 601,
665, 703
Standardized Test Practice, 10,
16, 21, 29, 30, 32, 39, 44, 51, 61,
68, 74, 76, 77, 79, 84, 89, 93, 102,
107, 112, 113, 114, 119, 124, 130,
136, 141, 152, 157, 163, 168, 171,
173, 179, 184, 190, 204, 209, 213,
219, 224, 230, 236, 240, 241, 242,
247, 252, 259, 268, 274, 280, 285,
292, 297, 302, 305, 306, 308, 314,
321, 333, 338, 344, 349, 351, 353,
354, 359, 363, 373, 379, 385, 389,
390, 391, 397, 401, 408, 413, 418,
422, 429, 440, 445, 451, 457, 461,
462, 464, 470, 475, 481, 487, 494,
495, 497, 504, 511, 517, 525, 531,
537, 543, 549, 561, 564, 566, 567,
572, 577, 582, 588, 594, 599, 611,
616, 621, 627, 633, 639, 645, 647,
648, 649, 655, 663, 672, 677, 681,
686, 689, 691, 695, 701
Test-Taking Tips, 29, 52, 76, 95,
143, 171, 196, 240, 305, 322, 351,
364, 389, 430, 461, 488, 494, 550,
564, 600, 647, 664, 689, 702. See
also Preparing for Standardized
Tests
Associative Property of
Multiplication, 24, 26, 49, 51, 76,
78, 114, 522, 725
Average (mean), 82, 92
B
Backsolving, 29, 112
Back-to-back stem-and-leaf plots,
607–608, 609, 611
Bar graphs, 722–723
double, 722–723
misleading, 631
Bar notation, 201
Base 2 numbers, 158
Base 10 numbers, 158
Bases, 153, 290, 299, 520, 557, 559,
570, 595, 599
Best-fit lines, 409–413, 427, 429
Bias, 634
Bilateral symmetry, 505
Binary numbers, 158
Binomials, 669, 671, 676, 681, 698,
755
Box-and-whisker plots, 617–621,
622, 633, 659, 753
double, 619
drawing, 619, 620
interpretation, 618–619
Brackets [ ], as grouping symbol, 12
C
Calculator skills, 437, 438, 439, 478,
479, 480, 497, 504, 531, 534, 561.
See also Graphing Calculator
Investigation
Career Choices
architect, 579
artist, 515
biologist, 42
business owner, 399
carpenter, 223
cartographer, 472
civil engineer, 480
ecologist, 670
interior designer, 278
marine biologist, 348
meteorologist, 129
musician, 172
real estate agent, 358
statistician, 649
veterinarian, 73
Center, circles, 533
Central angles, 452, 538
Challenge. See Critical Thinking:
Extend the Activity; Extending
the Lesson
Change, rate of, 393–397, 426
Checking reasonableness, 82, 586,
684
Checking solutions, 99, 111, 113,
116, 117, 118, 121, 122, 123, 124,
130, 136, 141, 152, 157, 163, 176,
201, 204, 212, 217, 230, 242, 245,
246, 248, 252, 258, 297, 330, 331,
332, 334, 335, 336, 338, 346, 347,
351, 352, 353, 354, 355, 356, 359,
360, 373, 377, 379, 382, 406, 413,
414, 420, 437, 438, 454, 514, 561,
588, 689, 729, 736, 739, 740, 741
Chords, 538
Circle graphs, 451, 452
Circles
area, 535–538, 548, 749
center, 533
circumference, 533–538, 548, 749
diameter, 533, 536, 749
pi, 208, 533, 534
radius, 533, 536, 749
Closure Property, 27
Coefficients, 103, 104, 105, 106
negative, 122, 161
Columns, 705
Combinations, 642–643, 644, 661, 754
notation, 643
Commission, 301
Compare and order
decimals, 710
fractions, 228
integers, 57, 59
numbers in scientific notation,
188
percents, 283, 284
real numbers, 442
Complementary angles, 493, 494,
495, 496, 517, 544
Complex solids, volume, 564
Common Misconceptions, 58, 132,
154, 175, 355, 420, 449, 467, 507,
557, 591, 617. See also Find the
Error
Compound events, 650–655, 662
Common multiples, 226
Compound interest, 303
Common ratios, 250, 251, 258
Commulative, 23
Communication
choose, 592
classify, 529
compare and contrast, 228, 251,
312, 455, 549, 637, 643, 653, 674
define, 19, 36, 59, 105, 207, 272,
300, 468, 523, 614
describe, 202, 234, 283, 371, 389,
395, 429, 515, 559, 580, 589, 599,
653, 680, 689, 694
determine, 150, 272, 684
display, 608
draw, 222, 266, 549
estimate, 295
explain, 59, 83, 87, 117, 122, 133,
141, 150, 155, 161, 166, 171, 177,
188, 202, 217, 241, 266, 295, 300,
306, 342, 347, 377, 384, 407, 410,
416, 421, 438, 443, 468, 495, 502,
529, 570, 575, 580, 586, 614, 619,
625, 637, 648, 670, 684, 689, 694
find, 228, 241, 540
identify, 207, 608
list, 42, 51, 128, 336, 353, 421, 438,
570
name, 36, 42, 246, 332, 449, 455,
631, 676
replace, 228
state, 67, 77, 117, 141, 177, 251,
400, 429
tell, 9, 14, 26, 30, 113, 312, 529,
535, 619
write, 19, 51, 77, 133, 207, 357,
421, 509, 540
Commutative Property of Addition,
23, 26, 32, 49, 63, 66, 107, 114, 725
Commutative Property of
Multiplication, 23, 26, 49, 61, 75,
78, 522, 725
Composite numbers, 159, 161, 162,
192, 229, 285, 731
Computation, choosing method, 8
Concept Summary, 41, 47, 48, 49,
50, 82, 90, 91, 92, 138, 139, 140,
148, 154, 191, 192, 193, 194, 207,
254, 255, 256, 257, 258, 289, 293,
298, 316, 317, 318, 319, 320, 341,
360, 361, 362, 377, 416, 424, 425,
426, 427, 428, 442, 483, 484, 485,
486, 495, 544, 545, 546, 547, 548,
595, 596, 597, 598, 658, 659, 660,
661, 662, 688, 698, 699, 700
Cones, 569
diameter, 571
radius, 571
surface area, 578–582, 597
volume, 568–572, 596, 616
Congruence statements, 501, 502,
503, 511, 517, 545, 549
Congruent angles, 493
Conjectures, 7, 12, 22, 25, 26, 32, 38,
39, 63, 137, 155, 162, 175, 180, 204,
215, 253, 275, 303, 368, 386, 392,
393, 445, 453, 476, 512, 563, 583,
584, 640, 697
Constants, 103, 104, 105, 106
proportionality, 394
variation, 394, 395
Constructed Response. See
Preparing for Standardized Tests
Constructions, 498–499
Converting measurements, 397, 566
Coordinate plane, 45, 57, 87, 88, 89,
92, 93, 124, 728
reflections, 508
rotations, 509
transformations, 506–511, 545–546
translations, 507
Index R55
Index
Cake method, 161
Cicumference
circles, 533–538, 548, 749
D
Coordinates, 69, 468, 486
Coordinate system, 33–34, 36, 38,
39, 44, 50, 51, 79, 85–89, 92, 367,
475, 504, 725
Index
Corresponding parts, 471, 500, 501,
502, 503
Cosine, 477–481, 486, 747
Counterexamples, 25, 26, 27, 73,
208, 444, 510, 684
Counting outcomes, 661, 635, 639
Critical Thinking, 10, 16, 21, 27, 32,
37, 44, 60, 61, 68, 73, 78, 84, 89,
102, 107, 114, 119, 124, 130, 135,
152, 157, 163, 168, 173, 179, 184,
190, 204, 209, 213, 219, 223, 230,
236, 242, 247, 251, 268, 274, 280,
284, 285, 292, 297, 302, 307, 314,
333, 338, 344, 348, 354, 358, 373,
379, 385, 391, 397, 401, 408, 412,
417, 422, 440, 445, 450, 457, 464,
469, 475, 481, 497, 504, 511, 517,
525, 531, 537, 543, 560, 567, 572,
577, 581, 587, 593, 610, 616, 621,
627, 633, 639, 644, 649, 654, 672,
677, 680, 685, 690, 695
Cross-Curriculum Connections. See
also Applications; More About
biology, 42, 156, 761
