answers (anticipation guide and lesson 7-1) · chapter 7 a1 glencoe algebra 2 answers answers...
TRANSCRIPT
Chapter 7 A1 Glencoe Algebra 2
An
swer
s
Answers (Anticipation Guide and Lesson 7-1)
STEP
1
Cha
pter
73
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Ant
icip
atio
n G
uide
Rad
ical
Eq
uat
ion
s
Chapter Resources
Bef
ore
you
beg
in C
ha
pte
r 7
•R
ead
each
sta
tem
ent.
•D
ecid
e w
het
her
you
Agr
ee (
A)
or D
isag
ree
(D)
wit
h t
he
stat
emen
t.
•W
rite
Aor
D i
n t
he
firs
t co
lum
n O
R i
f yo
u a
re n
ot s
ure
wh
eth
er y
ou a
gree
or
disa
gree
,w
rite
NS
(N
ot S
ure
).
Aft
er y
ou c
omp
lete
Ch
ap
ter
7
•R
erea
d ea
ch s
tate
men
t an
d co
mpl
ete
the
last
col
um
n b
y en
teri
ng
an A
or a
D.
•D
id a
ny
of y
our
opin
ion
s ab
out
the
stat
emen
ts c
han
ge f
rom
th
e fi
rst
colu
mn
?
•F
or t
hos
e st
atem
ents
th
at y
ou m
ark
wit
h a
D, u
se a
pie
ce o
f pa
per
to w
rite
an
exa
mpl
e of
wh
y yo
u d
isag
ree.
STEP
2
ST
EP
1S
TE
P 2
A,D
,or
NS
Sta
tem
ent
A o
r D
1.F
un
ctio
ns
can
be
adde
d or
su
btra
cted
in
th
e sa
me
way
as
poly
nom
ials
.A
2.A
com
posi
tion
of
fun
ctio
ns,
f[g
(x)]
, is
fou
nd
by m
ult
iply
ing
f(x)
by
g(x)
.D
3.T
he
inve
rse
of a
fu
nct
ion
is
the
set
of o
rder
ed p
airs
obt
ain
ed
by t
akin
g th
e op
posi
te o
f ea
ch c
oord
inat
e in
th
e or
igin
al
Dor
dere
d pa
irs.
4.Tw
o fu
nct
ion
s ar
e in
vers
es o
f ea
ch o
ther
on
ly i
f th
eir
com
posi
tion
s ar
e th
e id
enti
ty f
un
ctio
n.
A
5.T
he
dom
ain
of
y�
�(x
�3
�)�
wou
ld b
e x
�3.
A6.
Th
e pr
inci
pal
root
of
any
nth
roo
t is
alw
ays
posi
tive
. D
7.T
he
radi
cal
expr
essi
on�34�
is i
n s
impl
est
form
.D
8.4
��
3�an
d 4
��
3�ar
e co
nju
gate
s of
eac
h o
ther
.A
9.5
is t
he
sam
e as
�253 �
.D
10.
To s
olve
an
equ
atio
n c
onta
inin
g th
e sq
uar
e ro
ot o
f th
e va
riab
le, s
quar
e bo
th s
ides
of
the
equ
atio
n.
A
2 � 3
m � m3
Lesson 7-1
Cha
pter
75
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Op
erat
ion
s o
n F
un
ctio
ns
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 7
-1 i
n y
our
text
boo
k.
Des
crib
e tw
o w
ays
to c
alcu
late
Ms.
Cof
fmon
’s p
rofi
t fr
om t
he
sale
of
50 b
irdh
ouse
s. (
Do
not
act
ual
ly c
alcu
late
her
pro
fit.
)S
amp
le a
nsw
er:
1.F
ind
th
e re
ven
ue
by s
ub
stit
uti
ng
50
for
xin
th
e ex
pre
ssio
n 1
25x.
Nex
t,fi
nd
th
e co
st b
y su
bst
itu
tin
g 5
0 fo
r x
in t
he
exp
ress
ion
65x
�54
00.
Fin
ally
,su
btr
act
the
cost
fro
m t
he
reve
nu
e to
fin
d t
he
pro
fit.
2.F
orm
th
e p
rofi
t fu
nct
ion
p(x
) �
r(x
) �
c(x
) �
125x
�(6
5x�
5400
) �
60x
�54
00.S
ub
stit
ute
50
for
xin
th
e ex
pre
ssio
n 6
0x�
5400
.
Rea
d t
he
Less
on
1.D
eter
min
e w
het
her
eac
h s
tate
men
t is
tru
eor
fal
se. (
Rem
embe
r th
at t
rue
mea
ns
alw
ays
tru
e.)
a.If
fan
d g
are
poly
nom
ial
fun
ctio
ns,
th
en f
�g
is a
pol
ynom
ial
fun
ctio
n.
tru
e
b.
If f
and
gar
e po
lyn
omia
l fu
nct
ion
s, t
hen
is
a p
olyn
omia
l fu
nct
ion
.fa
lse
c.If
fan
d g
are
poly
nom
ial
fun
ctio
ns,
th
e do
mai
n o
f th
e fu
nct
ion
f�
gis
th
e se
t of
all
real
nu
mbe
rs.
tru
e
d.
If f
(x)
�3x
�2
and
g(x)
�x
�4,
th
e do
mai
n o
f th
e fu
nct
ion
is
th
e se
t of
all
rea
ln
um
bers
.fa
lse
e.If
fan
d g
are
poly
nom
ial
fun
ctio
ns,
th
en (
f�
g)(x
) �
(g�
f)(x
).fa
lse
f.If
fan
d g
are
poly
nom
ial
fun
ctio
ns,
th
en (
f�
g)(x
) �
(g�
f)(x
).tr
ue
2.L
et f
(x)
�2x
�5
and
g(x)
�x2
�1.
a.E
xpla
in i
n w
ords
how
you
wou
ld f
ind
(f�
g)(�
3). (
Do
not
act
ual
ly d
o an
y ca
lcu
lati
ons.
)S
amp
le a
nsw
er:
Sq
uar
e �
3 an
d a
dd
1.T
ake
the
nu
mb
er y
ou
get
,m
ult
iply
it b
y 2,
and
su
btr
act
5.
b.
Exp
lain
in
wor
ds h
ow y
ou w
ould
fin
d (g
�f)
(�3)
. (D
o n
ot a
ctu
ally
do
any
calc
ula
tion
s.)
Sam
ple
an
swer
:M
ult
iply
�3
by 2
an
d s
ub
trac
t 5.
Take
th
en
um
ber
yo
u g
et,s
qu
are
it,a
nd
ad
d 1
.
Rem
emb
er W
hat
Yo
u L
earn
ed
3.S
ome
stu
den
ts h
ave
trou
ble
rem
embe
rin
g th
e co
rrec
t or
der
in w
hic
h t
o ap
ply
the
two
orig
inal
fu
nct
ion
s w
hen
eva
luat
ing
a co
mpo
site
fu
nct
ion
. Wri
te t
hre
e se
nte
nce
s, e
ach
of
wh
ich
exp
lain
s h
ow t
o do
th
is i
n a
sli
ghtl
y di
ffer
ent
way
. (H
int:
Use
th
e w
ord
clos
est
inth
e fi
rst
sen
ten
ce, t
he
wor
ds i
nsi
de
and
outs
ide
in t
he
seco
nd,
an
d th
e w
ords
lef
tan
dri
ght
in t
he
thir
d.)
Sam
ple
an
swer
:1.
Th
e fu
nct
ion
th
at is
wri
tten
clo
sest
to
the
vari
able
is a
pp
lied
fir
st.2
.Wo
rk f
rom
th
e in
sid
e to
th
e o
uts
ide.
3.W
ork
fro
m r
igh
t to
left
.
f � g
f � g
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A1
Chapter 7 A2 Glencoe Algebra 2
Answers (Lesson 7-1)
Exer
cise
s
Exam
ple
Cha
pter
76
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y Gu
ide
and
Inte
rven
tion
Op
erat
ion
s o
n F
un
ctio
ns
Ari
thm
etic
Op
erat
ion
s
Sum
(f�
g)(x
) �
f(x)
�g
(x)
Diff
eren
ce(f
�g)
(x)
�f(
x) �
g(x
)O
per
atio
ns
wit
h F
un
ctio
ns
Pro
duct
(f�
g)(x
) �
f(x)
�g
(x)
Quo
tient
��(x
) �
, g
(x)
�0
Fin
d (
f�
g)(x
), (
f�
g)(x
), (
f�
g)(x
), a
nd
��(x
) fo
r f(
x) �
x2�
3x�
4an
d g
(x)
�3x
�2.
(f�
g)(x
) �
f(x)
�g(
x)A
dditi
on o
f fu
nctio
ns
�(x
2�
3x�
4) �
(3x
�2)
f(x)
�x2
�3x
�4,
g(x
) �
3x�
2
�x2
�6x
�6
Sim
plify
.
(f�
g)(x
) �
f(x)
�g(
x)S
ubtr
actio
n of
fun
ctio
ns
�(x
2�
3x�
4) �
(3x
�2)
f(x)
�x2
�3x
�4,
g(x
) �
3x�
2
�x2
�2
Sim
plify
.
(f�
g)(x
)�
f(x)
�g(
x)M
ultip
licat
ion
of f
unct
ions
�(x
2�
3x�
4)(3
x�
2)f(
x) �
x2�
3x�
4, g
(x)
�3x
�2
�x2
(3x
�2)
�3x
(3x
�2)
�4(
3x�
2)D
istr
ibut
ive
Pro
pert
y
�3x
3�
2x2
�9x
2�
6x�
12x
�8
Dis
trib
utiv
e P
rope
rty
�3x
3�
7x2
�18
x�
8S
impl
ify.
��(x
)�
Div
isio
n of
fun
ctio
ns
�, x
��2 3�
f(x)
�x2
�3x
�4
and
g(x
) �
3x�
2
Fin
d (
f�
g)(x
), (
f�
g)(x
), (
f�
g)(x
), a
nd
��(x
) fo
r ea
ch f
(x)
and
g(x
).
1.f(
x) �
8x�
3; g
(x)
�4x
�5
2.f(
x) �
x2�
x�
6; g
(x)
�x
�2
12x
�2;
4x�
8;32
x2
�28
x�
15;
x2
�2x
�8;
x2
�4;
,x�
�x
3�
x2
�8x
�12
;x
�3,
x�
2
3.f(
x) �
3x2
�x
�5;
g(x
) �
2x�
34.
f(x)
�2x
�1;
g(x
) �
3x2
�11
x�
4
3x2
�x
�2;
3x2
�3x
�8;
3x2
�13
x�
5;�
3x2
�9x
�3;
6x3
�11
x2
�13
x�
15;
6x3
�19
x2
�19
x�
4;
,x�
,x�
,�4
5.f(
x) �
x2�
1; g
(x)
�
x2�
1 �
,x�
�1;
x2
�1
�,
x�
�1;
x�
1,x
��
1;x
3�
x2
�x
�1,
x�
�1
1� x
�1
1� x
�1
1� x
�1
1 � 32x
�1
��
(3x
�1)
(x�
4)3 � 2
3x2
�x
�5
��
2x�
3
5 � 48x
�3
� 4x�
5
f � g
x2�
3x�
4�
�3x
�2
f(x)
� g(x)
f � g
f � g
f(x)
� g(x
)f � g
Exam
ple
1
Exam
ple
2
Exer
cise
s
7-1
Lesson 7-1
Cha
pter
77
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Co
mp
osi
tio
n o
f Fu
nct
ion
s
Co
mp
osi
tio
n
Sup
pose
fan
d g
are
func
tions
suc
h th
at t
he r
ange
of
gis
a s
ubse
t of
the
dom
ain
of f
.o
f F
un
ctio
ns
The
n th
e co
mpo
site
fun
ctio
n f
�g
can
be d
escr
ibed
by
the
equa
tion
[f�
g](
x) �
f[g
(x)]
.
For
f�
{(1,
2),
(3,
3),
(2,
4),
(4,
1)}
an
d g
�{(
1, 3
), (
3, 4
), (
2, 2
), (
4, 1
)},
fin
d f
�g
and
g�
fif
th
ey e
xist
.f[
g(1)
] �
f(3)
�3
f[g(
2)]
�f(
2) �
4f[
g(3)
] �
f(4)
�1
f[g(
4)]
�f(
1) �
2f
�g
�{(
1, 3
), (
2, 4
), (
3, 1
), (
4, 2
)}g[
f(1)
] �
g(2)
�2
g[f(
2)]
�g(
4) �
1g[
f(3)
] �
g(3)
�4
g[f(
4)]
�g(
1) �
3g
�f
�{(
1, 2
), (
2, 1
), (
3, 4
), (
4, 3
)}
Fin
d [
g�
h](
x) a
nd
[h
�g]
(x)
for
g(x)
�3x
�4
and
h(x
) �
x2�
1.[g
�h
](x)
�g[
h(x
)][h
�g]
(x)
�h
[g(x
)]�
g(x2
�1)
�h
(3x
�4)
�3(
x2�
1) �
4�
(3x
�4)
2�
1�
3x2
�7
�9x
2�
24x
�16
�1
�9x
2�
24x
�15
For
eac
h s
et o
f or
der
ed p
airs
, fin
d f
�g
and
g�
fif
th
ey e
xist
.
1.f
�{(
�1,
2),
(5,
6),
(0,
9)}
,2.
f�
{(5,
�2)
, (9,
8),
(�
4, 3
), (
0, 4
)},
g�
{(6,
0),
(2,
�1)
, (9,
5)}
g�
{(3,
7),
(�
2, 6
), (
4, �
2), (
8, 1
0)}
f�
g�
{(2,
2),(
6,9)
,(9,
6)};
f�
gd
oes
no
t ex
ist;
g�
f�
{(�
1,�
1),(
0,5)
,(5,
0)}
g�
f�
{(�
4,7)
,(0,
�2)
,(5,
6),(
9,10
)}
Fin
d [
f�
g](x
) an
d [
g�
f](x
).
3.f(
x) �
2x�
7; g
(x)
��
5x�
14.
f(x)
�x2
�1;
g(x
) �
�4x
2
[f�
g](
x)
��
10x
�5,
[f�
g](
x)
�16
x4
�1,
[g�
f](x
) �
�10
x�
36[g
�f]
(x)
��
4x4
�8x
2�
4
5.f(
x) �
x2�
2x; g
(x)
�x
�9
6.f(
x) �
5x�
4; g
(x)
�3
�x
[f�
g](
x)
�x
2�
16x
�63
,[f
�g
](x
) �
19 �
5x,
[g�
f](x
) �
x2
�2x
�9
[g�
f](x
) �
�1
�5x
Stud
y Gu
ide
and
Inte
rven
tion
(con
tinue
d)
Op
erat
ion
s o
n F
un
ctio
ns
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A2
Chapter 7 A3 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-1)
Cha
pter
78
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7-1
Skill
s Pr
actic
eO
per
atio
ns
on
Fu
nct
ion
s
Fin
d (
f�
g)(x
), (
f�
g)(x
), (
f�
g)(x
), a
nd
��(x
) fo
r ea
ch f
(x)
and
g(x
).
1.f(
x) �
x�
52x
�1;
9;2.
f(x)
�3x
�1
5x�
2;x
�4;
6x2
�7x
�3;
g(x)
�x
�4
�x x� �
5 4�
,x�
4g(
x) �
2x�
3�3 2x x
� �1 3
�,x
��3 2�
3.f(
x) �
x2x
2�
x�
4;x2
�x
�4;
4.f(
x) �
3x2�3x
3 x�5
�,x
�0;
�3x3 x�
5�
,x�
0;
g(x)
�4
�x
4x2
�x3
;,x
�4
g(x)
��5 x�
15x,
x�
0;�3 5x3 �
,x�
0
For
eac
h s
et o
f or
der
ed p
airs
, fin
d f
�g
and
g�
fif
th
ey e
xist
.
5.f
�{(
0, 0
), (
4, �
2)}
6.f
�{(
0, �
3), (
1, 2
), (
2, 2
)}g
�{(
0, 4
), (
�2,
0),
(5,
0)}
g�
{(�
3, 1
), (
2, 0
)}{(
0,�
2),(
�2,
0),(
5,0)
};{(
�3,
2),(
2,�
3)};
{(0,
4),(
4,0)
}{(
0,1)
,(1,
0),(
2,0)
}
7.f
�{(
�4,
3),
(�
1, 1
), (
2, 2
)}8.
f�
{(6,
6),
(�
3, �
3), (
1, 3
)}g
�{(
1, �
4), (
2, �
1), (
3, �
1)}
g�
{(�
3, 6
), (
3, 6
), (
6, �
3)}
{(1,
3),(
2,1)
,(3,
1)};
{(�
3,6)
,(3,
6),(
6,�
3)};
{(�
4,�
1),(
�1,
�4)
,(2,
�1)
}{(
6,�
3),(
�3,
6),(
1,6)
}
Fin
d [
g�
h](
x) a
nd
[h
�g]
(x).
9.g(
x) �
2x2x
�4;
2x�
210
.g(x
) �
�3x
�12
x�
3;�
12x
�1
h(x
) �
x�
2h
(x)
�4x
�1
11.g
(x)
�x
�6
x;x
12.g
(x)
�x
�3
x2
�3;
x2
�6x
�9
h(x
) �
x�
6h
(x)
�x2
13.g
(x)
�5x
5x2
�5x
�5;
14.g
(x)
�x
�2
2x2
�1;
2x2
�8x
�5
h(x
) �
x2�
x�
125
x2
�5x
�1
h(x
) �
2x2
�3
If f
(x)
�3x
, g(x
) �
x�
4, a
nd
h(x
) �
x2�
1, f
ind
eac
h v
alu
e.
15.f
[g(1
)]15
16.g
[h(0
)]3
17.g
[f(�
1)]
1
18.h
[f(5
)]22
419
.g[h
(�3)
]12
20.h
[f(1
0)]
899
21.f
[h(8
)]18
922
.[f
�(h
�g)
](1)
7223
.[f
�(g
�h
)](�
2)21
x2
� 4 �
x
f � g
x2
�x
�20
;
7-1
Lesson 7-1
Cha
pter
79
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Fin
d (
f�
g)(x
), (
f�
g)(x
), (
f�
g)(x
), a
nd
�� gf � �(x)
for
eac
h f
(x)
and
g(x
).
1.f(
x) �
2x�
12.
f(x)
�8x
23.
f(x)
�x2
�7x
�12
g(x)
�x
�3
g(x)
�g(
x) �
x2�
9
3x�
2;x
�4;
�8x4 x
� 21
�,x
�0;
2x2
�7x
�3;
7x�
21;
2x2
�5x
�3;
�8x4 x2�
1�
,x�
0;x
4�
7x3
�3x
2�
63x
�10
8;
�2 xx ��31
�,x
�3
8,x
�0;
8x4 ,
x�
0�x x
� �4 3
�,x
��
3
For
eac
h s
et o
f or
der
ed p
airs
, fin
d f
�g
and
g�
fif
th
ey e
xist
.