chemistry, 68, 178, 768
earth science, 235, 383
geography, 60, 73, 208, 284, 296,
332, 524, 543, 617, 759, 767
geology, 571, 758, 759
history, 151, 156, 168, 537, 570,
587, 766, 768
life science, 178, 291
physical science, 184, 190, 251, 396
physics, 765, 766
science, 20, 27, 36, 37, 45, 131,
291, 378, 438, 536, 571, 614, 696,
760, 761
Cross products, 270, 271, 272
Cubes, 584
surface area, 157, 694
volume, 157
Cubic functions, 688
graphing, 692–696, 700
Cubic units, 575
Cumulative frequencies, 627
Customary system, 118
converting measurements,
720–721, 734
Cylinders
volume, 563–567, 596
R56 Index
Data
analysis, 39, 180, 237, 240, 253, 275,
386, 392, 562, 583, 640, 656, 657
box-and-whisker plots, 633, 659,
753
collecting, 39, 180, 237, 253, 275,
369, 386, 392, 562, 583, 640, 656,
657
comparisons, 269
display, 606, 722–723
frequency tables, 627
histograms, 623–628, 629, 633,
660, 753
line plot, 239
matrices, 414, 669, 705
mean, 82, 92, 238–239, 240, 248,
252, 258, 605, 618, 735
median, 238–239, 240, 248, 252,
258, 605, 611, 615, 618, 735
mode, 238–239, 240, 248, 252, 258,
605, 735
modeling, 657
patterns, 22
scatter plots, 39, 40–42, 43, 45–46,
50, 61, 68, 107, 408, 410, 411,
412, 422, 427, 429, 726
stem-and-leaf plots, 606–611, 658,
681, 752
Decimal numbers, 158
Decimals, 206, 281–285, 318, 435
addition, 5, 538, 712, 713
comparison with fractions, 202
division, 242, 714, 715
estimating, 5
multiplication, 263, 491, 714, 715
with negative exponents, 183
ordering, 616, 710
repeating, 201, 202, 203, 206, 214,
224, 254, 338, 733
rounding, 588, 711
subtraction, 5, 712, 713
terminating, 200, 203, 206
writing as fractions or mixed
numbers, 207, 208, 224, 254, 422,
733
writing as percents, 282–283, 297,
302
writing fractions as, 200–209, 214,
338, 475
writing mixed numbers as, 209,
214
Decision making. See Critical
Thinking; Problem solving
Deductive reasoning, 25, 107
Degrees, 448
Density, 566
Dependent events, 652
Dependent variable, 375
Diagonals, 528, 558
Diameter
circles, 533, 536
cones, 571
Differences, 13, 21, 61, 70, 71, 72,
73, 74, 84, 91, 93, 118, 230, 235,
242, 256, 257, 327, 349, 605, 712,
716, 727, 734, 735, 756. See also
Subtraction
Dilations, 512
Dimensional analysis, 212, 213,
217, 266, 267, 280
Dimensions, 705
Direct variation, 394
Discounts, 299, 308, 738
Distance, 746
Distance Formula, 131, 212,
466–470, 485–486
Distributive Property, 98–102, 104,
107, 138, 147, 163, 164, 166, 185,
193, 209, 333, 334, 338, 349, 361,
667, 683, 686, 699, 728
Divisibility Rules, 148, 149, 150,
151, 157, 191, 730
Division, 11
decimals, 242, 714, 715
integers, 80–84, 92, 114, 199, 327
negative numbers, 351–352
notation, 13
positive numbers, 350–351
rational numbers, 215–219, 256
245, 435
Division expressions, 117
Division Property of Equality, 115
Division sentence, 80
Divisor, 69
Domain, 35, 36, 37, 38, 44, 50, 51,
136, 367, 725
Double bar graphs, 722–723
Double box-and-whisker plots, 619
Double line graphs, 722–723
E
Edges, 556, 557, 559, 595, 599
Element, 705
Endpoints, 468, 469, 481, 486, 527, 746
Enrichment. See Critical Thinking;
Extend the Activity; Extending
the Lesson
Equals sign, 126
negative, 181–185, 187, 194
positive, 182, 183, 185, 187, 194
Extending the Lesson, 32, 102, 168,
185, 214, 236, 252, 268, 280, 333,
344, 359, 392, 440, 445, 464, 497,
531, 538, 572, 577, 582, 594, 621,
627, 655, 696
Equilateral figures, 517
Extra Practice, 724–757
Equivalent equations, 104, 111
Extreme value, 239
Expressions, 12–13. See also
Addition expressions;
Algebraic expressions;
Binomial expressions;
Division expressions;
Equivalent expressions;
Numerical expressions;
Subtraction expressions;
Verbal expressions
evaluating, 12, 107, 154, 155, 724,
726, 727, 731, 732
with exponents, 154, 155
factoring, 731
finding value, 14, 21, 724
simplifying, 104, 114, 497, 525,
725, 727, 728
translating, into words, 11
Extend the Activity, 39, 158, 253,
368, 386, 392, 640, 656, 657, 682
Extended Response. See Preparing
for Standardized Tests
Equivalent expressions, 98
Error Analysis. See Find the Error;
Common Misconceptions
Estimation, 5, 9, 121, 209, 220, 230,
233, 294, 295, 296, 297, 298, 302,
308, 319, 321, 397, 437, 438, 439,
445, 456, 564, 567, 586, 712, 714,
716, 717, 738, 745
F
Free Response. See Preparing for
Standardized Tests
Frequencies
absolute, 627
cumulative, 627
relative, 627
Frequency distribution, 623
Factor expressions, 166
Frequency tables, comparison to
histograms, 627
Factorial notation, 642
Factoring, 157
Even numbers, 148
Factor tree, 160
Events
compound, 650–655, 662
dependent, 652
inclusive, 672
independent, 650–651
mutually exclusive, 652, 672
simple, 310
Families of quadratic functions, 697
Exponents, 153–157, 190, 192, 252,
435, 464, 731, 732
Fractions, 281, 318. See also
Algebraic fractions
addition, 220, 233, 716
comparison, 202, 228
computations, 605
division, 216, 717
multiplication, 567, 649, 717
percents as, 281–282, 283
simplifying, 171, 172, 173, 179,
185, 199, 732
subtraction, 221, 716
unit, 236
writing decimals, 200–209, 214,
224, 254, 338, 422, 475, 733
writing rational numbers, 205
writing ratios, 264–265
writing repeating decimals, 206
writing simplest form, 263
writing terminating decimals, 206
Frequency polygon, 628
Factor monomials, 161
Experimental probability, 311
Fraction bars as grouping symbol,
12, 13, 224, 264
Faces, 557, 559, 595, 599
Evaluating expressions. See
Expressions
Expanded form, 154, 156, 185, 192
Four-step problem-solving plan,
5, 6–8, 9, 10, 47–48, 51
Factors, 69, 79, 148–152, 151, 191, 730
Family of graphs, 402–403
Find the Error, 14, 26, 72, 87, 100,
105, 128, 161, 166, 212, 222, 234,
246, 278, 291, 306, 347, 353, 357,
389, 395, 400, 462, 479, 536, 565,
592, 643, 648, 671, 676. See also
Common Misconceptions
Foldables™ Study Organizer, iv, 1,
5, 55, 97, 147, 199, 263, 327, 367,
435, 491, 553, 605, 667
Functional notation, 380
Functions, 369–373, 424, 537, 741
graphing, 370, 757
quadratic and cubic, 692–696,
700
linear, 687–691, 700
nonlinear, 687–691, 700
Fundamental Counting Principle,
636, 661
G
Geometric sequences, 249–252, 258,
259, 268, 344, 736
Geometry
angles, 447–451, 484
acute, 449, 450, 451, 457, 484,
745
Index R57
Index
Equations, 28, 49, 96–143, 126, 326.
See also Algebraic equations;
Linear equations; Percent
equations; Systems of equations;
Two-step equations
graphing, 691
identifying functions, 687–688
negative coefficients, 122
solving, 28–29, 49, 68, 113, 118,
121, 122, 123, 124, 141, 157, 443,
491, 511, 588, 725, 729, 730, 736,
739, 740, 744, 745
addition, 111–112, 139
division, 115–119, 139, 435
with grouping symbols,
334–338, 361
by multiplication, 115–119, 139
rational numbers, 244–248, 258
subtraction, 110–111, 139
variables on each side, 330–333,
360
solving systems, 414–418, 428
solving two-step, 120–122, 140,
327, 354, 451
translating verbal sentences into,
30, 125
writing inequalities, 340–342
writing linear, 404–408, 427
writing two-step, 126–130
Formulas, 131–133, 140, 300
distance, 466–470, 485–486
midpoint, 466–470, 485–486
Index
adjacent, 476, 493, 495
alternate exterior, 492, 493
alternate interior, 492, 493
central, 452, 538
complementary, 493, 494, 495,
496, 517, 544
congruent, 493
corresponding, 474, 492, 493,
500, 544
of elevation, 480
exterior, 492, 531
inscribed, 538
interior, 492, 528, 530, 538, 543
measures, 447, 448, 454
obtuse, 449, 450, 451, 457, 484,
745
quadrilateral, 514
right, 449, 450, 451, 457, 484, 745
straight, 447, 449, 450, 451, 457,
484, 745
supplementary, 494, 495, 496
vertical, 493, 495
area
circles, 533–538, 548, 561, 749
irregular figures, 539–543, 548
parallelograms, 520–521, 547
rectangles, 132, 133, 134, 135,
140, 141, 152, 214, 224, 349, 671,
730, 767
shaded region, 770
squares, 439, 523
triangles, 445, 561
circumference of circle, 561, 749
diameter of circle, 533, 749
inequality involving acute angle,
764
isosceles triangle, 469
length of hypotenuse in right
triangles, 462, 470
length of rectangle, 764
length of sides of golden
rectangles, 675
line segments, 473, 644, 645
obtuse angles, 691
patterns, 9
perimeter, 469
equilateral triangles, 394
geometric figures, 106
golden rectangles, 675
isosceles trapezoid, 680
isosceles triangles, 680
rectangles, 132, 133, 134, 135, 140,
141, 152, 224, 302, 335, 336, 349,
359, 363, 385, 417, 676, 701, 730
squares, 378, 394, 440, 463, 760
triangles, 467, 503, 591, 681, 760,
770
pi, 208, 533, 534
radius of circle, 443, 533, 536, 749
ratio of width to length, 266
R58 Index
rectangular prism, 464
right angles, 464, 691
scalene triangle, 469
straight angles, 691
sum of angles of triangle, 676
surface area, 594, 751
cubes, 157, 694
prisms and cylinders, 573–577,
597
pyramids and cones, 578–582,
597
three-dimensional figures,
552–601
triangles, 38, 453–457, 468, 485, 528
acute, 454, 456, 746
angle measures, 453
area, 521, 522, 523, 547
congruent, 500–504, 545, 748
equilateral, 455
isosceles, 455
obtuse, 454, 456, 746
obtuse isosceles, 455, 470, 485
right, 454, 456, 460, 461, 462,
463, 464, 481, 485, 746
right scalene, 470, 485
scalene, 455
similar, 471–475, 486
vertice, 88
vertices, 88, 447, 453, 527,
545–546, 556, 557, 559, 595, 599
volume, 750, 751
complex solid, 564
cones, 568–572, 596, 616
cubes, 157
596
596
rectangular prisms, 695
Geometry Activity
Building Three-Dimensional
Figures, 554–555
Similar solids, 583
Volume, 562
systems of equations, 414, 416,
417, 422, 428
systems of inequalities, 346, 348
Graphing Calculator Investigation
Box-and-Whisker Plots, 622
Families of Graphs, 402–403
Families of Quadratic Functions,
697
Finding Angles of a Right
Triangle, 482
Function Tables, 374
Graphing Inequalities, 423
Histograms, 629
Mean and Median, 243
Probability Simulation, 315
Scatter Plots, 45–46
Graph pairs, 88
Graph points, 55, 85, 86, 87, 92, 93
Graphs
bar, 722–723
circle, 723
data display, 722–723
identifying functions, 687
line, 722–723
relations as, 35, 36, 37, 50
writing equations, 405
Greatest common factor (GCF),
164–168, 179, 193, 199, 214, 252,
731
Greatest possible error, 594
Grid In. See Assessment.
Gridded Response. See Preparing
Grouping symbols, 48
brackets, 12
fraction bars, 12, 13
inequalities, 356
parentheses, 12, 15, 75
solving equations, 334–338, 361
Guess and Check, 709
Golden ratio, 253, 268
Golden rectangle, 268
Graphing
algebraic relationships, 87
cubic functions, 692–696, 700
equations, 691
functions, 370, 757
inequalities, 342, 343, 353, 354,
361, 362, 379, 419–422, 440, 740,
744
linear equations, 376–377
quadratic functions, 692–696, 700
solutions of equations, 111, 113,
118, 428, 744
H
Half-Life Simulation, 180
Heptagon, 528
Hexagon, 528
Hexagonal prism, 572
Hexagonal pyramid, 571
Histograms, 623–628, 629, 633, 660,
753
comparison to frequency tables,
627
interpretation, 624
Horizontal lines, 383
Hypotenuse, 460, 463, 470, 475, 477,
481, 485, 487, 746
I
Identity Property, 32, 63
Inclusive events, 672
Independent events, 650–651
Independent variable, 375
Indirect measurement, 471–475, 486
Inductive reasoning, 7, 25, 71
Inequalities, 326, 340–344, 361, 367,
464
graphing, 342, 343, 353, 354, 361,
362, 379, 419–422, 428, 440, 740,
744
solving, 354, 373, 379, 385, 445,
481, 561, 567, 649, 740, 741
addition, 345–349, 361
division, 350–354, 362
multiplication, 350–354, 362
multi-step, 355–359, 362
symbols, 57
truth, 341
writing, 740
Integers, 69, 451, 487, 745
absolute value, 90
addition, 62–63, 64–66, 74, 82, 84,
91, 97, 107, 199, 327
comparing and ordering, 56, 57,
59, 60, 68
division, 80–84, 92, 114, 199, 327
modeling real-world situations,
61
multiplication, 75–79, 82, 84,
91–92, 97, 152, 199, 327
number line, 56, 57, 59, 68
problem solving, 66
for real-world situations, 56–57
subtraction, 70–72, 74, 82, 84, 91,
118, 199, 327, 385
writing as fractions, 205
Intercepts, graphing linear
equations using, 381–385, 425
Interest, 299, 738
Internet Connections
www.pre-alg.com/careers, 42, 73,
129, 172, 223, 278, 339, 348, 358,
399, 472, 480, 515, 579, 649, 670
www.pre-alg.com/chapter_test,
51, 93, 141, 259, 321, 363, 429,
487, 549, 599, 663, 701
www.pre-alg.com/data_update,
43, 68, 114, 119, 157, 190, 229,
267, 348, 396, 439, 543, 587, 649,
690
www.pre-alg.com/
extra_examples, 7, 13, 19, 25, 35,