4.f
�{(
�9,
�1)
, (�
1, 0
), (
3, 4
)}5.
f�
{(�
4, 3
), (
0, �
2), (
1, �
2)}
g�
{(0,
�9)
, (�
1, 3
), (
4, �
1)}
g�
{(�
2, 0
), (
3, 1
)}{(
0,�
1),(
�1,
4),(
4,0)
};{(
�2,
�2)
,(3,
�2)
};{(
�9,
3),(
�1,
�9)
,(3,
�1)
}{(
�4,
1),(
0,0)
,(1,
0)}
6.f
�{(
�4,
�5)
, (0,
3),
(1,
6)}
7.f
�{(
0, �
3), (
1, �
3), (
6, 8
)}g
�{(
6, 1
), (
�5,
0),
(3,
�4)
}g
�{(
8, 2
), (
�3,
0),
(�
3, 1
)}{(
6,6)
,(�
5,3)
,(3,
�5)
};d
oes
no
t ex
ist;
{(�
4,0)
,(0,
�4)
,(1,
1)}
{(0,
0),(
1,0)
,(6,
2)}
Fin
d [
g�
h](
x) a
nd
[h
�g]
(x).
8.g(
x) �
3x9.
g(x)
��
8x10
.g(x
) �
x�
6h
(x)
�x
�4
h(x
) �
2x�
3h
(x)
�3x
23x
2�
6;3x
�12
;3x
�4
�16
x�
24;
�16
x�
33x
2�
36x
�10
8
11.g
(x)
�x
�3
12.g
(x)
��
2x13
.g(x
) �
x�
2h
(x)
�2x
2h
(x)
�x2
�3x
�2
h(x
) �
3x2
�1
2x2
�3;
�2x
2�
6x�
4;3x
2�
1;2x
2�
12x
�18
4x2
�6x
�2
3x2
�12
x�
13
If f
(x)
�x2
, g(x
) �
5x, a
nd
h(x
) �
x�
4, f
ind
eac
h v
alu
e.
14.f
[g(1
)]25
15.g
[h(�
2)]
1016
.h[f
(4)]
20
17.f
[h(�
9)]
2518
.h[g
(�3)
]�
1119
.g[f
(8)]
320
20.h
[f(2
0)]
404
21.[
f�
(h�
g)](
�1)
122
.[f
�(g
�h
)](4
)16
00
23.B
USI
NES
ST
he
fun
ctio
n f
(x)
�10
00 �
0.01
x2m
odel
s th
e m
anu
fact
uri
ng
cost
per
ite
mw
hen
xit
ems
are
prod
uce
d, a
nd
g(x)
�15
0 �
0.00
1x2
mod
els
the
serv
ice
cost
per
ite
m.
Wri
te a
fu
nct
ion
C(x
) fo
r th
e to
tal
man
ufa
ctu
rin
g an
d se
rvic
e co
st p
er i
tem
.C
(x)
�11
50 �
0.01
1x2
24.M
EASU
REM
ENT
Th
e fo
rmu
la f
�� 1n 2�
con
vert
s in
ches
nto
fee
t f,
an
d m
�� 52
f 80�co
nve
rts
feet
to
mil
es m
. Wri
te a
com
posi
tion
of
fun
ctio
ns
that
con
vert
s in
ches
to
mil
es.
[m�
f]n
�� 63
,n 360
�
1 � x2
Prac
tice
Op
erat
ion
s o
n F
un
ctio
ns
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A3
Chapter 7 A4 Glencoe Algebra 2
Answers (Lesson 7-1)
1.A
REA
Ber
nar
d w
ants
to
know
th
e ar
ea o
f a
figu
re m
ade
by jo
inin
g an
equ
ilat
eral
tri
angl
e an
d sq
uar
e al
ong
an
edge
. Th
e fu
nct
ion
f(s
) �
�� 43 � �s2
give
s th
ear
ea o
f an
equ
ilat
eral
tr
ian
gle
wit
h s
ide
s.T
he
fun
ctio
n g
(s)
�s2
give
s th
e ar
ea o
f a
squ
are
wit
h s
ide
s.W
hat
fu
nct
ion
h(s
)gi
ves
the
area
of
the
figu
re a
s a
fun
ctio
n o
fit
s si
de l
engt
h s
?
h(s
) �
(f�
g)(
s) �
(�� 43 � ��
1)s2
2.PR
ICIN
GA
com
pute
r co
mpa
ny
deci
des
to c
onti
nu
ousl
y ad
just
th
e pr
icin
g of
an
ddi
scou
nts
to
its
prod
uct
s in
an
eff
ort
tore
mai
n c
ompe
titi
ve. T
he
fun
ctio
n P
(t)
give
s th
e sa
le p
rice
of
its
Su
per2
000
com
pute
r as
a f
un
ctio
n o
f ti
me.
Th
efu
nct
ion
D(t
) gi
ves
the
valu
e of
a s
peci
aldi
scou
nt
it o
ffer
s to
val
ued
cu
stom
ers.
How
mu
ch w
ould
val
ued
cu
stom
ers
hav
eto
pay
for
on
e S
upe
r200
0 co
mpu
ter?
(P�
D)(
t)
3.LA
VA
Afr
esh
ly e
ject
ed l
ava
rock
imm
edia
tely
beg
ins
to c
ool
dow
n. T
he
tem
pera
ture
of
the
lava
roc
k in
deg
rees
Fah
ren
hei
t as
a f
un
ctio
n o
f ti
me
is g
iven
by T
(t).
Let
C(F
) be
th
e fu
nct
ion
th
atgi
ves
degr
ees
Cel
siu
s as
a f
un
ctio
n o
fde
gree
s F
ahre
nh
eit.
Wh
at f
un
ctio
n g
ives
the
tem
pera
ture
of
the
lava
roc
k in
degr
ees
Cel
siu
s as
a f
un
ctio
n o
f ti
me?
C
(T(t
))
4.EN
GIN
EER
ING
Agr
oup
of e
ngi
nee
rs i
sde
sign
ing
a st
aple
gu
n. O
ne
team
dete
rmin
es t
hat
th
e sp
eed
of i
mpa
ct s
ofth
e st
aple
(in
fee
t pe
r se
con
d) a
s a
fun
ctio
n o
f th
e h
andl
e le
ngt
h �
(in
inch
es)
is g
iven
by
s(�)
�40
�3�
. Ase
con
d te
am d
eter
min
es t
hat
th
en
um
ber
of s
hee
ts N
that
can
be
stap
led
as a
fu
nct
ion
of
the
impa
ct s
peed
is
give
n b
y N
(s)
��s
� 310 �
. Wh
at f
un
ctio
n
give
s N
as a
fu
nct
ion
of
�?N
(s(�
)) �
10 �
�
HO
T A
IR B
ALL
OO
NS
For
Exe
rcis
es 5
and
6, u
se t
he
foll
owin
g in
form
atio
n.
Han
nah
an
d Te
rry
wen
t on
a o
ne-
hou
r h
otai
r ba
lloo
n r
ide.
Let
T(A
) be
th
e ou
tsid
e ai
rte
mpe
ratu
re a
s a
fun
ctio
n o
f al
titu
de a
nd
let
A(t
) be
th
e al
titu
de o
f th
e ba
lloo
n a
s a
fun
ctio
n o
f ti
me.
5.W
hat
fu
nct
ion
des
crib
es t
he
air
tem
pera
ture
Han
nah
an
d Te
rry
felt
at
diff
eren
t ti
mes
du
rin
g th
eir
trip
?T
(A(t
))
6.S
ketc
h a
gra
ph o
f th
e fu
nct
ion
you
wro
tefo
r E
xerc
ise
5 ba
sed
on t
he
grap
hs
for
T(A
) an
d A
(t)
that
are
giv
en.
Teperature (ºF) 10 02030405060
Tim
e (m
inu
tes)
1020
3040
5060
Teperature (ºF) 10 02030405060
Alt
itu
de
(km
)1
23
45
6
Altitude (km) 1 023456
Tim
e (m
inu
tes)
1020
3040
5060
s
Cha
pter
710
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Op
erat
ion
s o
n F
un
ctio
ns
Lesson 7-1
Cha
pter
711
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Rel
ativ
e M
axim
um
Val
ues
Th
e gr
aph
of
f(x)
�x3
�6x
�9
show
s a
rela
tive
max
imu
m v
alu
e so
mew
her
e be
twee
n f
(�2)
an
d f(
�1)
. You
can
obt
ain
a
clos
er a
ppro
xim
atio
n b
y co
mpa
rin
g va
lues
su
ch a
s th
ose
show
n i
n t
he
tabl
e.
To t
he
nea
rest
ten
th a
rel
ativ
e m
axim
um
va
lue
for
f(x)
is
�3.
3.
Usi
ng
a ca
lcu
lato
r to
fin
d p
oin
ts, g
rap
h e
ach
fu
nct
ion
. To
the
nea
rest
te
nth
, fin
d a
rel
ativ
e m
axim
um
val
ue
of t
he
fun
ctio
n.
1.f(
x) �
x(x2
�3)
rel.
max
.of
2.0
2.f(
x) �
x3�
3x�
3re
l.m
ax.o
f �
1.0
3.f(
x) �
x3�
9x�
2re
l.m
ax.o
f 8.
44.
f(x)
�x3
�2x
2�
12x
�24
rel.
max
.of
3.3
5
x
f(x)
O1
2
x
f(x)
O2
x
f(x)
O
x
f(x)
O
xf(
x)
�2
�5
�1.
5�
3.37
5
�1.
4�
3.34
4
�1.
3�
3.39
7
�1
�4
x
f(x)
O2
–2–4 –8 –12
–16
–20
–44
f(x)
� x
3 �
6x
� 9
Enri
chm
ent
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A4
Chapter 7 A5 Glencoe Algebra 2
An
swer
s
Answers (Lessons 7-1 and 7-2)
Cha
pter
712
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Spre
adsh
eet
Act
ivit
yO
per
atio
ns
on
Fu
nct
ion
s
Stu
dy
and
use
th
e sp
read
shee
t ab
ove.
1.F
ind
k(x)
�(3
x�
2) �
(x2
�2x
). H
ow d
oes
it c
ompa
re t
o h
(x)?
k(x)
�x
2�
x�
2 �
h(x
)
2.C
hang
e th
e fu
ncti
ons
in t
he s
prea
dshe
et t
o f(
x) �
� 2x �, g
(x)
�1
�x2
, and
h(x)
�1
�� 2x �
�x2
. How
are
th
ese
fun
ctio
ns
rela
ted?
Is
it t
rue
that
f(x)
�g(
x) �
h(x
)?(f
�g
)(x)
�h
(x);
yes
3.M
ake
a co
nje
ctu
re a
bou
t (f
�g)
(x)
for
any
fun
ctio
ns
f(x)
an
d g(
x).
(f�
g)(
x) �
f(x)
�g
(x)
4.M
ake
a co
nje
ctu
re a
bou
t (f
�g)
(x)
for
any
fun
ctio
ns
f(x)
an
d g(
x). U
se t
he
spre
adsh
eet
to t
est
you
r co
nje
ctu
re. D
oes
it a
ppea
r to
be
tru
e? E
xpla
inyo
ur
answ
er.
(f�
g)(
x) �
f(x)
�g
(x);
See
stu
den
ts’w
ork
.
Fin
d (
f�
g)(x
), (
f�
g)(x
), f
or e
ach
f(x
) an
d g
(x).
Use
th
e sp
read
shee
t to
fi
nd
fu
nct
ion
val
ues
to
veri
fy y
our
solu
tion
s. 5-
7.S
ee s
tud
ents
’sp
read
shee
ts.
5.f(
x) �
6x�
86.
f(x)
�x2
�1
7.f(
x) �
10x2
g(x)
�9
�x
g(x)
�3x
�4
g(x)
�6
�x2
7x�
17;
5x�
1x
2�
3x�
3;x
2�
3x�
59x
2�
6;11
x2
�6
It i
s po
ssib
le t
o pe
rfor
m o
pera
tion
s on
fu
nct
ion
s su
ch a
s ad
diti
on,
subt
ract
ion
, mu
ltip
lica
tion
an
d di
visi
on. Y
ou c
an u
se a
spr
eads
hee
t to
in
vest
igat
e th
e re
lati
onsh
ips
amon
g fu
nct
ion
s.
Con
sid
er t
he
fun
ctio
ns
f(x)
�3x
�2,
g(x
) �
x2�
2x, a
nd
h(x
) �
x2�
x+
2.F
ind
th
e fu
nct
ion
val
ues
of
each
fu
nct
ion
for
sev
eral
val
ues
of
x.D
oes
it a
pp
ear
that
f(x
) �
g(x)
�h
(x)?
Use
Col
um
n A
for
the
chos
en v
alu
es o
f x.
Col
um
ns
B, C
, an
d E
are
f(x
), g
(x),
an
d h
(x)
resp
ecti
vely
. Use
Col
um
n D
for
f(x
)�g(
x).
For
eve
ry v
alu
e of
x, f
(x)�
g(x)
�h
(x).
A1 9Fu
nct
ion
s.xl
s
x2 3 4 5 6 7 8
0–1–2
.5–4 1 4 12
Bf(
x)
2–1–5
.5–1
0 5 14 38
Cg(
x)
0311
.2524 –1 8
120
Eh(
x)
225.
7514 4 22 158
Df(
x) +
g(x
) 225.
7514 4 22 158
Sh
eet
1S
hee
t 2
Sh
eet
3
Exer
cise
s
Lesson 7-2
Cha
pter
713
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Inve
rse
Fu
nct
ion
s an
d R
elat
ion
sG
et R
ead
y fo
r th
e Le
sso
nR
ead
th
e in
trod
uct
ion
to
Les
son
7-2
in
you
r te
xtb
ook
.
Afu
ncti
on m
ulti
plie
s a
num
ber
by 3
and
the
n ad
ds 5
to
the
resu
lt.
Wha
t do
es t
he
inve
rse
fun
ctio
n d
o, a
nd
in w
hat
ord
er?
Sam
ple
an
swer
:It
fir
st s
ub
trac
ts 5
fro
m t
he
nu
mb
er a
nd
th
en d
ivid
es t
he
resu
lt b
y 3.
Rea
d t
he
Less
on
1.C
ompl
ete
each
sta
tem
ent.
a.If
tw
o re
lati
ons
are
inve
rses
, th
e do
mai
n o
f on
e re
lati
on i
s th
e of
the
oth
er.
b.
Su
ppos
e th
at g
is a
rel
atio
n a
nd
that
th
e po
int
(4, �
2) i
s on
its
gra
ph. T
hen
a p
oin
t
on t
he
grap
h o
f g�
1is
.
c.T
he
test
can
be
use
d on
th
e gr
aph
of
a fu
nct
ion
to
dete
rmin
e
wh
eth
er t
he
fun
ctio
n h
as a
n i
nve
rse
fun
ctio
n.
d.
If y
ou a
re g
iven
th
e gr
aph
of
a fu
nct
ion
, you
can
fin
d th
e gr
aph
of
its
inve
rse
by
refl
ecti
ng
the
orig
inal
gra
ph o
ver
the
lin
e w
ith
equ
atio
n
.
e.If
fan
d g
are
inve
rse
fun
ctio
ns,
th
en (
f�
g)(x
) �
an
d
(g�
f)(x
) �
.
f.A
fun
ctio
n h
as a
n i
nve
rse
that
is
also
a f
un
ctio
n o
nly
if
the
give
n f
un
ctio
n i
s
.
g.S
upp
ose
that
h(x
) is
a f
un
ctio
n w
hos
e in
vers
e is
als
o a
fun
ctio
n. I
f h
(5)
�12
, th
enh
�1 (
12)
�.
2.A
ssu
me
that
f(x
) is
a o
ne-
to-o
ne
fun
ctio
n d
efin
ed b
y an
alg
ebra
ic e
quat
ion
. Wri
te t
he
fou
r st
eps
you
wou
ld f
ollo
w i
n o
rder
to
fin
d th
e eq
uat
ion
for
f�
1 (x)
.
1.R
epla
ce f
(x)
wit
h y
in t
he
ori
gin
al e
qu
atio
n.
2.In
terc
han
ge
xan
d y
.
3.S
olv
e fo
r y.
4.R
epla
ce y
wit
h f
�1 (
x).
Rem
emb
er W
hat
Yo
u L
earn
ed
3.A
good
way
to
rem
embe
r so
met
hin
g n
ew i
s to
rel
ate
it t
o so
met
hin
g yo
u a
lrea
dy k
now
.H
ow a
re t
he v
erti
cal
and
hori
zont
al l
ine
test
s re
late
d?S
amp
le a
nsw
er:T
he
vert
ical
line
test
det
erm
ines
wh
eth
er a
rel
atio
n is
a f
un
ctio
n b
ecau
se t
he
ord
ered
pai
rs in
a f
un
ctio
n c
an h
ave
no
rep
eate
d x
-val
ues
.Th
e h
ori
zon
tal l
ine
test
det
erm
ines
wh
eth
er a
fu
nct
ion
is o
ne-
to-o
ne
bec
ause
a o
ne-
to-o
ne
fun
ctio
n c
ann
ot
hav
e an
y re
pea
ted
y-v
alu
es.
5
on
e-to
-on
e
xx
y �
x
ho
rizo
nta
l lin
e
(�2,
4)
ran
ge
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A5
Chapter 7 A6 Glencoe Algebra 2
Answers (Lesson 7-2)
Exam
ple
Exer
cise
s
Cha
pter
714
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y Gu
ide
and
Inte
rven
tion
Inve
rse
Fu
nct
ion
s an
d R
elat
ion
sFi
nd
Inve
rses
Inve
rse
Rel
atio
ns
Two
rela
tions
are
inve
rse
rela
tions
if a
nd o
nly
if w
hene
ver
one
rela
tion
cont
ains
the
el
emen
t (a
, b
), t
he o
ther
rel
atio
n co
ntai
ns t
he e
lem
ent
(b,
a).
Pro
per
ty o
f In
vers
e S
uppo
se f
and
f�1
are
inve
rse
func
tions
.F
un
ctio
ns
The
n f(
a) �
bif
and
only
if f
�1 (
b) �
a.
Fin
d t
he
inve
rse
of t
he
fun
ctio
n f
(x)
�x
�. T
hen
gra
ph
th
efu
nct
ion
an
d i
ts i
nve
rse.
Ste
p 1
Rep
lace
f(x
) w
ith
yin
th
e or
igin
al e
quat
ion
.
f(x)
��2 5� x
�→
y�
�2 5� x�
Ste
p 2
Inte
rch
ange
xan
d y.
x�
�2 5� y�
Ste
p 3
Sol
ve f
or y
.
x�
�2 5� y�
Inve
rse
5x�
2y�
1M
ultip
ly e
ach
side
by
5.
5x�
1 �
2yA
dd 1
to
each
sid
e.
(5x
�1)
�y
Div
ide
each
sid
e by
2.
Th
e in
vers
e of
f(x
) �
�2 5� x�
is f
�1 (
x) �
(5x
�1)
.
Fin
d t
he
inve
rse
of e
ach
fu
nct
ion
. Th
en g
rap
h t
he
fun
ctio
n a
nd
its
in
vers
e.
1.f(
x) �
x�
12.
f(x)
�2x
�3
3.f(
x) �
x�
2
f�1 (
x)
�x
�f�
1 (x
) �
x�
f�1 (
x)
�4x
�8
f–1(x
) � 4
x �
8
f(x)
� 1 – 4x
� 2 x
f(x)
O
f(x)
� 2
x �
3
f–1(x
) � 1 – 2x
� 3 – 2
x
f(x)
O
f(x)
� 2 – 3x
� 1
f–1(x
) � 3 – 2x
� 3 – 2
x
f(x)
O
3 � 21 � 2
3 � 23 � 2
1 � 42 � 3
1 � 21 � 5
1 � 2
1 � 51 � 5
1 � 51 � 5
x
f(x)
O
f(x)
� 2 – 5x
� 1 – 5
f–1(x
) � 5 – 2x
� 1 – 2
1 � 52 � 5
Exam
ple
1
Exam
ple
2
7-2
Lesson 7-2
Cha
pter
715
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Inve
rses
of
Rel
atio
ns
and
Fu
nct
ion
s
Inve
rse
Fu
nct
ion
sTw
o fu
nctio
ns f
and
gar
e in
vers
e fu
nctio
ns if
and
onl
y if
[f�
g](
x) �
xan
d [g
�f]
(x)
�x.
Det
erm
ine
wh
eth
er f
(x)
�2x
�7
and
g(x
) �
(x�
7) a
re
inve
rse
fun
ctio
ns.
[f�
g](x
) �
f[g(
x)]
[g�
f](x
) �
g[f(
x)]
�f ��1 2� (
x�
7)�
�g(
2x�
7)
�2 ��1 2� (
x�
7)��
7�
�1 2� (2x
�7
�7)
�x
�7
�7
�x
�x
Th
e fu
nct
ion
s ar
e in
vers
es s
ince
bot
h [
f�
g](x
) �
xan
d [g
�f]
(x)
�x.
Det
erm
ine
wh
eth
er f
(x)
�4x
�an
d g
(x)
�x
�3
are
inve
rse
fun
ctio
ns.
[f�
g](x
) �
f[g(
x)]
�f ��1 4� x
�3 �
�4 ��1 4� x
�3 �
��1 3�
�x
�12
��1 3�
�x
�11
�2 3�
Sin
ce [
f�
g](x
) �
x, t
he
fun
ctio
ns
are
not
in
vers
es.
Det
erm
ine
wh
eth
er e
ach
pai
r of
fu
nct
ion
s ar
e in
vers
e fu
nct
ion
s.
1.f(
x) �
3x�
12.
f(x)
��1 4� x
�5
3.f(
x) �
�1 2� x�
10
g(x)
��1 3� x
��1 3�
yes
g(x)
�4x
�20
yes
g(x)
�2x
�� 11 0�
no
4.f(
x) �
2x�
55.
f(x)
�8x
�12
6.f(
x) �
�2x
�3
g(x)
�5x
�2
no
g(x)
��1 8� x
�12
no
g(x)
��
�1 2� x�
�3 2�ye
s
7.f(
x) �
4x�
�1 2�8.
f(x)
�2x
��3 5�
9.f(
x) �
4x�
�1 2�
g(x)
��1 4� x
��1 8�
yes
g(x)
�� 11 0�
(5x
�3)
yes
g(x)
��1 2� x
��3 2�
no
10.f
(x)
�10
�� 2x �
11.f
(x)
�4x
��4 5�
12.f
(x)
�9
��3 2� x
g(x)
�20
�2x
yes
g(x)
�� 4x �
��1 5�
yes
g(x)
��2 3� x
�6
yes
1 � 41 � 3
1 � 2
Stud
y Gu
ide
and
Inte
rven
tion
(con
tinue
d)
Inve
rse
Fu
nct
ion
s an
d R
elat
ion
s
Exer
cise
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A6
Chapter 7 A7 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-2)
Cha
pter
716
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
actic
eIn
vers
e F
un
ctio
ns
and
Rel
atio
ns
Fin
d t
he
inve
rse
of e
ach
rel
atio
n.
1.{(
3, 1
), (
4, �
3), (
8, �
3)}
2.{(
�7,
1),
(0,
5),
(5,
�1)
}{(
1,3)
,(�
3,4)
,(�
3,8)
}{(
1,�
7),(
5,0)
,(�
1,5)
}
3.{(
�10
, �2)
, (�
7, 6
), (
�4,
�2)
, (�
4, 0
)}4.
{(0,
�9)
, (5,
�3)
, (6,
6),
(8,
�3)
}{(
�2,
�10
),(6
,�7)
,(�
2,�
4),(
0,�
4)}
{(�
9,0)
,(�
3,5)
,(6,
6),(
�3,
8)}
5.{(
�4,
12)
, (0,
7),
(9,
�1)
, (10
, �5)
}6.
{(�
4, 1
), (
�4,
3),
(0,
�8)
, (8,
�9)
}{(
12,�
4),(
7,0)
,(�
1,9)
,(�
5,10
)}{(
1,�
4),(
3,�
4),(
�8,
0),(
�9,
8)}
Fin
d t
he
inve
rse
of e
ach
fu
nct
ion
. Th
en g
rap
h t
he
fun
ctio
n a
nd
its
in
vers
e.
7.y
�4
8.f(
x) �
3x9.
f(x)
�x
�2
x�
4f�
1 (x
) �
�1 3� xf�
1 (x
) �
x�
2
10.g
(x)
�2x
�1
11.h
(x)
��1 4� x
12.y
��2 3� x
�2
g�
1 (x
) �
�x� 2
1�
h�
1 (x
) �
4xy
��3 2� x
�3
Det
erm
ine
wh
eth
er e
ach
pai
r of
fu
nct
ion
s ar
e in
vers
e fu
nct
ion
s.
13.f
(x)
�x
�1
no
14.f
(x)
�2x
�3
yes
15.f
(x)
�5x
�5
yes
g(x)
�1
�x
g(x)
��1 2� (
x�
3)g(
x) �
�1 5� x�
1
16.f
(x)
�2x
yes
17.h
(x)
�6x
�2
no
18.f
(x)
�8x
�10
yes
g(x)
��1 2� x
g(x)
��1 6� x
�3
g(x)
��1 8� x
��5 4�
x
y
Ox
h(x)
Ox
g(x)
O
x
f(x)
Ox
f(x)
Ox
y
O
7-2
Lesson 7-2
Cha
pter
717
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Fin
d t
he
inve
rse
of e
ach
rel
atio
n.
1.{(
0, 3
), (
4, 2
), (
5, �
6)}
2.{(
�5,
1),
(�
5, �
1), (
�5,
8)}
{(3,
0),(
2,4)
,(�
6,5)
}{(
1,�
5),(
�1,
�5)
,(8,
�5)
}
3.{(
�3,
�7)
, (0,
�1)
, (5,
9),
(7,
13)
}4.
{(8,
�2)
, (10
, 5),
(12
, 6),
(14
, 7)}
{(�
7,�
3),(
�1,
0),(
9,5)
,(13
,7)}
{(�
2,8)
,(5,
10),
(6,1
2),(
7,14
)}
5.{(
�5,
�4)
, (1,
2),
(3,
4),
(7,
8)}
6.{(
�3,
9),
(�
2, 4
), (
0, 0
), (
1, 1
)}{(
�4,
�5)
,(2,
1),(
4,3)
,(8,
7)}
{(9,
�3)
,(4,
�2)
,(0,
0),(
1,1)
}
Fin
d t
he
inve
rse
of e
ach
fu
nct
ion
. Th
en g
rap
h t
he
fun
ctio
n a
nd
its
in
vers
e.
7.f(
x) �
�3 4� x8.
g(x)
�3
�x
9.y
�3x
�2
f�1 (
x)
��4 3� x
g�
1 (x
) �
x�
3y
��x
� 32
�
Det
erm
ine
wh
eth
er e
ach
pai
r of
fu
nct
ion
s ar
e in
vers
e fu
nct
ion
s.
10.f
(x)
�x
�6
yes
11.f
(x)
��
4x�
1ye
s12
.g(x
) �
13x
�13
no
g(x)
�x
�6
g(x)
��1 4� (
1 �
x)h
(x)
�� 11 3�
x�
1
13.f
(x)
�2x
no
14.f
(x)
��6 7� x
yes
15.g
(x)
�2x
�8
yes
g(x)
��
2xg(
x) �
�7 6� xh
(x)
��1 2� x
�4
16. M
EASU
REM
ENT
Th
e po
ints
(63
, 121
), (
71, 1
80),
(67
, 140
), (
65, 1
08),
an
d (7
2, 1
65)
give
the
wei
ght
in p
oun
ds a
s a
fun
ctio
n o
f h
eigh
t in
in
ches
for
5 s
tude
nts
in
a c
lass
. Giv
e th
epo
ints
for
th
ese
stu
den
ts t
hat
rep
rese
nt
hei
ght
as a
fu
nct
ion
of
wei
ght.
(121
,63)
,(18
0,71
),(1
40,6
7),(
108,
65),
(165
,72)
REM
OD
ELIN
GF
or E
xerc
ises
17
and
18,
use
th
e fo
llow
ing
info
rmat
ion
.T
he
Cle
arys
are
rep
laci
ng
the
floo
rin
g in
th
eir
15 f
oot
by 1
8 fo
ot k
itch
en. T
he
new
flo
orin
gco
sts
$17.
99 p
er s
quar
e ya
rd. T
he
form
ula
f(x
) �
9xco
nve
rts
squ
are
yard
s to
squ
are
feet
.
17.F
ind
the
inve
rse
f�1 (
x). W
hat
is
the
sign
ific
ance
of
f�1 (
x) f
or t
he
Cle
arys
?f�
1 (x
) �
�x 9� ;It
will
allo
w t
hem
to
co
nver
t th
e sq
uar
e fo
ota
ge
of
thei
r ki
tch
en f
loo
r to
squ
are
yard
s,so
th
ey c
an t
hen
cal
cula
te t
he
cost
of
the
new
flo
ori
ng
.
18.W
hat
wil
l th
e n
ew f
loor
ing
cost
th
e C
lear
y’s?
$539
.70
x
y
Ox
g(x)
Ox
f(x)
OPrac
tice
Inve
rse
Fu
nct
ion
s an
d R
elat
ion
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A7
Chapter 7 A8 Glencoe Algebra 2
Answers (Lesson 7-2)
1.V
OLU
ME
Jaso
n w
ants
to
mak
e a
sph
eric
al w
ater
coo
ler
that
can
hol
d h
alf
a cu
bic
met
er o
f w
ater
. He
know
s th
at
V�
�
r3, b
ut
he
nee
ds t
o kn
ow h
ow t
o
fin
d r
give
n V
. Fin
d th
is i
nve
rse
fun
ctio
n.
r�
�3�
2.EX
ERC
ISE
Ale
x be
gan
a n
ew e
xerc
ise
rou
tin
e. T
o ga
in t
he
max
imu
m b
enef
itfr
om h
is e
xerc
ise,
Ale
x ca
lcu
late
d h
ism
axim
um
tar
get
hea
rt r
ate
usi
ng
the
fun
ctio
n. f
(x)
�0.
85(2
20 �
x) w
her
e x
repr
esen
ts h
is a
ge. F
ind
the
inve
rse
ofth
is f
un
ctio
n.
f�1 (
x) �
220
�
3.R
OC
KET
ST
he
alti
tude
of
a ro
cket
in
feet
as
a fu
nct
ion
of
tim
e is
giv
en b
yf(
t) =
49t
2 , w
her
e t
≥0.
Fin
d th
e in
vers
eof
th
is f
un
ctio
n a
nd
dete
rmin
e th
e ti
mes
wh
en t
he
rock
et w
ill
be 1
0, 1
00, a
nd
1000
fee
t h
igh
. Rou
nd
you
r an
swer
s to
the
nea
rest
hu
ndr
edth
of
a se
con
d.
f�1 (
t) �
; 10
ft a
t 0.
45 s
,
100
ft a
t 1.
43 s
, 100
0 ft
at
4.52
s
4.SE
LF-I
NV
ERTI
BLE
Kar
en f
inds
th
ein
com
plet
e gr
aph
of
a fu
nct
ion
in
th
eba
ck o
f h
er e
ngi
nee
rin
g h
andb
ook.
Th
efu
nct
ion
is
grap
hed
in
th
e fi
gure
bel
ow.
Kar
en k
now
s th
at t
his
fu
nct
ion
is
its
own
in
vers
e. A
rmed
wit
h t
his
know
ledg
e, e
xten
d th
e gr
aph
for
va
lues
of
xbe
twee
n �
7 an
d 2.
PLA
NET
SF
or E
xerc
ises
5 a
nd
6, u
seth
e fo
llow
ing
info
rmat
ion
.
Th
e ap
prox
imat
e di
stan
ce o
f a
plan
et f
rom
th
e S
un
is
give
n b
y d
�T
�2 3�w
her
e d
is
dist
ance
in
ast
ron
omic
al u
nit
s an
d T
isE
arth
yea
rs. A
n a
stro
nom
ical
un
it i
s th
edi
stan
ce o
f th
e E
arth
fro
m t
he
Su
n.
5.S
olve
for
Tin
ter
ms
of d
.T
�d
1.5
6.P
luto
is
abou
t 39
.44
tim
es a
s fa
r fr
omth
e S
un
as
the
Ear
th. A
bou
t h
ow m
any
year
s do
es i
t ta
ke P
luto
to
orbi
t th
eS
un
? 24
8 yr
y
xO
5
5
-5
-5
�t �
�7
x� 0.
85
3V � 4�
4 � 3
Cha
pter
718
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Inve
rse
Fu
nct
ion
s an
d R
elat
ion
s
Lesson 7-2
Cha
pter
719
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
Rea
din
g A
lgeb
raIn
mat
hem
atic
s, t
he
term
gro
up
has
a s
peci
al m
ean
ing.
Th
e fo
llow
ing
nu
mbe
red
sen
ten
ces
disc
uss
th
e id
ea o
f gr
oup
and
one
inte
rest
ing
exam
ple
of a
gro
up.
01To
be
a gr
oup,
a s
et o
f el
emen
ts a
nd
a bi
nar
y op
erat
ion
mu
st s
atis
fy f
our
con
diti
ons:
th
e se
t m
ust
be
clos
ed u
nde
r th
e op
erat
ion
, th
e op
erat
ion
mu
st b
e as
soci
ativ
e, t
her
e m
ust
be
an i
den
tity
ele
men
t, a
nd
ever
yel
emen
t m
ust
hav
e an
in
vers
e.
02T
he
foll
owin
g si
x fu
nct
ion
s fo
rm a
gro
up
un
der
the
oper
atio
n o
f
com
posi
tion
of
fun
ctio
ns:
f1(
x) �
x,f 2
(x)
��1 x� ,
f3(
x) �
1 �
x,
f 4(x
) �
�(x� x
1)�
, f5(
x) �
� (x�x
1)�
, an
d f 6
(x)
�� (1
�1x)
�.
03T
his
gro
up
is a
n e
xam
ple
of a
non
com
mu
tati
ve g
rou
p. F
or e
xam
ple,
f 3�
f 2�
f 4, b
ut
f 2�
f 3�
f 6.
04S
ome
expe
rim
enta
tion
wit
h t
his
gro
up
wil
l sh
ow t
hat
th
e id
enti
tyel
emen
t is
f1.
05E
very
ele
men
t is
its
ow
n i
nve
rse
exce
pt f
or f
4an
d f 6
, eac
h o
f w
hic
h i
s th
ein
vers
e of
th
e ot
her
.
Use
th
e p
arag
rap
h t
o an
swer
th
ese
qu
esti
ons.
1.E
xpla
in w
hat
it
mea
ns
to s
ay t
hat
a s
et i
s cl
osed
un
der
an o
pera
tion
. Is
the
set
of p
osit
ive
inte
gers
clo
sed
un
der
subt
ract
ion
?P
erfo
rmin
g t
he
op
er-
atio
n o
n a
ny t
wo
ele
men
ts o
f th
e se
t re
sult
s in
an
ele
men
t o
f th
esa
me
set.
No
,3 a
nd
4 a
re p
osi
tive
inte
ger
s bu
t 3
� 4
is n
ot.
2.S
ubt
ract
ion
is
a n
onco
mm
uta
tive
ope
rati
on f
or t
he
set
of i
nte
gers
. Wri
tean
in
form
al d
efin
itio
n o
f n
onco
mm
uta
tive
.T
he
ord
er in
wh
ich
th
eel
emen
ts a
re u
sed
wit
h t
he
op
erat
ion
can
aff
ect
the
resu
lt.
3.F
or t
he
set
of i
nte
gers
, wh
at i
s th
e id
enti
ty e
lem
ent
for
the
oper
atio
n o
fm
ult
ipli
cati
on?
Just
ify
you
r an
swer
. 1,
bec
ause
,fo
r ev
ery
inte
ger
a,a
�1
�a
and
1 �
a�
a.
4.E
xpla
in h
ow t
he
foll
owin
g st
atem
ent
rela
tes
to s
ente
nce
05:
(f6
�f 4
)(x)
�f 6
[f4(
x)]
�f 6�� (1
�1x)
���
�x
�f 1
(x).
It s
ho
ws
that
f4
is t
he
inve
rse
of
f 6.1
��
�1�
(x x�
1)�
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A8
Chapter 7 A9 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-3)
Cha
pter
720
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Sq
uar
e R
oo
t F
un
ctio
ns
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 7
-3 i
n y
our
text
boo
k.