41, 57, 65, 71, 77, 81, 87, 99, 105,
111, 117, 121, 127, 133, 149, 155,
161, 165, 171, 177, 187, 201, 207,
211, 217, 221, 227, 233, 239, 245,
249, 265, 271, 277, 283, 289, 295,
299, 305, 311, 331, 335, 341, 347,
351, 355, 369, 377, 383, 389, 395,
399, 405, 409, 415, 419–422, 437,
443, 449, 455, 461, 467, 473, 479,
493, 501, 507, 515, 521, 529, 535,
541, 557, 565, 569, 575, 579, 585,
591, 607, 613, 619, 625, 631, 637,
643, 647, 651, 669, 675, 679, 683,
689, 693
www.pre-alg.com/
other_calculator_keystrokes, 45,
243, 315, 402, 423, 482, 629, 697
www.pre-alg.com/
self_check_quiz, 9, 15, 21, 27,
31, 37, 43, 59, 67, 79, 83, 89, 101,
107, 113, 119, 123, 129, 135, 151,
157, 163, 167, 173, 179, 183, 189,
203, 209, 213, 219, 223, 229, 235,
241, 247, 251, 267, 273, 279, 285,
291, 297, 301, 307, 313, 333, 337,
343, 349, 353, 357, 371, 379, 385,
391, 397, 401, 407, 411, 417, 421,
439, 445, 451, 457, 463, 469, 475,
481, 497, 503, 511, 517, 525, 531,
537, 543, 559, 567, 571, 577, 581,
587, 593, 609, 615, 621, 627, 633,
639, 645, 649, 653, 671, 677, 681,
685, 691, 695
www.pre-alg.com/
standardized_test, 53, 95, 143,
197, 261, 322, 365, 430, 489, 551,
601, 665, 703
www.pre-alg.com/
vocabulary_review, 47, 90, 138,
191, 316, 360, 483, 595, 658, 698
www.pre-alg.com/
webquest.com, 43, 79, 135, 136,
145, 173, 242, 301, 314, 325, 333,
412, 422, 433, 481, 542, 571, 594,
603, 626, 690, 696
Interquartile range, 613, 614, 615,
628, 659, 753
Intersecting lines, 493, 560
Inverse operations, 110, 121, 258,
373, 440
Inverse Property of
Multiplication, 215
Investigations. See Algebra
Activity; Geometry Activity;
Graphing Calculator
Investigation; Spreadsheet
Investigation; WebQuest
Irrational numbers, 206, 441, 443,
444, 451, 484, 487, 745
Irregular figures, area, 539–543, 548
Isosceles triangles
obtuse, 455, 470, 485
K
Key Concepts, 18, 23, 29, 58, 64, 65,
66, 70, 75, 76, 80, 81, 111, 115, 117,
132, 175, 176, 181, 186, 210, 215,
216, 221, 232, 233, 238, 270, 271,
282, 288, 310, 345, 350, 352, 376,
382, 388, 394, 436, 441, 449, 453,
454, 455, 460, 466, 468, 472, 477,
492, 493, 500, 507, 508, 514, 520,
521, 522, 528, 533, 557, 563, 565,
568, 569, 573, 575, 579, 585, 636,
646, 650, 652, 688
Keystrokes. See Graphing
Calculator Investigation; Internet
Connections
L
Lateral area, 578
Lateral faces, 578
Least common denominator (LCD),
227, 228, 229, 234, 236, 252, 735
Least common multiple (LCM),
226–230, 228, 236, 257, 735
Leaves, 606
Like fractions
addition, 220–224, 256
Index R59
Index
Homework Help, 9, 14, 20, 26, 31,
36, 43, 59, 67, 73, 78, 83, 88, 101,
106, 113, 118, 123, 129, 134, 151,
156, 162, 167, 172, 178, 183, 189,
203, 208, 213, 218, 222, 229, 235,
241, 246, 251, 267, 273, 279, 284,
291, 296, 301, 307, 313, 332, 337,
343, 348, 353, 357, 371, 378, 384,
390, 396, 400, 407, 411, 417, 421,
439, 444, 450, 456, 463, 469, 474,
480, 496, 503, 510, 516, 524, 530,
542, 559, 566, 571, 576, 580, 587,
593, 609, 615, 620, 626, 632, 638,
644, 648, 653, 671, 676, 680, 685,
690, 695
Index
Like terms, 103, 104, 105, 106, 122,
674, 676, 677, 728
Linear equations, 408, 447, 667
graphing, 376–377
with intercepts, 381–385, 425
two variables, 375–379, 425
writing, 404–408, 427
Linear functions, 687–691, 700, 701,
757
Line graphs, 722–723
double, 722–723
Line of symmetry, 506, 507
Line plot, 239
Lines
best-fit, 409–413, 427, 429
horizontal, 383
intersecting, 493, 560
parallel, 492–497, 495, 497, 544, 560
perpendicular, 494, 495
skew, 558, 560, 567
vertical, 383
geometric measures, 137,
213–214, 272, 566–567, 718–721,
794–796
metric, 718–719, 790–796
multiplication, 592
temperatures, 59–61, 333, 792–793
times, 213, 219, 789
weights, 213, 218, 718–721,
791–793
Measures of central tendency,
238–242, 258, 605, 735
Measures of variation, 612–616, 659
Median, 238–239, 248, 252, 258, 605,
611, 615, 618, 735
Mental Math, 25, 26, 29, 30, 31, 38,
44, 49, 51, 66, 74, 79, 102, 104, 122,
127, 150, 160, 201, 282, 525, 725,
738
Metric system, converting
measurements, 718–719
Midpoint, 468, 486, 746
Line segments, 453, 644, 645
Midpoint Formula, 466–470,
485–486
Line symmetry, 505
Minimum point, 695
Lists, 708
Minor arc, 538
Logical Reasoning. See Critical
Thinking
Mixed numbers, 200–201
addition, 220, 233, 491, 716
division, 216, 717
multiplication, 211, 717
subtraction, 221, 234, 716
writing as decimals, 200, 201,
202, 214, 422
writing as fractions, 205, 209
writing decimals as, 207–208, 224,
733
Look Back, 18, 71, 76, 100, 111, 166,
176, 210, 244, 264, 266, 293, 330,
334, 335, 369, 442, 460, 466, 497,
523, 535, 540, 570, 584, 607, 635,
637, 652, 683, 684
M
Major arc, 538
Make a Conjecture. See Conjectures
Make a table or list, 708
Markup, 301
Matrices, 414, 669, 705
Maximum point, 695
Mean, 82, 92, 238–239, 248, 252, 258,
605, 618, 735
Measurements, 213
addition, 592
capacities, 566–567, 718–721,
791–793
comparing, 721, 790, 792
converting, 118, 168, 213–214, 263,
272, 274, 718–721, 734, 789–796
customary, 118, 720–721, 734,
790–796
R60 Index
Mode, 238–239, 248, 252, 258, 605,
735
Modeling, 276–280, 317, 464
adding integers, 62–63, 222
algebraic expressions, 103, 106
area
circles, 535
parallelograms, 520–521
rectangles, 132
trapezoids, 522
triangles, 521
area and geoboards, 518–519
circumference of circles, 533
congruent triangles, 500
constructions, 498–499
direct variation, 394, 395
distance formula, 466
Distributive Property, 99
equations with variables on each
side, 328–329
integers on number line, 65
irrational numbers, 465
manipulatives, 62–63
midpoint formula, 468
monomials, 673
multiplication, 682
polynomial by monomial, 683
percent, 286–287
polyhedrons, 557
polynomials, 673, 677
prime numbers, 162
properties of equality, 123
Pythagorean Theorem, 458–459,
460
rational numbers, 207, 210, 215
ratios of similar solids, 585
real-world situations, 61
right triangles, 476
similar triangles, 472
simulations, 656–657
slope, 388
solving two-step equations, 120
surface area
cones, 579
cylinders, 575
rectangular prisms, 573