If t
he
wei
ght
to b
e su
ppor
ted
by a
ste
el c
able
is
dou
bled
, sh
ould
th
e di
amet
er o
f th
e su
ppor
tca
ble
also
be
dou
bled
? If
not
, by
wh
at n
um
ber
shou
ld t
he
diam
eter
be
mu
ltip
lied
?
no
;�
2�
Rea
d t
he
Less
on
1.M
atch
eac
h s
quar
e ro
ot f
un
ctio
n f
rom
th
e li
st o
n t
he
left
wit
h i
ts d
omai
n a
nd
ran
ge f
rom
the
list
on
th
e ri
ght.
a.y
��
x�iv
i.do
mai
n: x
�0;
ran
ge: y
�3
b.
y�
�x
�3
�vi
iiii
.do
mai
n: x
�0;
ran
ge: y
�0
c.y
��
x��
3i
iii.
dom
ain
: x�
0; r
ange
: y�
�3
d.
y�
�x
�3
�v
iv.
dom
ain
: x�
0; r
ange
: y�
0
e.y
��
�x�
iiv.
dom
ain
: x�
3; r
ange
: y�
0
f.y
��
�x
�3
�vi
ivi
.do
mai
n: x
�3;
ran
ge: y
�3
g.y
��
3 �
x�
�3
vivi
i.do
mai
n: x
�3;
ran
ge: y
�0
h.
y�
��
x��
3iii
viii
.do
mai
n: x
��
3; r
ange
: y�
0
2.T
he
grap
h o
f th
e in
equ
alit
y y
��
3x�
6�
is a
sh
aded
reg
ion
. Wh
ich
of
the
foll
owin
gpo
ints
lie
in
side
th
is r
egio
n?
(3, 0
)(2
, 4)
(5, 2
)(4
, �2)
(6, 6
)
(3,0
),(5
,2),
(4,�
2)
Rem
emb
er W
hat
Yo
u L
earn
ed
3.A
good
way
to
rem
embe
r so
met
hin
g is
to
expl
ain
it
to s
omeo
ne
else
. Su
ppos
e yo
u a
rest
udy
ing
this
les
son
wit
h a
cla
ssm
ate
wh
o th
inks
th
at y
ou c
ann
ot h
ave
squ
are
root
fun
ctio
ns
beca
use
eve
ry p
osit
ive
real
nu
mbe
r h
as t
wo
squ
are
root
s. H
ow w
ould
you
expl
ain
th
e id
ea o
f sq
uar
e ro
ot f
un
ctio
ns
to y
our
clas
smat
e?
Sam
ple
an
swer
:To
fo
rm a
sq
uar
e ro
ot
fun
ctio
n,c
ho
ose
eit
her
the
po
siti
ve o
r n
egat
ive
squ
are
roo
t.F
or
exam
ple
,y�
�x�
and
y�
��
x�ar
etw
o s
epar
ate
fun
ctio
ns.
Exam
ple
Lesson 7-3
Cha
pter
721
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y Gu
ide
and
Inte
rven
tion
Sq
uar
e R
oo
t F
un
ctio
ns
and
Ineq
ual
itie
sSq
uar
e R
oo
t Fu
nct
ion
sA
fun
ctio
n t
hat
con
tain
s th
e sq
uar
e ro
ot o
f a
vari
able
expr
essi
on i
s a
squ
are
root
fu
nct
ion
.
Gra
ph
y�
�3x
��
2�. S
tate
its
dom
ain
an
d r
ange
.
Sin
ce t
he
radi
can
d ca
nn
ot b
e n
egat
ive,
3x
�2
�0
or x
��2 3� .
Th
e x-
inte
rcep
t is
�2 3� . T
he
ran
ge i
s y
�0.
Mak
e a
tabl
e of
val
ues
an
d gr
aph
th
e fu
nct
ion
.
Gra
ph
eac
h f
un
ctio
n. S
tate
th
e d
omai
n a
nd
ran
ge o
f th
e fu
nct
ion
.
1.y
��
2x�2.
y�
�3�
x�3.
y�
���� 2x �
D:
x
0;R
:y
0
D:
x
0;R
:y
0
D:
x
0;R
:y
0
4.y
�2�
x�
3�
5.y
��
�2x
�3
�6.
y�
�2x
�5
�
D:
x
3;R
:y
0
D:
x
�3 2� ;R
:y
0
D:
x
��5 2� ;
R:
y
0
y �
��
�2x
� 5
x
y
O
y �
��
��
�2x
� 3
x
y
O
y �
2�
��
x �
3
x
y
O
y �
���x – 2
x
y
Oy
� �
3��x
xy
O
y �
��2x
x
y
O
xy
�2 3�0
11
22
3�
7�
x
y
O
y �
��
��
3x �
2
Exer
cise
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A9
Chapter 7 A10 Glencoe Algebra 2
Answers (Lesson 7-3)
Exam
ple
Exer
cise
s
Cha
pter
722
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Squ
are
Ro
ot
Ineq
ual
itie
sA
squ
are
root
in
equ
alit
yis
an
in
equ
alit
y th
at c
onta
ins
the
squ
are
root
of
a va
riab
le e
xpre
ssio
n. U
se w
hat
you
kn
ow a
bou
t gr
aph
ing
squ
are
root
fun
ctio
ns
and
quad
rati
c in
equ
alit
ies
to g
raph
squ
are
root
in
equ
alit
ies.
Gra
ph
y
�2x
��
1��
2.G
raph
th
e re
late
d eq
uat
ion
y�
�2x
�1
��
2. S
ince
th
e bo
un
dary
sh
ould
be
incl
ude
d, t
he
grap
h s
hou
ld b
e so
lid.
Th
e do
mai
n i
ncl
ude
s va
lues
for
x�
�1 2� , s
o th
e gr
aph
is
to t
he
righ
t
of x
��1 2� .
Gra
ph
eac
h i
neq
ual
ity.
1.y
2�
x�2.
y
�x
�3
�3.
y
3�2x
�1
�
4.y
�
3x�
4�
5.y
��
x�
1�
�4
6.y
2�
2x�
3�
7.y
��
3x�
1�
�2
8.y
��
4x�
2�
�1
9.y
2�
2x�
1�
�4
y �
2�
���
2x �
1 �
4 x
y
O
y �
���
�4x
� 2
� 1 x
y
Oy
� �
��
�3x
� 1
� 2
x
y
O
y �
2�
��
�2x
� 3 x
y
Oy
� �
��
x �
1 �
4
x
y
O
y �
���
�3x
� 4
x
y
O
y �
3�
���
2x �
1
x
y
O
y �
��
�x
� 3
x
y
O
y �
2�
�x
x
y
O
x
y
O
y �
��
��
2x �
1 �
2
Stud
y Gu
ide
and
Inte
rven
tion
(con
tinue
d)
Sq
uar
e R
oo
t F
un
ctio
ns
and
Ineq
ual
itie
s
Lesson 7-3
Cha
pter
723
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
actic
eS
qu
are
Ro
ot
Fu
nct
ion
s an
d In
equ
alit
ies
Gra
ph
eac
h f
un
ctio
n. S
tate
th
e d
omai
n a
nd
ran
ge o
f ea
ch f
un
ctio
n.
1.y
��
2x�2.
y�
��
3x�3.
y�
2�x�
D:
x
0,R
:y
0
D:
x
0,R
:y
0
D:
x
0,R
:y
0
4.y
��
x�
3�
5.y
��
�2x
�5
�6.
y�
�x
�4
��
2
D:
x
�3,
R:
y
0D
:x
2.
5,R
:y
0
D:
x
�4,
R:
y
�2
Gra
ph
eac
h i
neq
ual
ity.
7.y
�
4x�8.
y�
�x
�1
�9.
y�
�4x
�3
�
x
y
Ox
y
Ox
y
O
x
y
Ox
y
O
x
y
O
x
y
O
x
y
Ox
y
O
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A10
Chapter 7 A11 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-3)
Cha
pter
724
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Gra
ph
eac
h f
un
ctio
n. S
tate
th
e d
omai
n a
nd
ran
ge o
f ea
ch f
un
ctio
n.
1.y
��
5x�2.
y�
��
x�
1�
3.y
�2�
x�
2�
D:
x
0,R
:y
0
D:
x
1,R
:y
0
D:
x
�2,
R:
y
0
4.y
��
3x�
4�
5.y
��
x�
7�
�4
6.y
�1
��
2x�
3�
D:
x
�4 3� ,R
:y
0
D:
x
�7,
R:
y
�4
D:
x
��3 2� ,
R:
y
1
Gra
ph
eac
h i
neq
ual
ity.
7.y
��
�6x�
8.y
��
x�
5�
�3
9.y
�
2�3x
�2
�
10.R
OLL
ER C
OA
STER
ST
he
velo
city
of
a ro
ller
coa
ster
as
it m
oves
dow
n a
hil
l is
v
��
v 02
��
64h
�, w
her
e v 0
is t
he
init
ial
velo
city
an
d h
is t
he
vert
ical
dro
p in
fee
t. I
f v
�70
fee
t pe
r se
con
d an
d v 0
�8
feet
per
sec
ond,
fin
d h
.ab
ou
t 75
.6 f
t
11.W
EIG
HT
Use
th
e fo
rmu
la d
���
�39
60, w
hic
h r
elat
es d
ista
nce
fro
m E
arth
d
in m
iles
to
wei
ght.
If
an a
stro
nau
t’s w
eigh
t on
Ear
th W
Eis
148
pou
nds
an
d in
spa
ce W
sis
115
pou
nds
, how
far
fro
m E
arth
is
the
astr
onau
t?ab
ou
t 53
2 m
i
3960
2W
E�
� Ws
x
y O
x
y
O
x
y
O
x
y Ox
y
O
x
y
O
x
y
O
x
y
O
x
y
O
Prac
tice
Sq
uar
e R
oo
t F
un
ctio
ns
and
Ineq
ual
itie
s
Lesson 7-3
Cha
pter
725
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
7-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.SQ
UA
RES
Cat
hy
is b
uil
din
g a
squ
are
roof
for
her
gar
age.
Th
e ro
of w
ill
occu
py62
5 sq
uar
e fe
et.W
hat
are
th
edi
men
sion
s of
th
e ro
of?
25 f
t b
y 25
ft
2.PE
ND
ULU
MS
Th
e pe
riod
of
ape
ndu
lum
,th
e ti
me
it t
akes
to
com
plet
eon
e sw
ing,
is g
iven
by
the
form
ula
p�
2��
3�w
her
e L
is t
he
len
gth
of
the
pen
dulu
m a
nd
gis
acc
eler
atio
n d
ue
to g
ravi
ty,9
.8 m
/s2 .
Fin
d th
e pe
riod
of
ape
ndu
lum
th
at i
s 0.
65 m
eter
s lo
ng.
Rou
nd
to t
he
nea
rest
ten
th.
1.6
seco
nds
3.R
EFLE
XES
Rac
hel
an
d A
shle
y ar
ete
stin
g on
e an
oth
er’s
ref
lexe
s.R
ach
eldr
ops
a ru
ler
from
a g
iven
hei
ght
so t
hat
it f
alls
bet
wee
n A
shle
y’s
thu
mb
and
inde
x fi
nge
r.A
shle
y tr
ies
to c
atch
th
eru
ler
befo
re i
t fa
lls
thro
ugh
her
han
d.T
he
tim
e re
quir
ed t
o ca
tch
th
e ru
ler
is
give
n b
y t
�w
her
e d
is m
easu
red
infe
et.C
ompl
ete
the
tabl
e.R
oun
d yo
ur
answ
ers
to t
he
nea
rest
hu
ndr
edth
.
4.D
ISTA
NC
EL
ance
is
stan
din
g at
th
esi
de o
f a
road
wat
chin
g a
cycl
ist
go b
y.T
he
dist
ance
bet
wee
n L
ance
an
d th
ecy
clis
t as
a f
un
ctio
n o
f ti
me
is g
iven
by
d�
�9
�3
�6t
2�
.Gra
ph t
his
fu
nct
ion
.F
ind
the
dist
ance
bet
wee
n L
ance
an
dth
e cy
clis
t af
ter
3 se
con
ds.
18.2
5 m
STA
RS
For
Exe
rcis
es 5
-7,u
se t
he
foll
owin
g in
form
atio
n.
Th
e in
ten
sity
of
the
ligh
t fr
om a
n o
bjec
tva
ries
in
vers
ely
wit
h t
he
squ
are
of t
he
dist
ance
.In
oth
er w
ords
,I�
.
5.S
olve
the
equ
atio
n to
fin
d d
in t
erm
s of
I.
d�
��
6.T
wo
star
s gi
ve o
ff t
he
sam
e am
oun
t of
ligh
t.H
owev
er,f
rom
Ear
th t
hei
rin
ten
siti
es d
iffe
r.L
et I
1an
d I 2
be t
hei
rin
ten
siti
es a
nd
let
d1
and
d2
be t
hei
rre
spec
tive
dis
tan
ces
from
Ear
th.W
hat
is
the
rati
o of
d2
to d
1?
��
��
7.If
on
e st
ar a
ppea
rs 9
tim
es a
s in
ten
se
as t
he
oth
er,h
ow m
uch
clo
ser
is i
t to
Ear
th?
3 ti
mes
as
clo
se
I 1I 2
� I 2
d2
� d1
kI � I
k � d2
y
xO
Dis
tan
ce (
in.)
Ref
lex
Tim
e (s
eco
nd
s)
3 in
.0.
136
in.
0.18
9 in
.0.
2212
in.
0.25
�d�
�4
L � gWor
d Pr
oble
m P
ract
ice
Sq
uar
e R
oo
t F
un
ctio
ns
and
Ineq
ual
itie
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A11
Chapter 7 A12 Glencoe Algebra 2
Answers (Lessons 7-3 and 7-4)
Cha
pter
726
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Rea
din
g A
lgeb
raIf
tw
o m
ath
emat
ical
pro
blem
s h
ave
basi
c st
ruct
ura
l si
mil
arit
ies,
th
ey a
re s
aid
to b
e an
alog
ous.
Usi
ng
anal
ogie
s is
on
e w
ay o
fdi
scov
erin
g an
d pr
ovin
g n
ew t
heo
rem
s.
Th
e fo
llow
ing
nu
mbe
red
sen
ten
ces
disc
uss
a t
hre
e-di
men
sion
alan
alog
y to
th
e P
yth
agor
ean
th
eore
m.
01C
onsi
der
a te
trah
edro
n w
ith
th
ree
perp
endi
cula
r fa
ces
that
mee
t at
ver
tex
O.
02S
uppo
se y
ou w
ant
to k
now
how
the
are
as A
, B,a
nd C
ofth
e th
ree
face
s th
at m
eet
at v
erte
x O
are
rela
ted
to t
he
area
Dof
th
e fa
ce o
ppos
ite
vert
ex O
.03
It i
s n
atu
ral
to e
xpec
t a
form
ula
an
alog
ous
to t
he
Pyt
hag
orea
n t
heo
rem
z2
�x2
�y2
, wh
ich
is
tru
e fo
r a
sim
ilar
sit
uat
ion
in
tw
o di
men
sion
s.04
To e
xplo
re t
he
thre
e-di
men
sion
al c
ase,
you
mig
ht
gues
s a
form
ula
an
d th
en t
ry t
o pr
ove
it.
05Tw
o re
ason
able
gu
esse
s ar
e D
3�
A3
�B
3�
C3
and
D2
�A
2�
B2
�C
2 .
Ref
er t
o th
e n
um
ber
ed s
ente
nce
s to
an
swer
th
e q
ues
tion
s.
1.U
se s
ente
nce
01
and
the
top
diag
ram
. Th
e pr
efix
tet
ra-
mea
ns
fou
r. W
rite
an
info
rmal
def
init
ion
of
tetr
ahed
ron
.
a th
ree-
dim
ensi
on
al f
igu
re w
ith
fo
ur
face
s
2.U
se s
ente
nce
02
and
the
top
diag
ram
. Wh
at a
re t
he
len
gth
s of
th
e si
des
ofea
ch f
ace
of t
he
tetr
ahed
ron
?a,
b,a
nd
c;
a,q
,an
d r
;b
,p,a
nd
r;
c,p
,an
d q
3.R
ewri
te s
ente
nce
01
to s
tate
a t
wo-
dim
ensi
onal
an
alog
ue.
Co
nsi
der
a t
rian
gle
wit
h t
wo
per
pen
dic
ula
r si
des
th
at m
eet
at v
erte
x C
.
4.R
efer
to
the
top
diag
ram
an
d w
rite
exp
ress
ion
s fo
r th
e ar
eas
A, B
,an
d C
men
tion
ed i
n s
ente
nce
02.
Po
ssib
le a
nsw
er:
A�
�1 2� pr,
B�
�1 2� pq
,C�
�1 2� rq
5.To
exp
lore
th
e th
ree-
dim
ensi
onal
cas
e, y
ou m
igh
t be
gin
by
expr
essi
ng
a, b
,an
d c
in t
erm
s of
p, q
,an
d r.
Use
th
e P
yth
agor
ean
th
eore
m t
o do
th
is.
a2
�q
2�
r2,b
2�
r2�
p2,c
2�
p2
�q
2
6.W
hic
h g
ues
s in
sen
ten
ce 0
5 se
ems
mor
e li
kely
? Ju
stif
y yo
ur
answ
er.
See
stu
den
ts’e
xpla
nat
ion
s.
y O
z
x
b
c
Op
a
qr
Enri
chm
ent
Lesson 7-4
Cha
pter
727
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
nth
Ro
ots
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 7
-4 i
n y
our
text
boo
k.
Aba
sket
ball
has
a v
olu
me
of a
bou
t 38
2 cu
bic
inch
es. E
xpla
in h
ow y
ou w
ould
fin
d th
e ra
diu
sof
th
e ba
sket
ball
usi
ng
a ca
lcu
lato
r. (
Do
not
act
ual
ly c
alcu
late
th
e ra
diu
s.)
Sam
ple
an
swer
:U
sin
g a
cal
cula
tor,
fin
d t
he
pro
du
ct o
f 3
tim
es t
he
volu
me.
Div
ide
th
is n
um
ber
by
4�.T
hen
fin
d t
he
po
siti
ve c
ub
e ro
ot
resu
lt.R
ou
nd
the
answ
er t
o t
he
nea
rest
ten
th.
Rea
d t
he
Less
on
1.F
or e
ach
rad
ical
bel
ow, i
den
tify
th
e ra
dica
nd
and
the
inde
x.
a.3 �
23�ra
dica
nd:
in
dex:
b.
�15
x2�
radi
can
d:
inde
x:
c.5 �
�34
3�
radi
can
d:
inde
x:
2.C
ompl
ete
the
foll
owin
g ta
ble.
(D
o n
ot a
ctu
ally
fin
d an
y of
th
e in
dica
ted
root
s.)
Nu
mb
erN
um
ber
of
Po
siti
ve
Nu
mb
er o
f N
egat
ive
Nu
mb
er o
f P
osi
tive
N
um
ber
of
Neg
ativ
eS
qu
are
Ro
ots
Sq
uar
e R
oo
tsC
ub
e R
oo
ts
Cu
be
Ro
ots
271
11
0
�16
00
01
3.S
tate
wh
eth
er e
ach
of
the
foll
owin
g is
tru
eor
fal
se.
a.A
neg
ativ
e n
um
ber
has
no
real
fou
rth
roo
ts.
tru
e
b.
��
121
�re
pres
ents
bot
h s
quar
e ro
ots
of 1
21.
tru
e
c.W
hen
you
tak
e th
e fi
fth
roo
t of
x5 ,
you
mu
st t
ake
the
abso
lute
val
ue
of x
to i
den
tify
the
prin
cipa
l fi
fth
roo
t.fa
lse
Rem
emb
er W
hat
Yo
u L
earn
ed
4.W
hat
is
an e
asy
way
to
rem
embe
r th
at a
neg
ativ
e n
um
ber
has
no
real
squ
are
root
s bu
th
as o
ne
real
cu
be r
oot?
Sam
ple
an
swer
:Th
e sq
uar
e o
f a
po
siti
ve o
r n
egat
ive
nu
mb
er is
po
siti
ve,s
o t
her
e is
no
rea
l nu
mb
er w
ho
se s
qu
are
is n
egat
ive.
Ho
wev
er,t
he
cub
e o
f a
neg
ativ
e n
um
ber
is n
egat
ive,
so a
neg
ativ
en
um
ber
has
on
e re
al c
ub
e ro
ot,
wh
ich
is a
neg
ativ
e n
um
ber
.
5�
343
215
x2
323
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A12
Chapter 7 A13 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-4)
Cha
pter
728
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
nth
Ro
ots
Sim
plif
y R
adic
als
Sq
uar
e R
oo
tF
or a
ny r
eal n
umbe
rs a
and
b, if
a2
�b,
the
n a
is a
squ
are
root
of
b.
nth
Ro
ot
For
any
rea
l num
bers
aan
d b,
and
any
pos
itive
inte
ger
n, if
an
�b,
the
n a
is a
n n
thro
ot o
f b.
1.If
nis
eve
n an
d b
0,
the
n b
has
one
posi
tive
root
and
one
neg
ativ
e ro
ot.
Rea
l nth
Ro
ots
of
b,
2.If
nis
odd
and
b
0, t
hen
bha
s on
e po
sitiv
e ro
ot.
n �b�,
�n �
b�3.
If n
is e
ven
and
b
0, t
hen
bha
s no
rea
l roo
ts.
4.If
nis
odd
and
b
0, t
hen
bha
s on
e ne
gativ
e ro
ot.
Sim
pli
fy �
49z8
�.
�49
z8�
��
(7z4
)2�
�7z
4
z4m
ust
be
posi
tive
, so
ther
e is
no
nee
d to
take
th
e ab
solu
te v
alu
e.
Sim
pli
fy �
3 �(2
a�
�1)
6�
�3 �
(2a
��
1)6
��
�3 �
[(2a
��
1)2 ]
3�
�(2
a�
1)2
Sim
pli
fy.
1.�
81�2.
3 ��
343
�3.
�14
4p6
�9
�7
12| p
3|
4.�
�4a
10�
5.5 �
243p
1�
0 �6.
�3 �
m6 n
9�
�2a
53p
2�
m2 n
3
7.3 �
�b1
2�
8.�
16a1
0�
b8 �9.
�12
1x6
��
b4
4| a5 | b
411
| x3|
10.�
(4k)
4�
11.�
�16
9r4
�12
.�3 �
�27
p�
6 �16
k2
�13
r23p
2
13.�
�62
5y2
�z4 �
14.�
36q3
4�
15.�
100x
2�
y4z6
��
25| y
| z2
6| q
17|
10| x
| y2| z
3 |
16.
3 ��
0.02
�7�
17.�
��
0.36
�18
.�0.
64p
�10 �
�0.
3n
ot
a re
al n
um
ber
0.8
| p5 |
19.
4 �(2
x)8
�20
.�(1
1y2 )
�4 �
21.
3 �(5
a2b)
�6 �
4x2
121y
425
a4 b
2
22.�
(3x
��
1)2
�23
.3 �
(m�
�5)
6�
24.�
36x2
��
12x
��
1�| 3x
�1|
(m�
5)2
| 6x�
1|
Exam
ple
1Ex
amp
le 2
Exer
cise
s
Exam
ple
Lesson 7-4
Cha
pter
729
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Ap
pro
xim
ate
Rad
ical
s w
ith
a C
alcu
lato
r
Irra
tio
nal
Nu
mb
era
num
ber
that
can
not
be e
xpre
ssed
as
a te
rmin
atin
g or
a r
epea
ting
deci
mal
Rad
ical
s su
ch a
s �
2�an
d �
3�ar
e ex
ampl
es o
f ir
rati
onal
nu
mbe
rs. D
ecim
al a
ppro
xim
atio
ns
for
irra
tion
al n
um
bers
are
oft
en u
sed
in a
ppli
cati
ons.
Th
ese
appr
oxim
atio
ns
can
be
easi
lyfo
un
d w
ith
a c
alcu
lato
r.
Ap
pro
xim
ate
5 �18
.2�
wit
h a
cal
cula
tor.
5 �18
.2�
1.
787
Use
a c
alcu
lato
r to
ap
pro
xim
ate
each
val
ue
to t
hre
e d
ecim
al p
lace
s.
1.�
62�2.
�10
50�
3.3 �
0.05
4�
7.87
432
.404
0.37
8
4.�
4 �5.
45�
5.�
5280
�6.
�18
,60
�0�
�1.
528
72.6
6413
6.38
2
7.�
0.09
5�
8.3 �
�15
�9.
5 �10
0�
0.30
8�
2.46
62.
512
10.
6 �85
6�
11.�
3200
�12
.�0.
05�
3.08
156
.569
0.22
4
13.�
12,5
0�
0�14
.�0.
60�
15.�
4 �50
0�
111.
803
0.77
5�
4.72
9
16.
3 �0.
15�
17.
6 �42
00�
18.�
75�
0.53
14.
017
8.66
0
19.L
AW
EN
FOR
CEM
ENT
Th
e fo
rmu
la r
�2�
5L�is
use
d by
pol
ice
to e
stim
ate
the
spee
d r
in m
iles
per
hou
r of
a c
ar i
f th
e le
ngt
h L
of t
he
car’
s sk
id m
ark
is m
easu
res
in f
eet.
Est
imat
e to
th
e n
eare
st t
enth
of
a m
ile
per
hou
r th
e sp
eed
of a
car
th
at l
eave
s a
skid
mar
k 30
0 fe
et l
ong.
77.5
mi/h
20.S
PAC
E TR
AV
ELT
he
dist
ance
to
the
hor
izon
dm
iles
fro
m a
sat
elli
te o
rbit
ing
hm
iles
abov
e E
arth
can
be
appr
oxim
ated
by
d�
�80
00h
��
h2
�. W
hat
is
the
dist
ance
to
the
hor
izon
if
a sa
tell
ite
is o
rbit
ing
150
mil
es a
bove
Ear
th?
abo
ut
1100
mi
Stud
y G
uide
and
Inte
rven
tion
(con
tinue
d)
nth
Ro
ots
Exer
cise
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A13
Chapter 7 A14 Glencoe Algebra 2
Answers (Lesson 7-4)
Cha
pter
730
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
cen
thR
oo
tsU
se a
cal
cula
tor
to a
pp
roxi
mat
e ea
ch v
alu
e to
th
ree
dec
imal
pla
ces.
1.�
230
�15
.166
2.�
38�6.
164
3.�
�15
2�
�12
.329
4.�
5.6
�2.
366
5.3 �
88�4.
448
6.3 �
�22
2�
�6.
055
7.�
4 �0.
34�
�0.
764
8.5 �
500
�3.
466
Sim
pli
fy.
9.�
�81�
�9
10.�
144
�12
11.�
(�5)
2�
512
.��
52�
no
t a
real
nu
mb
er
13.�
0.36
�0.
614
.���
�
15.
3 ��
8�
�2
16.�
3 �27�
�3
17.
3 �0.
064
�0.
418
.5 �
32�2
19.
4 �81�
320
.�y2 �
| y|
21.
3 �12
5s3
�5s
22.�
64x6
�8| x
3 |
23.
3 ��
27a
�6 �
�3a
224
.�m
8 n4
�m
4 n2
25.�
�10
0p4
�q2 �
�10
p2 | q
|26
.4 �
16w
4 v�
8 �2| w
| v2
27.�
(�3c
)4�
9c2
28.�
(a�
b�
)2 �| a
�b
|
2 � 34 � 9
Lesson 7-4
Cha
pter
731
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use
a c
alcu
lato
r to
ap
pro
xim
ate
each
val
ue
to t
hre
e d
ecim
al p
lace
s.
1.�
7.8
�2.
��
89�3.
3 �25�
4.3 �
�4
�2.
793
�9.
434
2.92
4�
1.58
7
5.4 �
1.1
�6.
5 ��
0.1
�7.
6 �55
55�
8.4 �
(0.9
4)�
2 �1.
024
�0.
631
4.20
80.
970
Sim
pli
fy.
9.�
0.81
�10
.��
324
�11
.�4 �
256
�12
.6 �
64�
0.9
�18
�4
2
13.
3 ��
64�
14.
3 �0.
512
�15
.5 �
�24
3�
16.�
4 �12
96�
�4
0.8
�3
�6
17.
5 ��18
.5 �
243x
1�
0 �19
.�(1
4a)2
�20
.��
(14a
�)2 �
no
t a
��4 3�
3x2
14| a|
real
nu
mb
er
21.�
49m
2 t�
8 �22
. ��
23.
3 ��
64r6
�w
15�
24.�
(2x)
8�
7| m| t4
�4r
2 w5
16x
4
25.�
4 �62
5s8
�26
.3 �
216p
3�
q9 �27
.�67
6x4
�y6 �
28.
3 ��
27x9
�y1
2�
�5s
26p
q3
26x
2 | y3 |
�3x
3 y4
29.�
�14
4m�
8 n6
�30
.5 �
�32
x5�
y10
�31
.6 �
(m�
�4)
6�
32.
3 �(2
x�
�1)
3�
�12
m4 | n
3 |�
2xy
2| m
�4|
2x�
1
33.�
�49
a10
�b1
6�
34.
4 �(x
�5
�)8 �
35.
3 �34
3d6
�36
.�x2
�1
�0x
�2
�5�
�7| a
5| b
8(x
�5)
27d
2| x
�5|
37.R
AD
IAN
T TE
MPE
RA
TUR
ET
her
mal
sen
sors
mea
sure
an
obj
ect’s
rad
ian
tte
mpe
ratu
re,
wh
ich
is
the
amou
nt
of e
ner
gy r
adia
ted
by t
he
obje
ct. T
he
inte
rnal
tem
pera
ture
of
an
obje
ct i
s ca
lled
its
kin
etic
tem
pera
ture
. The
for
mul
a T r
�T k
4 �e�
rela
tes
an o
bjec
t’s r
adia
ntte
mpe
ratu
re T
rto
its
kin
etic
tem
pera
ture
Tk.
Th
e va
riab
le e
in t
he
form
ula
is
a m
easu
reof
how
wel
l th
e ob
ject
rad
iate
s en
ergy
. If
an o
bjec
t’s k
inet
ic t
empe
ratu
re i
s 30
°C a
nd
e�
0.94
, wh
at i
s th
e ob
ject
’s r
adia
nt
tem
pera
ture
to
the
nea
rest
ten
th o
f a
degr
ee?
29.5
�C
38.H
ERO
’S F
OR
MU
LAS
alva
tore
is
buyi
ng
fert
iliz
er f
or h
is t
rian
gula
r ga
rden
. He
know
sth
e le
ngt
hs
of a
ll t
hre
e si
des,
so
he
is u
sin
g H
ero’
s fo
rmu
la t
o fi
nd
the
area
. Her
o’s
form
ula
sta
tes
that
th
e ar
ea o
f a
tria
ngl
e is
�s(
s�
�a)
(s�
�b)
(s�
�c)�
, wh
ere
a, b
, an
d c
are
the
len
gth
s of
th
e si
des
of t
he
tria
ngl
e an
d s
is h
alf
the
peri
met
er o
f th
e tr
ian
gle.
If
the
len
gth
s of
th
e si
des
of S
alva
tore
’s g
arde
n a
re 1
5 fe
et, 1
7 fe
et, a
nd
20 f
eet,
wh
at i
s th
ear
ea o
f th
e ga
rden
? R
oun
d yo
ur
answ
er t
o th
e n
eare
st w
hol
e n
um
ber.
124
ft2
4|m
|�
516m
2�
25
�10
24�
243
Prac
tice
nth
Ro
ots
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A14
Chapter 7 A15 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-4)
Cha
pter
732
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.C
UB
ESC
ath
y is
bu
ildi
ng
a cu
bic
stor
age
room
. Sh
e w
ants
th
e vo
lum
e of
the
spac
e to
be
1728
cu
bic
feet
. Wh
atsh
ould
th
e di
men
sion
s of
th
e cu
be b
e?
12 f
t b
y 12
ft
by
12 f
t
2.A
STR
ON
OM
YA
spec
ial
form
of
Kep
ler’
s T
hir
d L
aw o
f P
lan
etar
y M
otio
n
is g
iven
by
a�
�3P
2�
wh
ere
ais
th
e av
erag
e di
stan
ce o
f an
obj
ect
from
th
eS
un
in
AU
(as
tron
omic
al u
nit
s) a
nd
Pis
the
peri
od o
f th
e or
bit
in y
ears
. If
anob
ject
is
orbi
tin
g th
e S
un
wit
h a
per
iod
of 1
2 ye
ars,
wh
at i
s it
s di
stan
ce f
rom
th
e S
un
?5.
24 A
U
3.TU
NIN
GTw
o n
otes
are
an
oct
ave
apar
tif
th
e fr
equ
ency
of
the
hig
her
not
e is
twic
e th
e fr
equ
ency
of
the
low
er n
ote.
Cas
ey i
s ex
peri
men
tin
g w
ith
an
inst
rum
ent
that
has
6 n
otes
tu
ned
so
that
th
e fr
equ
ency
of
each
su
cces
sive
not
e in
crea
ses
by t
he
sam
e fa
ctor
an
dth
e fi
rst
and
last
not
e ar
e an
oct
ave
apar
t. B
y w
hat
fac
tor
does
th
e fr
equ
ency
incr
ease
fro
m n
ote
to n
ote?
�52�
or
app
roxi
mat
ely
1.15
4.M
AR
KU
PSA
wh
oles
aler
man
ufa
ctu
res
a pa
rt f
or D
doll
ars.
Th
e w
hol
esal
er s
ells
the
part
to
a de
aler
for
a P
perc
ent
mar
kup.
Th
e de
aler
sel
ls t
he
part
to
are
tail
er a
t an
add
itio
nal
Ppe
rcen
tm
arku
p. T
he
reta
iler
in
tu
rn s
ells
th
epa
rt t
o it
s cu
stom
ers
mar
kin
g u
p th
epr
ice
yet
anot
her
Ppe
rcen
t. W
hat
is
the
pric
e th
at c
ust
omer
s se
e? I
f th
ecu
stom
er b
uys
th
e pa
rt f
or $
80 a
nd
the
mar
kup
is 4
0%, w
hat
app
roxi
mat
ely
was
the
orig
inal
cos
t to
mak
e th
e pa
rt?
D(1
�P
)3; $
29.1
5
PEN
DU
LUM
SF
or E
xerc
ises
5 a
nd
6,
use
th
e fo
llow
ing
info
rmat
ion
.
Mr.
Top
alia
n’s
phys
ics
clas
s is
exp
erim
enti
ngw
ith
pend
ulum
s. T
he c
lass
lea
rned
the
form
ula
T�
2��
3�w
hich
rel
ates
the
ti
me
Tth
at i
t ta
kes
for
a pe
ndul
um t
o sw
ing
back
and
for
th b
ased
on
grav
ity
geq
ual
to32
fee
t pe
r se
cond
squ
ared
, and
the
len
gth
of t
he p
endu
lum
Lin
fee
t.
5.O
ne
grou
p in
th
e cl
ass
mad
e a
2-fo
otlo
ng
pen
dulu
m. U
se t
he
form
ula
to
dete
rmin
e h
ow l
ong
it w
ill
take
for
th
eir
pen
dulu
m t
o sw
ing
back
an
d fo
rth
. 1.
57 s
eco
nds
6.A
not
her
gro
up
deci
ded
they
wan
ted
to m
ake
a pe
ndu
lum
th
at t
ook
abou
t1.
76 s
econ
ds t
o go
bac
k an
d fo
rth
.A
ppro
xim
atel
y h
ow l
ong
shou
ld t
hei
rpe
ndu
lum
be?
2.5
feet
L � g
xx
xWor
d Pr
oble
m P
ract
ice
nth
Ro
ots
Lesson 7-4
Cha
pter
733
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
7-4
Ap
pro
xim
atin
g S
qu
are
Ro
ots
Con
side
r th
e fo
llow
ing
expa
nsi
on.
(a�� 2b a�
)2�
a2�
�2 2a ab ��
� 4b a2 2�
�a2
�b
�� 4b a2 2�
Th
ink
wh
at h
appe
ns
if a
is v
ery
grea
t in
com
pari
son
to
b. T
he
term
� 4b a2 2�is
ver
y sm
all
and
can
be
disr
egar
ded
in a
n a
ppro
xim
atio
n.
(a�� 2b a�
)2
a2
�b
a�
� 2b a�
�a2
�b
�
Su
ppos
e a
nu
mbe
r ca
n b
e ex
pres
sed
as a
2�
b, a
b
. Th
en a
n a
ppro
xim
ate
valu
e
of t
he
squ
are
root
is
a�
� 2b a�. Y
ou s
hou
ld a
lso
see
that
a�
� 2b a�
�a2
�b
�.
Use
th
e fo
rmu
la �
a2
��
b��
a�
� 2b a�to
ap
pro
xim
ate
�10
1�
and
�62
2�
.
a.�
101
��
�10
0�
�1�
��
102
��
1�b
.�
622
��
�62
5 �
�3�
��
252
��
3�
Let
a�
10 a
nd
b�
1.L
et a
�25
an
d b
�3.
�10
1�
1
0 �
� 2(1 10
)�
�62
2�
2
5 �
� 2(3 25
)�
1
0.05
2
4.94
Use
th
e fo
rmu
la t
o fi
nd
an
ap
pro
xim
atio
n f
or e
ach
sq
uar
e ro
ot t
o th
e n
eare
st h
un
dre
dth
. Ch
eck
you
r w
ork
wit
h a
cal
cula
tor.
1.�
626
�25
.02
2.�
99�9.
953.
�40
2�
20.0
5
4.�
1604
�40
.05
5.�
223
�14
.93
6.�
80�8.
94
7.�
4890
�69
.93
8.�
2505
�50
.05
9.�
3575
�59
.79
10.
�1,
441
�,1
00�
1200
.46
11.