three-dimensional figures,
554–555, 560
triangles, 453
trigonometric ratios, 477
volume, 562
cones, 569
cylinders, 565
prisms, 563, 565
pyramids, 568
Monomials, 148–152, 161, 163, 191,
195, 667, 668, 669, 671, 681, 698,
730, 731, 755
degrees, 670
division, 175–179, 176, 194
factoring, 161, 162, 192, 195
greatest common factor (GCF),
166, 167, 193
identify, 150
least common multiple (LCM),
227
multiplication, 175–179, 194, 681
powers, 179
More About. See also Applications;
Cross-Curriculum Connections
airports, 247
amusement parks, 99, 644
animals, 474
architecture, 277, 503
art, 560
astronomy, 66
attractions, 272
aviation, 112
Multiple Choice. See Assessment
Multiple representations, 18, 23, 29,
58, 64, 65, 66, 70, 75, 76, 80, 81,
98, 110, 111, 115, 117, 132, 175,
176, 186, 207, 210, 215, 216, 221,
225, 232, 233, 238, 270, 288, 298,
310, 345, 350, 352, 377, 388, 394,
436, 453, 460, 466, 468, 472, 477,
500, 514, 522, 533, 535, 563, 565,
568, 569, 573, 575, 579, 613, 636,
650, 652
Multiplication, 11, 756
algebraic fractions, 211
decimals, 263, 491, 714, 715
fractions, 567, 649
integers, 75–79, 82, 84, 91–92, 97,
152, 199, 327
measurements, 592
mixed numbers, 211
monomials, 176, 681
negative fractions, 211
negative numbers, 351–352
notation, 13
polynomials by monomials,
683–686, 699
positive numbers, 350–351
rational numbers, 256, 553, 577
245
Multiplication Properties
Associative, 24, 26, 49, 522
Commutative, 23, 26, 49, 75, 522
of Zero, 24, 49, 61, 725
Multiplicative identity, 24, 38, 49,
725
Multiplicative inverse, 215–216,
218, 504, 734
Multi-step inequalities, solving,
355–359, 362
Mutually exclusive events, 652, 672
N
Natural numbers, 205, 444, 451, 487,
745
multiplication, 75, 77
subtraction, 70
Numbers, 12–13, 48
base 2, 158
base 10, 158
binary, 158
comparison, 283
composite, 159, 161, 162, 192, 229,
285, 731
decimal, 158
even, 148
factoring, 149
irrational, 206, 441, 443, 444, 451,
484, 487, 745
mixed, 200–201
natural, 205, 444, 451, 487, 745
negative, 56, 351–352
odd, 148
positive, 56, 350–351
prime, 159, 161, 162, 192, 440,
731
properties, 24
rational, 198–261, 205–209,
210–214, 215–219, 244–248,
255, 256, 258, 440, 441, 443,
444, 451, 487, 553, 577, 745
real, 441, 745
triangular, 457
whole, 27, 84, 205, 216, 444, 451
Number theory, 156, 162, 740
Numerical expressions, 12, 14
evaluating, 13, 17, 21, 22, 58, 60,
72, 74
finding value, 14
translating, 11, 13, 14, 15, 38, 51
writing for verbal phase, 724
Negative coefficients, 122, 161
Negative exponents, 181–185, 187,
194
Negative fractions, multiplication,
211
O
Octagonal prism, 566
Octagons, 528
Negative integers, 64
Odd numbers, 148
Negative numbers, 56
division, 351–352
multiplication, 351–352
Odds, 646–649, 662, 755
notation, 647
Negative slope, 388
Nonlinear functions, 687–691, 700,
701, 757
Nonscientific calculators, 12
Number line, 56, 57, 113, 740
absolute value, 58
addition, 64, 65, 68
comparison and ordering of
integers, 56, 57
integers, 56, 57, 59
Online Research. See also Internet
Connections; Research
career choices, 42, 73, 129, 172,
223, 278, 348, 358, 399, 472, 480,
515, 579, 649, 670
data update, 43, 68, 114, 119, 157,
190, 229, 267, 348, 396, 439, 543,
587, 625, 690
Open circles, 346
Open Ended, 9, 14, 19, 26, 30, 36, 42,
59, 67, 72, 77, 83, 87, 100, 105, 113,
117, 128, 133, 155, 158, 161, 162,
Index R61
Index
baby-sitting, 106
backpacking, 356
baseball cards, 105
basketball, 610, 685
billiards, 456
calling cards, 123
candy, 10
cheerleading, 217
decorating, 337
food, 284
football, 15
fruit drinks, 575
games, 511, 651
golf, 57
gymnastics, 463
hang gliding, 401
Internet, 654
movie industry, 31
oceans, 189
parks, 116
planets, 229
plants, 35
pole vaulting, 412
pools, 395
population, 267
presidents, 607
rafting, 422
ranching, 118
recycling, 208
scooters, 127
scuba diving, 370
skateboards, 299, 638
skydiving, 693
snow, 529
snowboards, 417
soccer, 19, 134
sound, 408
space, 586
sports, 344
state fairs, 347
stock market, 306
tides, 78
track and field, 165
travel, 219
videos, 331
water, 182
weather, 444
weddings, 149
Index
166, 171, 177, 183, 188, 202, 212,
217, 222, 228, 234, 241, 246, 266,
272, 278, 283, 291, 295, 300, 306,
312, 332, 336, 342, 347, 353, 357,
371, 377, 384, 389, 395, 400, 407,
410, 416, 421, 429, 438, 443, 449,
455, 462, 468, 473, 479, 487, 495,
502, 509, 515, 523, 529, 535, 540,
559, 565, 570, 575, 580, 586, 592,
599, 608, 614, 619, 625, 631, 637,
643, 648, 653, 670, 676, 680, 684,
689, 694
Open Response. See Preparing for
Standardized Tests
Open sentences, 28, 31, 32
solving, 28
Operations
integers, 82
inverse, 110
Opposites, 66, 476
Ordered pairs, 33–35, 36, 37, 39, 44,
50, 51, 55, 61, 79, 84, 85, 86, 87,
88, 124, 136, 367, 377, 378, 391,
422, 425, 429, 725, 728, 742
functions, 369–370
Ordered pair solutions, tables, 375,
378, 686
Ordering decimals, 616
Ordering integers, 59, 68, 87, 88, 726
Order of operations, 12–13, 14, 16,
24, 48, 51, 147, 154, 192, 401, 464,
525
Origin, 33, 34
Pentagon, 528
Percent equations, 298–302, 319,
373
Percent-fraction equivalents, 293
Percent of change, 304–308, 320
Percent of decrease, 306, 320, 739
Percent of increase, 305, 306, 320,
739
Percent proportion, 288–292, 297,
318, 321, 738
Percents, 281–308, 318, 359, 525, 737,
738
applying, 289, 290, 299–308
of change, 304–308
comparing, 283
compound interest, 303
decimals as, 282–283
equations, 298–302
estimating with, 294–295
finding mentally, 293
finding percent, 288, 289, 299
finding the base, 290, 299
finding the part, 290, 298
fractions as, 282
greater than 100%, 283
less than 1%, 283
modeling, 281, 286, 287
and predictions, 312
and probability, 310
proportion, 288–292
simple interest, 299, 300
writing as decimals, 282, 298
writing as fractions, 281–282, 283,
288, 475
Perfect squares, 436, 438
Outcomes, 310
Outliers, 621
P
Parabola, 697
Perimeter, 137
polygon, 530
rectangle, 132, 134, 140
rectangles, 132, 133, 134, 135, 140,
141, 152, 224, 302, 335, 336, 349,
359, 363, 385, 417, 676, 701, 730