�29
0�
17.0
312
.�
260
�16
.12
13.
Sh
ow t
hat
a�
� 2b a�
�a2
�b
�fo
r a
b
. �a
�� 2b a�
�2�
a2
�b
�� 4b a2 2�
;
dis
reg
ard
� 4b a2 2�;�a
�� 2b a�
�2�
a2
�b
;a
�� 2b a�
��
a2
�b
�
Enri
chm
ent
Exer
cise
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A15
Chapter 7 A16 Glencoe Algebra 2
Answers (Lesson 7-5)
Cha
pter
734
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Op
erat
ion
s w
ith
Rad
ical
Exp
ress
ion
sG
et R
ead
y fo
r th
e Le
sso
nR
ead
th
e in
trod
uct
ion
to
Les
son
7-5
in
you
r te
xtb
ook
.
Des
crib
e h
ow y
ou c
ould
use
th
e go
lden
rat
io t
o fi
nd
the
hei
ght
of a
gol
den
tr
ian
gle
if y
ou k
new
its
wid
th.
Sam
ple
an
swer
:U
se a
cal
cula
tor
to m
ult
iply
th
e w
idth
by
2 an
d d
ivid
e th
e re
sult
by
the
qu
anti
ty o
f �
5 ��
1.R
ou
nd
th
is a
nsw
er t
o t
he
nea
rest
ten
th.
Rea
d t
he
Less
on
1.C
ompl
ete
the
cond
itio
ns t
hat
mus
t be
met
for
a r
adic
al e
xpre
ssio
n to
be
in s
impl
ifie
d fo
rm.
•T
he
nis
as
as p
ossi
ble.
•T
he
con
tain
s n
o (o
ther
th
an 1
) th
at a
re n
th
pow
ers
of a
(n)
or p
olyn
omia
l.
•T
he
radi
can
d co
nta
ins
no
.
•N
o ap
pear
in
th
e .
2.a.
Wh
at a
re c
onju
gate
s of
rad
ical
exp
ress
ion
s u
sed
for?
to r
atio
nal
ize
bin
om
ial
den
om
inat
ors
b.
How
wou
ld y
ou u
se a
con
juga
te t
o si
mpl
ify
the
radi
cal
expr
essi
on
?
Mu
ltip
ly n
um
erat
or
and
den
om
inat
or
by 3
��
2�.c.
In o
rder
to
sim
plif
y th
e ra
dica
l ex
pres
sion
in
par
t b,
tw
o m
ult
ipli
cati
ons
are
nece
ssar
y. T
he m
ulti
plic
atio
n in
the
num
erat
or w
ould
be
done
by
the
met
hod
, an
d th
e m
ult
ipli
cati
on i
n t
he
den
omin
ator
wou
ld b
e do
ne
byfi
ndi
ng
the
of
.
Rem
emb
er W
hat
Yo
u L
earn
ed
3.O
ne w
ay t
o re
mem
ber
som
ethi
ng is
to
expl
ain
it t
o an
othe
r pe
rson
. Whe
n ra
tion
aliz
ing
the
deno
min
ator
in
the
expr
essi
on
, man
y st
uden
ts t
hink
the
y sh
ould
mul
tipl
y nu
mer
ator
and
den
omin
ator
by
. How
wou
ld y
ou e
xpla
in t
o a
clas
smat
e w
hy
this
is
inco
rrec
t
and
wh
at h
e sh
ould
do
inst
ead.
Sam
ple
an
swer
:B
ecau
se y
ou
are
wo
rkin
g w
ith
cub
e ro
ots
,no
t sq
uar
e ro
ots
,yo
u n
eed
to
mak
e th
e ra
dic
and
in t
he
den
om
inat
or
a p
erfe
ct c
ub
e,n
ot
a p
erfe
ct s
qu
are.
Mu
ltip
ly n
um
erat
or
and
den
om
inat
or
by
to m
ake
the
den
om
inat
or
3 �8�,
wh
ich
eq
ual
s 2.
3 �4�
� 3 �4 �
3 �2�
� 3 �2�
1� 3 �
2�
squ
ares
two
dif
fere
nce
FO
IL
1 �
�2�
� 3 �
�2�
den
om
inat
or
rad
ical
s
frac
tio
ns
inte
ger
fact
ors
rad
ican
d
smal
lin
dex
Exam
ple
1Ex
amp
le 2
Lesson 7-5
Cha
pter
735
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Op
erat
ion
s w
ith
Rad
ical
Exp
ress
ion
sSi
mp
lify
Rad
ical
Exp
ress
ion
s
For
any
rea
l num
bers
aan
d b,
and
any
inte
ger
n
1:
Pro
du
ct P
rop
erty
of
Rad
ical
s1.
if n
is e
ven
and
aan
d b
are
both
non
nega
tive,
the
n n �
ab��
n �a�
�n �
b�.2.
if n
is o
dd,
then
n �
ab��
n �a�
�n �
b�.
To s
impl
ify
a sq
uar
e ro
ot, f
ollo
w t
hes
e st
eps:
1.F
acto
r th
e ra
dica
nd
into
as
man
y sq
uar
es a
s po
ssib
le.
2.U
se t
he
Pro
duct
Pro
pert
y to
iso
late
th
e pe
rfec
t sq
uar
es.
3.S
impl
ify
each
rad
ical
.
Qu
oti
ent
Pro
per
ty o
f R
adic
als
For
any
rea
l num
bers
aan
d b
�0,
and
any
inte
ger
n
1,
n ���
, if
all r
oots
are
def
ined
.
To e
lim
inat
e ra
dica
ls f
rom
a d
enom
inat
or o
r fr
acti
ons
from
a r
adic
and,
mu
ltip
ly t
he
nu
mer
ator
an
d de
nom
inat
or b
y a
quan
tity
so
that
th
e ra
dica
nd
has
an
exa
ct r
oot.
n �a�
� n �b �
a � b
Sim
pli
fy
3 ��
16a
�5 b
7�
.3 �
�16
a�
5 b7
��
3 �(�
2)3
��
2 �
a�
3�
a2�
�(b
2 )3
��
b�
��
2ab2
3 �2a
2 b�
Sim
pli
fy
.
���
Quo
tient
Pro
pert
y
�F
acto
r in
to s
quar
es.
�P
rodu
ct P
rope
rty
�S
impl
ify.
��
Rat
iona
lize
the
deno
min
ator
.
�S
impl
ify.
2|x|
�10
xy�
��
15y3
�5y�
� �5y�
2|x|
�2x�
� 3y2 �
5y�
2|x|
�2x�
� 3y2 �
5y�
�(2
x)2
��
�2x�
��
�(3
y2 )2
��
�5y�
�(2
x)2
��
2x��
��
(3y2 )
2�
�5y
�
�8x
3�
� �45
y5�
8x3
� 45y5
8x3
� 45y5
Sim
pli
fy.
1.5 �
54�15
�6�
2.4 �
32a9
b�
20 �2a
2 | b5 |
4 �2a�
3.�
75x4
y�
7 �5x
2 y3�
3y�
4.��
5.��
6.3 ��
pq
�325
p2
��
� 10p5 q
3�40
| a3| b
�2b�
�� 14
a6 b3
�98
6�5�
�25
36 � 125
Exer
cise
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A16
Chapter 7 A17 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-5)
Exam
ple
1
Exam
ple
2
Cha
pter
736
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Op
erat
ion
s w
ith
Rad
ical
sW
hen
you
add
exp
ress
ion
s co
nta
inin
g ra
dica
ls, y
ou c
anad
d on
ly l
ike
term
s or
lik
e ra
dic
al e
xpre
ssio
ns.
Tw
o ra
dica
l ex
pres
sion
s ar
e ca
lled
lik
era
dic
al e
xpre
ssio
ns
if b
oth
th
e in
dice
s an
d th
e ra
dica
nds
are
ali
ke.
To m
ult
iply
rad
ical
s, u
se t
he
Pro
duct
an
d Q
uot
ien
t P
rope
rtie
s. F
or p
rodu
cts
of t
he
form
(a
�b�
�c�
d�)�
(e�
f��
g�h�)
, use
th
e F
OIL
met
hod
. To
rati
onal
ize
den
omin
ator
s, u
se
con
juga
tes.
Nu
mbe
rs o
f th
e fo
rm a
�b�
�c�
d�an
d a�
b��
c�d�,
wh
ere
a, b
, c, a
nd
dar
era
tion
al n
um
bers
, are
cal
led
con
juga
tes.
Th
e pr
odu
ct o
f co
nju
gate
s is
alw
ays
a ra
tion
aln
um
ber.
Sim
pli
fy 2
�50�
�4�
500
��
6�12
5�
.
2�50�
�4�
500
��
6�12
5�
�2�
52�
2�
�4�
102
�5
��
6�52
�5
�F
acto
r us
ing
squa
res.
�2
�5
��
2��
4 �
10 �
�5�
�6
�5
��
5�S
impl
ify s
quar
e ro
ots.
�10
�2�
�40
�5�
�30
�5�
Mul
tiply
.
�10
�2�
�10
�5�
Com
bine
like
rad
ical
s.
Stud
y G
uide
and
Inte
rven
tion
(con
tinue
d)
Op
erat
ion
s w
ith
Rad
ical
Exp
ress
ion
s
Sim
pli
fy (2
�3�
�4�
2�)(�
3��
2�2�)
.
(2�
3��
4�2�)
(�3�
�2�
2�)�
2�3�
��
3��
2�3�
�2�
2��
4�2�
��
3��
4�2�
�2�
2��
6 �
4�6�
�4�
6��
16�
�10
Sim
pli
fy
.
��
� � �11
�5�
5��
� 4
6 �
5�5�
�5
��
9 �
5
6 �
2 �5�
�3�
5��
(�5�)
2�
��
32�
(�5� )
2
3 �
�5�
� 3 �
�5 �
2 �
�5�
� 3 �
�5 �
2 �
�5�
� 3 �
�5 �
2 �
�5�
� 3 �
�5�
Sim
pli
fy.
1.3 �
2��
�50�
�4�
8�2.
�20�
��
125
��
�45�
3.�
300
��
�27�
��
75�
04�
5�2�
3�
4.3 �
81��
3 �24�
5.3 �
2�(3 �
4��
3 �12�
)6.
2�3�(
�15�
��
60�)
63 �
9�2
�2
3 �3�
18�
5�
7.(2
�3�
7�)(4
��
7�)8.
(6�
3��
4�2�)
(3�
3��
�2�)
9.(4
�2�
�3�
5�)(2
�20
��
5�)
29 �
14�
7�46
�6�
6�40
�2�
�30
�5�
10.
511
.5
�3�
2�12
.13
�3�
�23
�� 11
5 �
3�3�
��
1 �
2�3�
4 �
�2�
� 2 �
�2�
5�48�
��
75��
�5�
3�
Exer
cise
s
Exam
ple
3
Lesson 7-5
Cha
pter
737
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceO
per
atio
ns
wit
h R
adic
al E
xpre
ssio
ns
Sim
pli
fy.
1.�
24�2�
6�2.
�75�
5�3�
3.3 �
16�2
3 �2�
4.�
4 �48�
�2
4 �3�
5.4�
50x5
�20
x2 �
2x�6.
4 �64
a4b
�4 �
2|ab
| �2�
7.3 ���
d2 f
5�
f3 �
d2 f
2�
8.��
s2t
| s| �
t�
9.���
�10
.3 ��
11. �
��2 5g z3 �12
.(3�
3�)(5
�3�)
45
13.(
4�12�
)(3�
20�)
48�
15�14
.�2�
��
8��
�50�
8�2�
15.�
12��
2�3�
��
108
�6�
3�16
.8�
5��
�45�
��
80��
5�
17.2
�48�
��
75��
�12�
�3�
18.(
2 �
�3�)
(6 �
�2�)
12 �
2�2�
�6�
3��
�6�
19.(
1 �
�5�)
(1 �
�5�)
�4
20.(
3 �
�7�)
(5 �
�2�)
15 �
3�2�
�5�
7��
�14�
21.(
�2�
��
6�)2
8 �
4�3�
22.
23.
24.
40 �
5�6�
�� 58
5� 8
��
6�12
�4�
2��
� 74
� 3 �
�2�
21 �
3�2�
�� 47
3� 7
��
2�
g�
10g
z�
�� 5z
3 �6 �
�3
2 � 9�
21��
73 � 7
5 � 625 � 36
1 � 21 � 8
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A17
Chapter 7 A18 Glencoe Algebra 2
Answers (Lesson 7-5)
Cha
pter
738
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Sim
pli
fy.
1.�
540
�6�
15�2.
3 ��
432
��
63 �
2�3.
3 �12
8�
43 �
2�
4.�
4 �40
5�
�3
4 �5�
5.3 �
�50
0�
0��
103 �
5�6.
5 ��
121
�5�
�3
5 �5�
7.3 �
125t
6 w�
2 �5t
23 �
w2
�8.
4 �48
v8z
�13 �
2v2 z
34 �
3z�9.
3 �8g
3 k8
�2g
k2
3 �k
2 �
10.�
45x3
y�
8 �3x
y4 �
5x�11
. ��
12.
3 ��3 �
9�
13. ��c
4 d7
c2 d
3 �2d�
14. ��
15.
4 ��16
.(3�
15�)(�
4�45�
)17
.(2�
24�)(7
�18�
)18
.�81
0�
��
240
��
�25
0�
�18
0�3�
168�
3�4�
10��
4�15�
19.6
�20�
�8�
5��
5�45�
20.8
�48�
�6�
75��
7�80�
21.(
3�2�
�2�
3�)2
5�5�
2�3�
�28
�5�
30 �
12�
6�
22.(
3 �
�7�)
223
.(�
5��
�6�)
(�5�
��
2�)24
.(�
2��
�10�
)(�2�
��
10�)
16 �
6�7�
5 �
�10�
��
30��
2�3�
�8
25.(
1 �
�6�)
(5 �
�7�)
26.(
�3�
�4�
7�)2
27.(
�10
8�
�6�
3�)2
5 �
�7�
�5�
6��
�42�
115
�8�
21�0
28.
�15�
�2�
3�29
.6�
2��
630
.
31.
32.
27 �
11�
6�33
.
34.B
RA
KIN
GT
he
form
ula
s�
2�5��
esti
mat
es t
he
spee
d s
in m
iles
per
hou
r of
a c
ar w
hen
it l
eave
s sk
id m
arks
�fe
et l
ong.
Use
th
e fo
rmu
la t
o w
rite
a s
impl
ifie
d ex
pres
sion
for
sif
�
�85
. Th
en e
valu
ate
sto
th
e n
eare
st m
ile
per
hou
r.10
�17�
;41
mi/h
35.P
YTH
AG
OR
EAN
TH
EOR
EMT
he
mea
sure
s of
th
e le
gs o
f a
righ
t tr
ian
gle
can
be
repr
esen
ted
by t
he
expr
essi
ons
6x2 y
and
9x2 y
. Use
th
e P
yth
agor
ean
Th
eore
m t
o fi
nd
asi
mpl
ifie
d ex
pres
sion
for
th
e m
easu
re o
f th
e h
ypot
enu
se.
3x2
| y| �
13 �
6 �
5�x�
�x
��
4 �
x3
��
x�� 2
��
x�3
��
6��
�5
��
24�8
�5�
2��
� 23
��
2�� 2
��
2�
17 �
�3�
�� 13
5 �
�3�
� 4 �
�3�
6� �
2��
1�
3�� �
5��
2
4 �72
a�
�3a
8� 9a
33a
2 �a�
�8b
29a
5� 64
b41 � 16
1� 12
8
216
� 24�
11��
311 � 9
Prac
tice
Op
erat
ion
s w
ith
Rad
ical
Exp
ress
ion
s
Lesson 7-5
Cha
pter
739
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.C
UB
ESC
ath
y h
as a
rec
tan
gula
r bo
xw
ith
dim
ensi
ons
20 i
nch
es b
y 35
in
ches
by 4
0 in
ches
. Sh
e w
ould
lik
e to
rep
lace
it
wit
h a
box
in
th
e sh
ape
of a
cu
be b
ut
wit
h t
he
sam
e vo
lum
e. W
hat
sh
ould
th
ele
ngt
h o
f a
side
of
the
cube
be?
Exp
ress
you
r an
swer
as
a ra
dica
l ex
pres
sion
in
sim
ples
t fo
rm.
10�3
28�in
.
2.PH
YSI
CS
Th
e sp
eed
of a
wav
e tr
avel
ing
over
a s
trin
g is
giv
en b
y w
her
e t
is
the
ten
sion
of
the
stri
ng
and
uis
th
ede
nsi
ty. R
ewri
te t
he
expr
essi
on i
nsi
mpl
est
form
by
rati
onal
izin
g th
ede
nom
inat
or.
3.TU
NIN
GW
ith
eac
h n
ote
hig
her
on
api
ano,
th
e fr
equ
ency
of
the
pitc
hin
crea
ses
by a
fac
tor
of �12
2�. W
hat
is
the
rati
o of
th
e fr
equ
enci
es o
f tw
o n
otes
th
atar
e 6
step
s ap
art
on t
he
pian
o? W
hat
is
the
rati
o of
th
e fr
equ
enci
es o
f tw
o n
otes
that
are
9 s
teps
apa
rt o
n t
he
pian
o?E
xpre
ss y
our
answ
ers
in s
impl
est
form
.
�2�
and
�4
8 �
4.LI
GH
TSS
upp
ose
a li
ght
has
abr
igh
tnes
s in
ten
sity
of
I 1w
hen
it
is a
t a
dist
ance
of
d1
and
a br
igh
tnes
s in
ten
sity
of I
2w
hen
it
is a
t a
dist
ance
of
d2.
Th
ese
quan
titi
es a
re r
elat
ed b
y th
e eq
uat
ion
���
. Su
ppos
e I 1
�50
un
its
and
I 2�
24 u
nit
s. W
hat
wou
ld
be?
Exp
ress
you
r an
swer
in
sim
ples
t fo
rm.
RA
CIN
GF
or E
xerc
ises
5 a
nd
6, u
se t
he
foll
owin
g in
form
atio
n a
nd
exp
ress
you
ran
swer
s in
sim
ple
st f
orm
.
Joh
n i
s Ja
y’s
you
nge
r br
oth
er. T
hey
lik
e to
race
an
d, a
fter
man
y ra
ces,
th
ey f
oun
d th
atth
e fa
ires
t ra
ce w
as t
o ru
n s
ligh
tly
diff
eren
tdi
stan
ces.
Th
ey b
oth
sta
rt a
t th
e sa
me
plac
ean
d ru
n s
trai
ght
for
0.2
mil
es. T
hen
th
eyh
ead
for
diff
eren
t fi
nis
hes
. In
th
e fi
gure
,Jo
hn
an
d Ja
y’s
fin
ish
ing
path
s ar
e m
arke
d.