Parallel lines, 495, 560
angles and, 492–497, 497, 544
Permutations, 641–645, 661, 754
Parallelogram, 514, 515, 546
altitude, 520
area, 520–521, 547
base, 520
Perspective, 554–555
Parentheses ( ), 15, 75
as grouping symbol, 12, 15
Points, 447
writing equations given two, 406
Pascal’s triangle, 640
Patterns, 9, 16, 47, 48, 55, 74, 84, 102,
167
R62 Index
Perpendicular lines, 494, 495
Pi, 208, 533, 534
Plane, 556
Polygons, 527–531, 547, 553
classification, 527–528, 530, 549, 749
frequency, 628
interior angles, 528
measures of angles, 528–529, 530
regular, 529
Polyhedron, 556
Polynomials, 669–672, 698, 755
addition, 674–677, 699
classification, 669, 681, 698, 701
degrees, 670, 671, 677, 681, 698,
701
multiplication, 683–686, 699
monomials, 683–686, 699
Positive exponents, 182, 183, 185,
187, 194
Positive integer, 64
Positive numbers, 56
division, 350–351
multiplication, 350–351
Positive slope, 388, 391
Powers, 153–157, 174, 192, 194
Practice Chapter Test. See
Assessment
Practice Quiz. See Assessment
Precision, 589, 590–594, 598
Precision unit, 590, 591, 592, 593
Predictions, 310–314, 320, 395
best-fit lines, 409, 410, 412, 413
equations, 410
scatter plots, 42
sequences, 251
Preparing for Standardized Tests,
771–778
Constructed Response, 780–783,
784–788
Extended Response, 771, 784–788
Free Response, 780–783
Grid In, 776–779
Gridded Response, 771, 776–779
Multiple Choice, 771, 772–775
Open Response, 780–783
Selected Response, 772–775
Short Response, 771, 780–783
Student-Produced Questions,
780–783
Student-Produced Response,
776–779
Test-Taking Tips, 771, 773, 776,
777, 780, 781
Prerequisite Skills. See also
Assessment
Adding and Subtracting
Decimals, 713
Comparing and Ordering
Decimals, 710
Prime, 285
relatively, 168
twin, 162
Prime factorization, 159–162, 192,
224, 236, 731
Prime factors, 227, 230
Prime numbers, 159, 161, 162, 192,
440, 731
Prisms, 557, 595
height, 564
hexagonal, 572
octagonal, 566
rectangular, 557, 560, 563, 565,
566, 575, 576, 582, 597
triangular, 557, 562, 564, 566, 572,
587
volume, 563–567, 596
Probability, 310–314, 320, 333, 338,
604–605, 672, 677, 739, 754, 755
compound events, 650–655, 662
dependent events, 652
event, 636–637
experimental, 311
mutually exclusive events, 652
notation, 650
outcomes, 310
simple, 605
simple events, 310
theoretical, 311
two independent events, 650–651
Probability simulation, 315
Problem solving
adding polynomials, 675
angles, 449
area, 523
circumference, 534
combinations, 643
comparing fractions in, 202
direct variation, 395
distance formula, 467
distributive property, 99
dividing powers, 177
divisibility rules, 149
equations, 116, 125, 405
four-step plan, 5, 6–8, 9, 10,
47–48, 51
fractions, 234
functions, 693
graphing equations, 399
graphing inequalities, 420
guess and check, 709
inequalities, 347
integers, 66, 76
integers in, 76
making a table or list, 708
mixed, 758–770
polynomials, 675, 684
proportions, 271
scientific notation, 187
solving simpler problem, 706
square roots, 438
subtracting integers, 71
subtracting polynomials, 679
trigonometric ratios, 479
volume, 570
work backward, 122, 707, 709,
712, 713, 714, 715, 716, 717, 719
Product of Powers rule, 184
Products, 27, 69, 74, 78, 79, 84,
91–92, 93, 147, 175, 176, 177, 178,
185, 224, 252, 255, 280, 285, 327,
567, 577, 605, 715, 725, 727, 732,
756. See also Multiplication
estimating, 714, 717
signs, 79
Profit, 301
Projects. See WebQuest
Properties of Equality, 23–25, 29,
30, 31, 49
Substitution, 18
Symmetric, 29, 30, 31
Transitive, 29, 30, 31
Proportions, 262, 270–274, 280, 285,
317, 413, 440, 470, 473, 474, 553,
582, 599, 677, 747
identifying, 271
property, 271
solving, 271, 272, 737
Protractor, 448, 449, 450, 457, 464,
484, 497, 512, 745
Pyramids, 557, 595
hexagonal, 571
rectangular, 557, 570, 572, 577
square, 557, 571, 581, 582, 585
triangular, 557
volume, 568–572, 596
Pythagorean Theorem, 460–464,
469, 485
converse, 462
Pythagorean triple, 459
Q
Quadrants, 86, 87, 92
Quadratic functions, 688
families, 697
graphing, 692–696, 700
Quadrilaterals, 513–517, 528, 546
angles of, 514
classification, 514–515, 516, 531
naming, 513
Quantitative relationships, 96
Quartiles, 613
Quotient of Powers rule, 184
Quotients, 13, 38, 69, 79, 83, 84, 89,
92, 93, 177, 178, 185, 218, 224, 230,
242, 252, 256, 274, 280, 327, 714,
715, 717, 727, 732, 734. See also
Division
Index R63
Index
Converting Measurements
within the Customary System,
720–721
Converting Measurements
within the Metric System,
718–719
Displaying Data in Graphs,
722–723
Estimating Products and
Quotients of Decimals, 714
Estimating Products and
Quotients of Fractions and
Mixed Numbers, 717
Estimating Sums and Differences
of Decimals, 712
Estimating Sums and Differences
of Fractions and Mixed
Numbers, 716
Getting Ready for the Next
Lesson, 10, 16, 21, 27, 32, 38, 61,
68, 74, 79, 84, 102, 107, 114, 119,
124, 130, 152, 157, 163, 168, 173,
179, 185, 204, 209, 213, 219, 224,
230, 236, 242, 248, 268, 274, 280,
285, 292, 297, 302, 308, 333, 338,
344, 349, 354, 373, 379, 385, 391,
397, 401, 408, 413, 418, 440, 445,
451, 457, 464, 470, 475, 497, 504,
511, 517, 525, 531, 538, 561, 567,
572, 577, 582, 588, 611, 616, 621,
628, 633, 639, 645, 649, 672, 677,
681, 686, 691
Getting Started, 5, 55, 97, 147,
199, 263, 327, 367, 435, 491, 553,
605, 667
Multiplying and Dividing
Decimals, 715
Problem-Solving Strategy
Guess and Check, 709
Make a Table or List, 708
Solve a Simpler Problem, 706
Work Backward, 707, 709, 712,
713, 714, 715, 716, 717, 719
Rounding Decimals, 711
Index
R
Real numbers, 441, 745
Rhombus, 514, 546
Radical sign, 436, 437
Real number system, 441–445, 484
Rotational symmetry, 505
Radius
circles, 443, 533, 536, 749
cones, 571
Reasonableness, 7, 586
Rotations, 506, 507, 508, 509, 510,
512, 532, 686
coordinate plane, 509
Range, 35, 36, 37, 44, 50, 51, 136, 367,
612–616, 618, 628, 659, 725, 753
Rate of change, 392, 393–397, 426,
743
Rates, 264–268, 316
converting, 266, 280
Rational numbers, 198–261, 440,