Th
is t
ime,
th
ey t
ied.
Bot
h o
f th
em f
inis
hed
the
race
in
exa
ctly
4 m
inu
tes.
5.If
Joh
n a
nd
Jay
con
tin
ued
at
thei
rav
erag
e pa
ces
duri
ng
the
race
, exa
ctly
how
man
y m
inu
tes
wou
ld i
t ta
ke t
hem
each
to
run
a m
ile?
Exp
ress
you
r an
swer
as a
rad
ical
exp
ress
ion
in
sim
ples
t fo
rm.
Joh
n:
or
40 �
20�
2�m
in;
Jay:
or
40�
5��
80 m
in
6.E
xact
ly h
ow m
any
tim
es a
s fa
st d
idJo
hn
ru
n a
s Ja
y?
2 �
�2�
��
5��
�10�
�2
0.8
�4�
0.05
��
��
0.01
0.8
�4
�0.
02�
��
0.02
Sta
rt
0.2
mile
0.1
mile
0.1
mile
0.1
mile
John
’s
Fini
shJa
y’s
Fini
sh
5�3�
�6
d2
� d1
I 1� I 2
d2
� d1
�tu�
�u
�t�
� �u�,
Wor
d Pr
oble
m P
ract
ice
Op
erat
ion
s w
ith
Rad
ical
Exp
ress
ion
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A18
Chapter 7 A19 Glencoe Algebra 2
An
swer
s
Answers (Lessons 7-5 and 7-6)
Exam
ple
1
Exam
ple
2
Exer
cise
s
Cha
pter
740
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Sp
ecia
l Pro
du
cts
wit
h R
adic
als
Not
ice
that
( �3�)
(�3�)
�3,
or
( �3�)
2�
3. I
n g
ener
al, (
�x�)
2�
xw
hen
x �
0.
Als
o, n
otic
e th
at (�
9�)(�
4�)�
�36�
. In
gen
eral
, (�
x�)(�
y�)�
�xy�
wh
en x
and
yar
e n
ot n
egat
ive.
You
can
use
th
ese
idea
s to
fin
d th
e sp
ecia
l pr
odu
cts
belo
w.
Fin
d t
he
pro
du
ct: (
�2�
��
5�)( �
2��
�5�)
.
(�2�
��
5�)(�
2��
�5�)
�(�
2�)2
�(�
5�)2
�2
�5
��
3
Eva
luat
e ( �
2��
�8�)
2 .
(�2�
��
8�)2
�(�
2�)2
�2�
2��8�
�(�
8�)2
�2
�2�
16��
8 �
2 �
2(4)
�8
�2
�8
�8
�18
Mu
ltip
ly.
1.(�
3��
�7�)
(�3�
��
7�)�
42.
(�10�
��
2�)(�
10��
�2�)
8
3.(�
2x��
�6�)
(�2x�
��
6�)2x
�6
4.(�
3��
(�7)
)252
�14
�3�
5.(�
1000
��
�10�
)212
106.
(�y�
��
5�)(�
y��
�5�)
y�
5
7.(�
50��
�x�)
250
�10
�2x�
�x
8.(�
x��
20)2
x�
40�
x��
400
You
can
ext
end
th
ese
idea
s to
pat
tern
s fo
r su
ms
and
dif
fere
nce
s of
cu
bes
. S
tud
y th
e p
atte
rn b
elow
. Th
en c
omp
lete
Exe
rcis
es 9
–12.
(3 �8�
� 3 �
x�)(3 �
82 ��
3 �8x�
�3 �
x2 �)�
3 �83 �
� 3 �
x3 ��
8 �
x
9.(3 �
2��
3 �5�)
(3 �22 �
�3 �
10��
3 �52 �
)�
3
10.(
3 �y�
�3 �
w�)(
3 �y2 �
�3 �
yw��
3 �w
2�
)y
�w
11.(
3 �7�
�3 �
20�)(
3 �72 �
�3 �
140
��
3 �20
2�
)27
12.(
3 �11�
�3 �
8�)(3 �
112
��
3 �88�
�3 �
82 �)
3
(�a�
��
b�)(�
a��
�b�)
�(�
a�)2
�(�
b�)2
�a
�b
(�a�
��
b�)2
�(�
a�)2
�2�
ab��
(�b�)
2�
a�
2�ab�
�b
(�a�
��
b�)2
�(�
a�)2
�2�
ab��
(�b�)
2�
a�
2�ab�
�b
Enri
chm
ent
Lesson 7-6
Cha
pter
741
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Rat
ion
al E
xpo
nen
tsG
et R
ead
y fo
r th
e Le
sso
nR
ead
th
e in
trod
uct
ion
to
Les
son
7-6
in
you
r te
xtb
ook
.
The
for
mul
a in
the
int
rodu
ctio
n co
ntai
ns t
he e
xpon
ent
. Wha
t do
you
thi
nk
it m
igh
t m
ean
to
rais
e a
nu
mbe
r to
th
e po
wer
?
Sam
ple
an
swer
:Tak
e th
e fi
fth
ro
ot
of
the
nu
mb
er a
nd
sq
uar
e it
.
Rea
d t
he
Less
on
1.C
ompl
ete
the
foll
owin
g de
fin
itio
ns
of r
atio
nal
exp
onen
ts.
•F
or a
ny
real
nu
mbe
r b
and
for
any
posi
tive
in
tege
r n
, b� n1 �
�ex
cept
wh
en b
and
nis
.
•F
or a
ny
non
zero
rea
l n
um
ber
b, a
nd
any
inte
gers
man
d n
, wit
h n
,
b�m n��
�
, exc
ept
wh
en b
and
nis
.
2.C
ompl
ete
the
con
diti
ons
that
mu
st b
e m
et i
n o
rder
for
an
exp
ress
ion
wit
h r
atio
nal
expo
nen
ts t
o be
sim
plif
ied.
•It
has
no
expo
nen
ts.
•It
has
no
expo
nen
ts i
n t
he
.
•It
is
not
a
frac
tion
.
•T
he
of a
ny
rem
ain
ing
is t
he
nu
mbe
r po
ssib
le.
3.M
arga
rita
an
d P
ierr
e w
ere
wor
kin
g to
geth
er o
n t
hei
r al
gebr
a h
omew
ork.
On
e ex
erci
se
aske
d th
em t
o ev
alu
ate
the
expr
essi
on 2
7�4 3� . Mar
gari
ta t
hou
ght
that
th
ey s
hou
ld r
aise
27
to
the
fou
rth
pow
er f
irst
an
d th
en t
ake
the
cube
roo
t of
th
e re
sult
. Pie
rre
thou
ght
that
they
sh
ould
tak
e th
e cu
be r
oot
of 2
7 fi
rst
and
then
rai
se t
he
resu
lt t
o th
e fo
urt
h p
ower
.W
hos
e m
eth
od i
s co
rrec
t?B
oth
met
ho
ds
are
corr
ect.
Rem
emb
er W
hat
Yo
u L
earn
ed
4.S
ome
stu
den
ts h
ave
trou
ble
rem
embe
rin
g w
hic
h p
art
of t
he
frac
tion
in
a r
atio
nal
expo
nen
t gi
ves
the
pow
er a
nd
wh
ich
par
t gi
ves
the
root
. How
can
you
r kn
owle
dge
ofin
tege
r ex
pon
ents
hel
p yo
u t
o ke
ep t
his
str
aigh
t?S
amp
le a
nsw
er:
An
inte
ger
ex
po
nen
t ca
n b
e w
ritt
en a
s a
rati
on
al e
xpo
nen
t.F
or
exam
ple
,23
�2�3 1� .
You
kn
ow
th
at t
his
mea
ns
that
2 is
rai
sed
to
th
e th
ird
po
wer
,so
th
en
um
erat
or
mu
st g
ive
the
po
wer
,an
d,t
her
efo
re,t
he
den
om
inat
or
mu
stg
ive
the
roo
t.
leas
tra
dic
alin
dexco
mp
lex
den
om
inat
or
frac
tio
nal
neg
ativ
e
even
�0
(n �b�)
mn �
bm �
1
even
�0
n �b �
2 � 5
2 � 5
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A19
Chapter 7 A20 Glencoe Algebra 2
Answers (Lesson 7-6)
Exam
ple
1
Cha
pter
742
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Rat
ion
al E
xpo
nen
tsR
atio
nal
Exp
on
ents
an
d R
adic
als
Def
init
ion
of
b� n1 �
For
any
rea
l num
ber
ban
d an
y po
sitiv
e in
tege
r n,
b�1 n��
n �b�,
exc
ept
whe
n b
0
and
nis
eve
n.
Def
init
ion
of
b�m n�
For
any
non
zero
rea
l num
ber
b, a
nd a
ny in
tege
rs m
and
n, w
ith n
1,
b�m n��
n �bm �
�(n �
b�)m
, ex
cept
whe
n b
0
and
nis
eve
n.
Wri
te 2
8�1 2�in
rad
ical
for
m.
Not
ice
that
28
0.
28�1 2�
��
28��
�22
�7
��
�22 �
��
7��
2�7�
Eva
luat
e �
��1 3� .
Not
ice
that
�8
0,
�12
5
0, a
nd
3 is
odd.
���1 3�
� ��
2� �
53 ��
8�
� 3 ��
125
��
8� �
125
�8
� �12
5
�
Wri
te e
ach
exp
ress
ion
in
rad
ical
for
m.
1.11
�1 7�
2.15
�1 3�
3.30
0�3 2�
7 �11�
3 �15�
3000
�3�
Wri
te e
ach
rad
ical
usi
ng
rati
onal
exp
onen
ts.
4.�
47�5.
3 �3a
5 b2
�6.
4 �16
2p5
�
47�1 2�
3�1 3� a�5 3� b�2 3�
3 �
2�1 4��
p�5 4�
Eva
luat
e ea
ch e
xpre
ssio
n.
7.�
27�2 3�
8.9.
(0.0
004)
�1 2�
90.
021 � 105�
�1 2�
� 2�5�
2 � 5
Exam
ple
2
Exer
cise
s
Exam
ple
1Ex
amp
le 2
Lesson 7-6
Cha
pter
743
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Sim
plif
y Ex
pre
ssio
ns
All
th
e pr
oper
ties
of
pow
ers
from
Les
son
6-1
app
ly t
o ra
tion
alex
pon
ents
. Wh
en y
ou s
impl
ify
expr
essi
ons
wit
h r
atio
nal
exp
onen
ts, l
eave
th
e ex
pon
ent
inra
tion
al f
orm
, an
d w
rite
th
e ex
pres
sion
wit
h a
ll p
osit
ive
expo
nen
ts. A
ny
expo
nen
ts i
n t
he
den
omin
ator
mu
st b
e po
siti
ve i
nte
gers
.
Wh
en y
ou s
impl
ify
radi
cal
expr
essi
ons,
you
may
use
rat
ion
al e
xpon
ents
to
sim
plif
y, b
ut
you
ran
swer
sh
ould
be
in r
adic
al f
orm
. Use
th
e sm
alle
st i
nde
x po
ssib
le.
Stud
y G
uide
and
Inte
rven
tion
(con
tinue
d)
Rat
ion
al E
xpo
nen
ts
Sim
pli
fy y
�2 3��
y�3 8� .
y�2 3��
y�3 8��
y�2 3��
�3 8��
y�2 25 4�
Sim
pli
fy
4 �14
4x6
�.
4 �14
4x6
��
(144
x6)�1 4�
�(2
4�
32�
x6)�1 4�
�(2
4 )�1 4�
�(3
2 )�1 4�
�(x
6 )�1 4�
�2
�3�1 2�
�x�3 2�
�2x
�(3
x)�1 2�
�2x
�3x�
Sim
pli
fy e
ach
exp
ress
ion
.
1.x�4 5�
�x�6 5�
2.� y�2 3� ��3 4�
3.p�4 5�
�p� 17 0�
x2
y�1 2�
p�3 2�
4.� m
��6 5� ��2 5�
5.x�
�3 8��
x�4 3�6.
� s��1 6� ��
�4 3�
or
x�2 23 4�
s�2 9�
7.8.
� a�2 3� ��6 5�
�� a
�2 5� �39.
p�2 3�
a2
or
10.
6 �12
8�
11.
4 �49�
12.
5 �28
8�
26 �
2��
7�2
5 �9�
13.�
32��
3�16�
14.
3 �25�
��
125
�15
.6 �
16�
48�
2�25
6 �5�
3 �4�
16.
17.�
�3 �48�
18.
6 �48�
�a�
6 �b
5 ��
bx
�3�
�6 �
35 ��
� 6
a3 �
b4 �� �
ab3
�x
�3 �
3��
�12�
x�5 6�
� x
1 � x�1 6�
x��1 2�
� x��1 3�
p � p�1 3�
m�1 23 5�
�� m
1 m� 212
5�
Exer
cise
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A20
Chapter 7 A21 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-6)
Cha
pter
744
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceR
atio
nal
Exp
on
ents
Wri
te e
ach
exp
ress
ion
in
rad
ical
for
m.
1.3�1 6�
6 �3�
2.8�1 5�
5 �8�
3.12
�2 3�3 �
122
�o
r (3 �
12�)2
or
2�3
18�4.
(s3 )
�3 5�s
5 �s4 �
Wri
te e
ach
rad
ical
usi
ng
rati
onal
exp
onen
ts.
5.�
51�51
�1 2�6.
3 �37�
37�1 3�
7.4 �
153
�15
�3 4�8.
3 �6x
y2�
6�1 3� x�1 3� y
�2 3�
Eva
luat
e ea
ch e
xpre
ssio
n.
9.32
�1 5�2
10.8
1�1 4�3
11.2
7��1 3�
12.4
��1 2�
13.1
6�3 2�64
14.(
�24
3)�4 5�
81
15.2
7�1 3��
27�5 3�
729
16. �
��3 2�
Sim
pli
fy e
ach
exp
ress
ion
.
17.c
�1 52 ��
c�3 5�c
318
.m�2 9�
�m
�1 96 �m
2
19.� q
�1 2� �3q
�3 2�20
.p�
�1 5�o
r
21.x
�� 16 1�
or
22.
x� 15 2�
23.
or
24.
or
25.
12 �64�
�2�
26.
8 �49
a8b
�2 �
| a|4 �
7b�n�2 3�
� n1 � n
�1 3�
n�1 3�
� n�1 6�
�n
�1 2�
y�1 4�
� y1 � y
�3 4�
y��1 2�
� y�1 4�
x�2 3�
� x�1 4�
x� 15 1�
� x1 � x
� 16 1�
p�4 5�
� p1 � p
�1 5�8 � 274 � 9
1 � 21 � 3
Lesson 7-6
Cha
pter
745
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wri
te e
ach
exp
ress
ion
in
rad
ical
for
m.
1.5�1 3�
2.6�2 5�
3.m
�4 7�4.
(n3 )�2 5�
3 �5�
5 �62 �
or
(5 �6�)
27 �
m4
�o
r (7 �
m�)4
n5 �
n�
Wri
te e
ach
rad
ical
usi
ng
rati
onal
exp
onen
ts.
5.�
79�6.
4 �15
3�
7.3 �
27m
6 n�
4 �8.
5�2a
10b
�
79�1 2�
153�1 4�
3m2 n
�4 3�5
�2�1 2�
| a5
| b�1 2�
Eva
luat
e ea
ch e
xpre
ssio
n.
9.81
�1 4�3
10.1
024�
�1 5�11
.8�
�5 3�
12.�
256�
�3 4��
13.(
�64
)��2 3�
14.2
7�1 3��
27�4 3�
243
15. �
��2 3�16
.17
.� 25�1 2� �� �
64�
�1 3� � �
Sim
pli
fy e
ach
exp
ress
ion
.
18.g
�4 7��
g�3 7�g
19.s
�3 4��
s�1 43 �s
420
.� u�
�1 3� ���4 5�
u� 14 5�
21.y
��1 2�
or
22.b
��3 5�
or
23.
q�1 5�
24.
25.
26.10 �
85 �2�
2�27
.�12�
�5 �
123
�28
.4 �
6��
34 �
6�29
.
1210 �
12�3�
6�
30.E
LEC
TRIC
ITY
Th
e am
oun
t of
cu
rren
t in
am
pere
s I
that
an
app
lian
ce u
ses
can
be
calc
ula
ted
usi
ng
the
form
ula
I�
���1 2� , w
her
e P
is t
he
pow
er i
n w
atts
an
d R
is t
he
resi
stan
ce i
n o
hm
s. H
ow m
uch
cu
rren
t do
es a
n a
ppli
ance
use
if
P�
500
wat
ts a
nd
R�
10 o
hm
s? R
oun
d yo
ur
answ
er t
o th
e n
eare
st t
enth
.7.
1 am
ps
31.B
USI
NES
SA
com
pan
y th
at p
rodu
ces
DV
Ds
use
s th
e fo
rmu
la C
�88
n�1 3�
�33
0 to
calc
ula
te t
he
cost
Cin
dol
lars
of
prod
uci
ng
nD
VD
s pe
r da
y. W
hat
is
the
com
pan
y’s
cost
to p
rodu
ce 1
50 D
VD
s pe
r da
y? R
oun
d yo
ur
answ
er t
o th
e n
eare
st d
olla
r.$7
98
P � R
a�3b�
�3b
a� �
3b�
2z�
2z�1 2�
��
z�
12z
�1 2�
� z�1 2��
1
t�1 11 2�
� 5t�2 3�
� 5t�1 2�
�t�
�3 4�
q�3 5�
� q�2 5�
b�2 5�
� b1 � b
�3 5�
y�1 2�
� y1 � y
�1 2�
5 � 416 � 49
64�2 3�
� 343�2 3�
25 � 3612
5� 21
6
1 � 161 � 64
1 � 321 � 4
Prac
tice
Rat
ion
al E
xpo
nen
ts
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A21
Chapter 7 A22 Glencoe Algebra 2
Answers (Lesson 7-6)
Cha
pter
746
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.SQ
UA
RIN
G T
HE
CU
BE
Acu
be h
as s
ide
len
gth
s. W
hat
is
the
side
len
gth
of
the
squ
are
that
has
an
are
a eq
ual
to
the
volu
me
of t
his
cu
be?
Wri
te y
our
answ
eru
sin
g ra
tion
al e
xpon
ents
.
s�3 2�
2.W
ATE
R T
OW
ERA
larg
e w
ater
tow
erst
ores
dri
nki
ng
wat
er i
n a
big
sph
eric
alta
nk.
Th
e m
ayor
of
the
tow
n d
ecid
esth
at t
he
wat
er t
ower
m
ust
be
repl
aced
w
ith
a l
arge
r ta
nk.