441, 443, 444, 451, 487, 745
division, 215–219, 256
identifying and classifying, 206
multiplication, 210–214, 255, 553,
577
solving equations, 244–248, 258
writing as fractions, 205–206
Reasoning. See also Critical Thinking
deductive, 25
inductive, 7, 25, 71
Reciprocals, 215, 247
Rectangles, 514, 546
area, 132, 133, 134, 135, 140, 141,
152, 214, 224, 349, 671, 730, 767
perimeter, 132, 133, 134, 135, 140,
141, 152, 224, 302, 335, 336, 349,
359, 363, 385, 417, 676, 701, 730
Rectangular prisms, 557, 560, 563,
565, 566, 575, 576, 582, 597
Rounding, 9, 10, 201, 242, 283, 284,
291, 314, 443, 445, 457, 462, 463,
468, 469, 475, 478, 480, 481, 482,
484, 486, 487, 491, 531, 534, 535,
536, 543, 548, 549, 565, 566, 568,
569, 570, 571, 572, 577, 580, 581,
582, 588, 592, 593, 596, 597, 598,
599, 605, 611, 672, 711, 735, 736,
737, 738, 745, 746, 747, 749, 750,
751, 752
Rows, 705
Rectangular pyramid, 557, 570, 572,
577
Reflections, 506, 508, 509, 510, 512,
686, 748
S
Sample space, 311
Ratios, 264–268, 273, 316, 321, 359,
386, 445, 454, 481, 553, 645, 736
common, 250, 251, 258
comparison, 269
writing as fractions, 264–265
Regular tessellations, 527
Reading and Writing, 5, 55, 97, 147,
199, 263, 327, 367, 435, 491, 553,
605, 667
Relationships, types of, 41, 42, 43,
51 50, 68
Scalene triangles
right, 470, 485
Relative frequencies, 627
Scatter plots, 39, 40–42, 43, 45–46,
50, 61, 68, 107, 408, 410, 411, 412,
422, 427, 429, 726
constructing, 40
interpreting, 41
predictions, 42
trends, 44
Reading Math, 17, 23, 24, 56, 57, 64,
75, 80, 88, 98, 103, 148, 149, 150,
159, 177, 200, 205, 206, 281, 300,
311, 341, 370, 381, 383, 437, 448,
453, 471, 472, 477, 493, 500, 508,
624, 641, 642, 643, 647, 650, 678,
688
Reading Mathematics
Dealing with Bias, 634
Factors and Multiples, 225
Language of Functions, 380
Learning Geometry Vocabulary,
446
Learning Mathematics Prefixes,
526
Learning Mathematics Vocabulary,
69
Making Comparisons, 269
Meanings of At Most and At
Least, 339
Powers, 174
Precision and Accuracy, 589
Prefixes and Polynomials, 668
Translating Expressions into
Words, 11
Translating Verbal Problems into
Equations, 125
R64 Index
Regular polygon, 529
Relations, 35, 50, 367
as tables and graphs, 35, 36, 37, 50
Relatively prime, 168
Repeating decimals, 201, 202, 203,
206, 214, 224, 254, 338, 733
Replacement set, 102
Research, 43, 46, 83, 113, 151, 225,
253, 268, 291, 308, 380, 446, 526,
530, 543, 560, 583, 589, 610, 668,
672. See also Online Research
Review
Lesson-by-Lesson, 47–53, 90–92,
138, 191–194, 254–258, 316,
360–362, 424–428, 483–486,
544–548, 595, 658–662, 698
Mixed, 16, 21, 27, 32, 44, 61, 68,
74, 79, 84, 89, 102, 107, 114, 119,
124, 130, 136, 152, 157, 163, 168,
173, 179, 185, 190, 204, 209, 213,
219, 224, 230, 236, 242, 248, 252,
268, 274, 280, 285, 292, 297, 302,
308, 314, 333, 338, 344, 349, 354,
359, 373, 379, 385, 391, 397, 401,
408, 413, 418, 422, 440, 445, 451,
457, 464, 470, 475, 481, 497, 504,
511, 517, 525, 538, 543, 561, 567,
572, 577, 582, 588, 594, 611, 616,
621, 628, 633, 639, 649, 655, 672,
677, 681, 686, 691, 696
Scale, 276, 631, 737
Scale drawings, 276–280, 317
Scale factor, 277, 285, 583, 587
Scale model, 276
Scientific calculators, 12, 16
Scientific notation, 186–190, 194,
195, 204, 268, 733
Segment measure, 472
Selected Response. See Preparing
Sequences
arithmetic, 249–252, 258, 259, 268,
344, 736
Fibonacci, 253
geometric, 249–252, 258, 259, 344,
736
Sets, 733
replacement, 102
Shadow reckoning, 473
Short Response. See Preparing for
Standardized Tests
Side lengths of rectangles, 152
Sides of the angle, 447
Sierpinski’s triangle, 471
Significant digits, 590–594, 598,
599, 752
Standardized Test Practice. See
Assessment
Statistics, 418, 604–665, See also Data
bias, 634
misleading, 630–633, 661
Simple interest, 300
Stems, 606
Simplest form, 104
Straight line, 102
Similar figures, 471–475, 486
Simulation
probability, 315
Simulations, 656–657
half-life, 180
Sine, 477–481, 486, 747
Skew lines, 558, 560, 567
Slant height, 578
Slides, 506
Slope, 387–391, 395, 397, 398, 400,
401, 404, 408, 412, 413, 418, 426,
427, 429, 470, 639, 742, 743
negative, 388
positive, 388, 391
undefined, 389
zero, 388
Slope-intercept form, 398–401, 401,
406, 407, 413, 418, 427, 696, 742,
743
Solids, 556, 750, 751, 752
similar, 584–588, 598
Solution, 28
Solving Equations. See Equations
Spreadsheet Investigation
Circle Graphs and Spreadsheets,
452
Compound Interest, 303
Expressions and Spreadsheets, 22
Perimeter and Area, 137
Spreadsheets, 22
Square pyramid, 557, 571, 581, 582,
585
Square roots, 436–440, 451, 483, 628,
745
solving equations, 443
Squares, 436–440, 483, 514, 546
area, 439, 523
Square units, 575
Standard form, 154, 188, 189, 194,
195, 209, 733
Student-Produced Questions. See
Student-Produced Response. See
Study organizer. See Foldables™
Study Organizer
Study Tips, 6, 7, 12, 13, 18, 25, 28,
34, 41, 58, 60, 65, 70, 71, 76, 82, 86
algebra tiles, 674
alternate strategy, 406
alternative methods, 128, 170,
220, 250, 265, 335, 522
altitudes, 521
angles, 447
Base, 289
box-and-whisker plots, 618
break in scale, 624
calculating with Pi, 534
calculator, 187
checking equations, 111, 405
checking reasonableness of
results, 494
checking solutions, 121, 346
check your work, 443
choosing a method, 164
choosing points, 388
choosing x values, 376
circles and rectangles, 574
classifying polynomials, 669
common misconceptions, 58, 132,
154, 175, 355, 420, 449, 467, 507,
557, 591, 617
commutative, 160
cones, 569
congruence statements, 501
cross products, 271
degrees, 670
dependent variable, 375
diagonals, 558
different forms, 398
dimensions, 556
dividing by a whole number, 216
division expressions, 117
equiangular, 454
equivalent expressions, 104
estimation, 288, 409
Index R65
Index
Similar solids, 599
Stem-and-leaf plots, 606–611, 658,
681, 752
back-to-back, 607–608, 609, 611
interpretation, 607
exponents, 155
expression, 126
finding percents, 295
first power, 153
fractions, 283
frequency distribution, 623
graphing, 692
graphing shortcuts, 382
growth of functions, 688
height of pyramid, 568
hypotenuse, 460
independent variable, 375
inequalities, 341, 345
irregular figures, 539
labels and scales, 631
Look Back, 18, 71, 76, 100, 111,
166, 176, 210, 244, 264, 266, 293,
330, 334, 335, 369, 442, 466, 472,
523, 535, 540, 570, 584, 635, 637,
652, 683, 684
matrices, 414, 669
mean, median, mode, 238
measures of volume, 563
mental computation, 122
mental math, 127, 160, 201, 282
multiplying more than two
factors, 636
naming quadrilaterals, 513
negative fractions, 211
negative number, 352
negative signs, 233, 675
negative slopes, 399
n-gon, 528
notation, 507
parallel lines, 492
percents, 294
pi, 533, 565
plotting points, 377
positive and negative exponents,
187
positive number, 350
powers of ten, 186
precision, 590, 592
precision units, 591
prime factors, 226
probability, 310
properties, 270
Reading Math, 215, 455
reciprocals, 245
relatively prime, 230
remainders, 161
repeating decimals, 206
rolling number cubes, 646
rounding, 478
scale factors, 277, 585
slopes, 394
slopes/intercepts, 415
solutions, 421
statistics, 613, 630
substitution, 467
trends, 372
Index
triangular pyramids, 581
use a table, 405
use a venn diagram, 169
writing prime factors, 165
zeros, 679
Substitution, 107, 379, 413, 440
solving equations, 744
solving systems of equations,
416, 417, 418, 428
Substitution Property of Equality, 18
Subtraction, 11, 328, 727, 734, 735,
756
decimals, 5, 712, 713
fractions, 221, 716
integers, 70–72, 74, 82, 84, 91, 118,
199, 327, 385
like fractions, 220–224, 256
mixed numbers, 221, 234, 716
polynomials, 678–681, 699
simplifying expressions, 100
139, 244
unlike fractions, 232–236, 257
Subtraction expressions, 100, 102,
104
Subtraction Property of Equality,
110, 111, 360
Sums, 61, 64, 67, 74, 79, 91, 93, 107,
230, 235, 242, 256, 257, 327, 605,
712, 716, 725, 726, 734, 735, 756.
See also Addition
Surface area, 594, 751
cubes, 157, 694
597
pyramids and cones, 578–582, 597
Symbols. See also Grouping symbols
bar notation, 201
break in scale, 624
congruent, 493
equality, 28
equals sign, 126
inequality, 28, 57, 59, 90, 93
(is about equal to), 437
negative signs, 675
radical sign, 436
variable, 17
Symmetric Property of Equality, 29,
30, 31
Symmetry, 505
bilateral, 505
line, 505
rotational, 505
turn, 505
R66 Index
Systems of equations
graphing, 422
solving, 414–418, 428, 440, 582
Systems of inequalities, 422
graphing, 346, 348
T
Tables, 708
functions, 369–370
identifying functions, 688
ordered pair solutions, 375, 378,
686
relations, 35, 36, 37, 50
writing equations, 406
Tangent, 747
Tangent ratios, 477–481, 479, 486
Term, 103
area, 521, 522–523, 547
Tree diagram, 635, 637, 638, 645
Triangles, 38, 453–457, 485, 528
acute, 454, 456, 746
angle measures, 453
area, 521, 522, 523, 547
congruent, 500–504, 545, 748
equilateral, 455
isosceles, 455
obtuse, 454, 456, 746
obtuse isosceles, 455, 470, 485
right, 454, 456, 460, 461, 462, 463,
464, 481, 485, 746
right scalene, 470, 485
scalene, 455
similar, 471–475, 486
vertex, 88
Triangular numbers, 457
Terminating decimals, 200, 203, 206
Triangular prisms, 557, 562, 564,
566, 572, 587
Tessellations, 527, 529, 530, 531, 532
Triangular pyramid, 557
Test preparation. See Assessment
Trigonometric ratios, 477–481, 486
Test-Taking Tips. See Assessment
Trigonometry terms, 477
Theoretical probability, 311
Trinomials, 669, 671, 681, 698, 755
Three-dimensional figures,
552–601
building, 554–555
identifying, 556–561
precision and significant digits,
589, 590–594, 598
similar solids, 583, 584–588, 598
surface area
597
597
volume
596
596
Turn symmetry, 505
Transformations, 512, 686
coordinate plane, 506–511,
545–546
Unlike fractions
addition, 232–236, 257
Transitive Property of Equality, 29,
30, 31
Unlike terms, 674, 677
Translations, 506, 507, 509, 510, 512,
686, 748
Transversal, 492–493, 495, 496, 544,
549, 747
Trapezoids, 514, 515, 546
Twin primes, 162
Two-dimensional figures, 490–551,
561
Two-step equations, 120
solve, 327
solving, 120–122, 140, 327, 354,
451
writing, 126–130, 140
U
Unit fraction, 236
Unit rates, 265–268, 359, 445, 736
V
Variables, 17, 18, 19, 28, 30, 31, 48,
49, 725
defining, 18
dependent, 375
independent, 375
linear equations in two, 375–379,
425
showing relationships, 17, 21
solving equations, 328–329,
330–333, 360, 397
Venn diagram, 164, 441
Verbal problems, two-step, 127
Vertical lines, 383
Vertical line test, 370
Vertices, 88, 447, 453, 527, 545–546,
556, 557, 559, 595, 599
Volume, 750, 751
complex solid, 564
cones, 568–572, 596, 616
596
596
WebQuest, 43, 79, 135, 136, 145, 173,
242, 301, 314, 325, 333, 412, 422,
433, 481, 543, 571, 594, 603, 626,
691, 696
Whole numbers, 27, 84, 205, 216,
444, 451
x-axis, 33, 36, 40, 86, 92, 508
x-coordinate, 33, 34, 35, 38, 50, 85,
86, 508
x-intercept, 381–385, 391, 397, 425,
429, 742
Work backward, 122, 240, 362, 707,
709, 712, 713, 714, 715, 716, 717,
719
Writing in Math, 10, 16, 27, 32, 37,
44, 61, 68, 74, 79, 84, 89, 101, 106,
114, 119, 123, 130, 136, 152, 157,
162, 168, 173, 179, 184, 190, 204,
213, 219, 223, 236, 242, 247, 251,
268, 274, 280, 285, 292, 297, 302,
307, 314, 333, 338, 344, 349, 354,
359, 373, 379, 385, 391, 397, 401,
408, 412, 418, 422, 440, 445, 451,
457, 464, 469, 475, 481, 497, 504,
511, 517, 525, 531, 537, 543, 561,
567, 571, 577, 582, 588, 594, 611,
616, 621, 627, 633, 639, 645, 649,
654, 672, 677, 681, 686, 691, 695
Y
y-axis, 33, 36, 40, 86, 92, 508, 509
y-coordinate, 33, 34, 35, 36, 38, 50,
85, 86, 508
y-intercept, 381–385, 391, 397,
398–399, 400, 401, 404, 406, 408,
410, 412, 413, 418, 425, 427, 429,
470, 639, 742, 743
Z
Zero, 56
Multiplicative Property, 24, 49,
61, 725
Zero pair, 62
Zero slope, 388
Index R67
Index
Verbal expressions
translating expressions into, 11,
38, 124, 125
translating into expressions, 13,
14, 15, 18, 19, 20, 30, 32, 51, 74,
105
writing numerical phrases, 724
X
W

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