Tow
n r
esid
ents
in
sist
that
th
e n
ew t
ower
be
a s
pher
e. I
f th
en
ew t
ank
wil
l h
old
10 t
imes
as
mu
chw
ater
as
the
old
tan
k, h
ow m
any
tim
es l
ong
shou
ld
the
radi
us
of t
he
new
tan
k be
com
pare
dto
th
e ol
d ta
nk?
Wri
te y
our
answ
eru
sin
g ra
tion
al e
xpon
ents
.
10�1 3�
3.B
ALL
OO
NS
Asp
her
ical
bal
loon
is
bein
g in
flat
ed f
aste
r an
d fa
ster
. Th
evo
lum
e of
th
e ba
lloo
n a
s a
fun
ctio
n o
fti
me
is 9
�t2
. Wh
at i
s th
e ra
diu
s of
th
eba
lloo
n a
s a
fun
ctio
n o
f ti
me?
Wri
te y
our
answ
er u
sin
g ra
tion
al e
xpon
ents
.
3 ()�2 3�
4.IN
TER
EST
Rit
a op
ened
a b
ank
acco
un
tth
at a
ccu
mu
late
d in
tere
st a
t th
e ra
te o
f1%
com
pou
nde
d an
nu
ally
. Her
mon
eyac
cum
ula
ted
inte
rest
in
th
at a
ccou
nt
for
8 ye
ars.
Sh
e th
en t
ook
all
of h
er m
oney
out
of t
hat
acc
oun
t an
d pl
aced
it
into
anot
her
acc
oun
t th
at p
aid
5% i
nte
rest
com
pou
nde
d an
nu
ally
. Aft
er 4
yea
rs,
she
took
all
of
her
mon
ey o
ut
of t
hat
acco
un
t. W
hat
sin
gle
inte
rest
rat
e w
hen
com
pou
nde
d an
nu
ally
wou
ld g
ive
her
the
sam
e ou
tcom
e fo
r th
ose
12 y
ears
?R
oun
d yo
ur
answ
er t
o th
e n
eare
sth
un
dred
th o
f a
perc
ent.
2.32
%
CEL
LSF
or E
xerc
ises
5-7
, use
th
efo
llow
ing
info
rmat
ion
.
Th
e n
um
ber
of c
ells
in
a c
ell
cult
ure
gro
ws
expo
nen
tial
ly. T
he
nu
mbe
r of
cel
ls i
n t
he
cult
ure
as
a fu
nct
ion
of
tim
e is
giv
en b
y th
e ex
pres
sion
N()
tw
her
e t
is m
easu
red
in
hou
rs a
nd
Nis
th
e in
itia
l si
ze o
f th
ecu
ltu
re.
5.A
fter
3 h
ours
, th
ere
wer
e 17
28 c
ells
in
the
cult
ure
. Wh
at i
s N
?10
00
6.H
ow m
any
cell
s w
ere
in t
he
cult
ure
afte
r 20
min
ute
s? E
xpre
ss y
our
answ
erin
sim
ples
t fo
rm.
200
�15
0�1 3�
7.H
ow m
any
cell
s w
ere
in t
he
cult
ure
afte
r 2.
5 h
ours
? E
xpre
ss y
our
answ
er i
nsi
mpl
est
form
.
288
�30
�1 2�6 � 5
t � 2
Wor
d Pr
oble
m P
ract
ice
Rat
ion
al E
xpo
nen
ts
Lesson 7-6
Cha
pter
747
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Les
ser-
Kn
ow
n G
eom
etri
c F
orm
ula
sM
any
geom
etri
c fo
rmu
las
invo
lve
radi
cal
expr
essi
ons.
Mak
e a
dra
win
g to
ill
ust
rate
eac
h o
f th
e fo
rmu
las
give
n o
n t
his
pag
e.
Th
en e
valu
ate
the
form
ula
for
th
e gi
ven
val
ue
of t
he
vari
able
. Rou
nd
an
swer
s to
th
e n
eare
st h
un
dre
dth
.
Enri
chm
ent
1.T
he
area
of
an i
sosc
eles
tri
angl
e. T
wo
side
s h
ave
len
gth
a; t
he
oth
er s
ide
has
len
gth
c. F
ind
Aw
hen
a�
6 an
d c
�7.
A�
� 4c � �4a
2�
�c2 �
A�
17.0
6 u
nit
s2
3.T
he
area
of
a re
gula
r pe
nta
gon
wit
h a
side
of
len
gth
a. F
ind
Aw
hen
a�
4.
A�
�a 42 ��
25 �
�10
�5�
�A
�27
.53
un
its2
5.T
he
volu
me
of a
reg
ula
r te
trah
edro
nw
ith
an
edg
e of
len
gth
a. F
ind
Vw
hen
a
�2.
V�
� 1a 23 ��
2�
V�
0.94
un
its3
7.H
eron
’s F
orm
ula
for
th
e ar
ea o
f a
tria
ngl
e u
ses
the
sem
i-pe
rim
eter
s,
wh
ere
s�
�a�
2b�
c�
. Th
e si
des
of t
he
tria
ngl
e h
ave
len
gth
s a,
b, a
nd
c. F
ind
Aw
hen
a�
3, b
�4,
an
d c
�5.
A�
�s(
s�
�a)
(s�
�b)
(s�
�c)�
A�
6 u
nit
s2
2.T
he
area
of
an e
quil
ater
al t
rian
gle
wit
ha
side
of
len
gth
a. F
ind
Aw
hen
a�
8.
A�
�a 42 ��
3�
A�
27.7
1 u
nit
s2
4.T
he
area
of
a re
gula
r h
exag
on w
ith
asi
de o
f le
ngt
h a
. Fin
d A
wh
en a
�9.
A�
�3 2a2 ��
3�
A�
210.
44 u
nit
s2
6.T
he
area
of
the
curv
ed s
urf
ace
of a
rig
ht
con
e w
ith
an
alt
itu
de o
f h
and
radi
us
ofba
se r
. Fin
d S
wh
en r
�3
and
h�
6.
S�
�r �
r2�
h�
2 �S
�63
.22
un
its2
8.T
he r
adiu
s of
a c
ircl
e in
scri
bed
in a
giv
entr
ian
gle
also
use
s th
e se
mi-
peri
met
er.
Fin
d r
wh
en a
�6,
b�
7, a
nd
c�
9.
r�
r�
1.91
un
its
rb ca
�s(
s�
�a)
(s�
�b)
(s�
�c)�
��
�s
r
h
aa
aa
aa
a
a
a
a
b
c
aa
a
aa
a
aa
a
a
a
a
c
a
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A22
Chapter 7 A23 Glencoe Algebra 2
An
swer
s
Answers (Lessons 7-6 and 7-7)
Exam
ple
Cha
pter
748
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Spre
adsh
eet
Act
ivit
yA
pp
reci
atio
n a
nd
Dep
reci
atio
n
1.If
Mr.
Bla
ckst
ock
choo
ses
anot
her
pro
pert
y in
th
e n
eigh
borh
ood
that
cos
ts$9
9,90
0, w
hat
are
the
expe
cted
val
ues
of t
hat
hom
e in
the
sam
e pe
riod
s of
tim
e?$1
03,8
96.0
0,$1
05,9
53.5
5,$1
16,8
68.8
7,$1
30,1
78.8
8
2.W
hat
wou
ld M
r. B
lack
stoc
k’s
prof
it b
e on
th
e $9
9,90
0 h
ome
if h
e so
ld i
taf
ter
9 ye
ars
and
3 m
onth
s?$4
3,68
9.89
3.If
an
an
tiqu
e ch
air
wor
th $
165.
00 i
ncr
ease
s in
val
ue
an a
vera
ge o
f 3 �
1 2�%ev
ery
year
, how
mu
ch w
ill
it b
e w
orth
nex
t ye
ar?
$170
.78
4.O
ften
ass
ets
like
car
s de
crea
se i
n v
alu
e ov
er t
ime.
Th
is a
sset
is
said
to
dep
reci
ate.
If
the
valu
e de
crea
ses
by a
fix
ed p
erce
nt
each
yea
r, o
r ot
her
peri
od o
f ti
me,
th
e am
oun
t y
of t
hat
qu
anti
ty a
fter
tye
ars
is g
iven
by
y�
a(1
�r)
t , w
her
e a
is t
he
init
ial
amou
nt
and
ris
th
e pe
rcen
t of
decr
ease
exp
ress
ed a
s a
deci
mal
. Use
a s
prea
dsh
eet
to f
ind
the
valu
e of
aca
r pu
rch
ased
for
$18
,500
aft
er 2
yea
rs, 2
yea
rs a
nd
6 m
onth
s, a
nd
4 ye
ars
and
3 m
onth
s if
th
e ca
r de
prec
iate
s at
a r
ate
of 1
2% p
er y
ear.
Mic
hae
l B
lack
stoc
k i
s co
nsi
der
ing
bu
yin
g a
pie
ce o
fin
vest
men
t p
rop
erty
for
$95
,000
. Th
e h
omes
in
th
e ar
ea a
re
app
reci
atin
g at
an
ave
rage
rat
e of
4%
per
yea
r. F
ind
th
e ex
pec
ted
valu
e of
th
e h
ome
in 1
yea
r, 1
yea
r an
d 6
mon
ths,
4 y
ears
, an
d
6 ye
ars
and
9 m
onth
s.U
se r
ows
1 an
d 2
to e
nte
r th
e in
itia
l am
oun
t an
d th
e ra
teof
in
crea
se. T
hen
use
Col
um
n A
to e
nte
r th
e am
oun
ts o
fti
me.
En
ter
the
nu
mbe
rs o
f m
onth
s as
a f
ract
ion
of
a ye
arsi
nce
tis
mea
sure
d in
yea
rs. C
olu
mn
B c
onta
ins
the
form
ula
s fo
r th
e va
lue
of t
he
hom
e.
For
mat
th
e ce
lls
con
tain
ing
the
valu
es a
s cu
rren
cy s
oth
at t
hey
are
dis
play
ed a
s do
llar
s an
d ce
nts
. Th
e ex
pect
-ed
val
ue
of t
he
hom
e af
ter
each
am
oun
t of
tim
e is
sh
own
in t
he
spre
adsh
eet.
Wh
en a
n a
sset
su
ch a
s a
hou
se i
ncr
ease
s in
val
ue
over
tim
e, i
t is
sai
d to
appr
ecia
te. I
f th
e va
lue
incr
ease
s by
a f
ixed
per
cen
t ea
ch y
ear,
or
oth
er
peri
od o
f ti
me,
th
e am
oun
t y
of t
hat
qu
anti
ty a
fter
tye
ars
is g
iven
by
y�
a(1
�r)
t ,
wh
ere
ais
th
e in
itia
l am
oun
t an
d r
is t
he
perc
ent
of i
ncr
ease
exp
ress
ed a
s a
deci
mal
. You
can
use
a s
prea
dsh
eet
to i
nve
stig
ate
futu
re v
alu
es o
f an
ass
et.
A1
B
9Ap
pre
ciat
ion
.xls
Initi
al v
alue
=$9
5,00
0.00
2R
ate
=0.
043 4
Year
sV
alue
5$9
8,80
0.00
6$1
00,7
56.6
37
$111
,136
.56
8$1
23,7
93.7
3
11.
5 46.
75
Sh
eet
1S
hee
t 2
Exer
cise
s
Lesson 7-7
Cha
pter
749
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
So
lvin
g R
adic
al E
qu
atio
ns
and
Ineq
ual
itie
sG
et R
ead
y fo
r th
e le
sso
nR
ead
th
e in
trod
uct
ion
to
Les
son
7-7
in
you
r te
xtb
ook
.
Exp
lain
how
you
wou
ld u
se t
he
form
ula
in
you
r te
xtbo
ok t
o fi
nd
the
cost
of
prod
ucin
g12
5,00
0 co
mpu
ter
chip
s. (
Des
crib
e th
e st
eps
of t
he c
alcu
lati
on in
the
ord
er in
whi
ch y
ou w
ould
perf
orm
the
m, b
ut d
o no
t ac
tual
ly d
o th
e ca
lcul
atio
n.)
Sam
ple
an
swer
:R
aise
125
,000
to
th
e p
ow
er b
y ta
kin
g t
he
cub
e ro
ot
of
125,
000
and
sq
uar
ing
th
e re
sult
(o
r ra
ise
125,
000
to t
he
po
wer
by
ente
rin
g 1
25,0
00 ^
(2/
3) o
n a
cal
cula
tor)
.
Mu
ltip
ly t
he
nu
mb
er y
ou
get
by
10 a
nd
th
en a
dd
150
0.
Rea
d t
he
Less
on
1.a.
Wh
at i
s an
ext
ran
eou
s so
luti
onof
a r
adic
al e
quat
ion
?S
amp
le a
nsw
er:
a n
um
ber
that
sat
isfi
es a
n e
qu
atio
n o
bta
ined
by
rais
ing
bo
th s
ides
of
the
ori
gin
aleq
uat
ion
to
a h
igh
er p
ow
er b
ut
do
es n
ot
sati
sfy
the
ori
gin
al e
qu
atio
n
b.
Des
crib
e tw
o w
ays
you
can
ch
eck
the
prop
osed
sol
uti
ons
of a
rad
ical
equ
atio
n i
n o
rder
to d
eter
min
e w
het
her
an
y of
th
em a
re e
xtra
neo
us
solu
tion
s.S
amp
le a
nsw
er:
On
ew
ay is
to
ch
eck
each
pro
po
sed
so
luti
on
by
sub
stit
uti
ng
it in
to t
he
ori
gin
al e
qu
atio
n.A
no
ther
way
is t
o u
se a
gra
ph
ing
cal
cula
tor
to g
rap
hb
oth
sid
es o
f th
e o
rig
inal
eq
uat
ion
.See
wh
ere
the
gra
ph
s in
ters
ect.
Th
is c
an h
elp
yo
u id
enti
fy s
olu
tio
ns
that
may
be
extr
aneo
us.
2.C
ompl
ete
the
step
s th
at s
hou
ld b
e fo
llow
ed i
n o
rder
to
solv
e a
radi
cal
ineq
ual
ity.
Ste
p 1
If t
he
of t
he
root
is
, ide
nti
fy t
he
valu
es o
f
the
vari
able
for
wh
ich
th
e is
.
Ste
p 2
Sol
ve t
he
alge
brai
call
y.
Ste
p 3
Test
to
ch
eck
you
r so
luti
on.
Rem
emb
er W
hat
Yo
u L
earn
ed
3.O
ne
way
to
rem
embe
r so
met
hin
g is
to
expl
ain
it
to a
not
her
per
son
. Su
ppos
e th
at y
our
frie
nd
Leo
ra t
hin
ks t
hat
sh
e do
es n
ot n
eed
to c
hec
k h
er s
olu
tion
s to
rad
ical
equ
atio
ns
bysu
bsti
tuti
on b
ecau
se s
he
know
s sh
e is
ver
y ca
refu
l an
d se
ldom
mak
es m
ista
kes
in h
erw
ork.
How
can
you
exp
lain
to
her
th
at s
he
shou
ld n
ever
thel
ess
chec
k ev
ery
prop
osed
solu
tion
in
th
e or
igin
al e
quat
ion
?S
amp
le a
nsw
er:
Sq
uar
ing
bo
th s
ides
of
aneq
uat
ion
can
pro
du
ce a
n e
qu
atio
n t
hat
is n
ot
equ
ival
ent
to t
he
ori
gin
alo
ne.
Fo
r ex
amp
le,t
he
on
ly s
olu
tio
n o
f x
�5
is 5
,bu
t th
e sq
uar
edeq
uat
ion
x2
�25
has
tw
o s
olu
tio
ns,
5 an
d �
5.
valu
es
ineq
ual
ity
no
nn
egat
ive
rad
ican
d
even
ind
ex
2 � 3
2 � 3
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A23
Chapter 7 A24 Glencoe Algebra 2
Answers (Lesson 7-7)
Exam
ple
1Ex
amp
le 2
Cha
pter
750
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
So
lvin
g R
adic
al E
qu
atio
ns
and
Ineq
ual
itie
sSo
lve
Rad
ical
Eq
uat
ion
sT
he
foll
owin
g st
eps
are
use
d in
sol
vin
g eq
uat
ion
s th
at h
ave
vari
able
s in
th
e ra
dica
nd.
Som
e al
gebr
aic
proc
edu
res
may
be
nee
ded
befo
re y
ou u
se t
hes
est
eps.
Ste
p 1
Isol
ate
the
radi
cal o
n on
e si
de o
f th
e eq
uatio
n.S
tep
2To
elim
inat
e th
e ra
dica
l, ra
ise
each
sid
e of
the
equ
atio
n to
a p
ower
equ
al t
o th
e in
dex
of t
he r
adic
al.
Ste
p 3
Sol
ve t
he r
esul
ting
equa
tion.
Ste
p 4
Che
ck y
our
solu
tion
in th
e or
igin
al e
quat
ion
to m
ake
sure
that
you
hav
e no
t obt
aine
d an
y ex
tran
eous
roo
ts.
Sol
ve 2
�4x
��
8��
4 �
8.
2�4x
�8
��
4 �
8O
rigin
al e
quat
ion
2�4x
�8
��
12A
dd 4
to
each
sid
e.
�4x
�8
��
6Is
olat
e th
e ra
dica
l.
4x�
8 �
36S
quar
e ea
ch s
ide.
4x�
28S
ubtr
act
8 fr
om e
ach
side
.
x�
7D
ivid
e ea
ch s
ide
by 4
.
Ch
eck
2�4(
7) �
�8�
�4
�8
2�36�
�4
�8
2(6)
�4
�8
8 �
8T
he
solu
tion
x�
7 ch
ecks
.
Sol
ve �
3x�
�1�
��
5x��
1.
�3x
�1
��
�5x�
�1
Orig
inal
equ
atio
n
3x�
1�
5x�
2�5x�
�1
Squ
are
each
sid
e.
2�5x�
�2x
Sim
plify
.
�5x�
�x
Isol
ate
the
radi
cal.
5x�
x2S
quar
e ea
ch s
ide.
x2�
5x�
0S
ubtr
act
5xfr
om e
ach
side
.
x(x
�5)
�0
Fac
tor.
x�
0 or
x�
5C
hec
k�
3(0)
��
1��
1, b
ut
�5(
0)�
�1
��
1, s
o 0
isn
ot a
sol
uti
on.
�3(
5) �
�1�
�4,
an
d �
5(5)
��
1 �
4, s
o th
eso
luti
on i
s x
�5.
Sol
ve e
ach
eq
uat
ion
.
1.3
�2x
�3�
�5
2.2�
3x�
4�
�1
�15
3.8
��
x�
1�
�2
15n
o s
olu
tio
n
4.�
5 �
x�
�4
�6
5.12
��
2x�
1�
�4
6.�
12 �
�x�
�0
�95
no
so
luti
on
12
7.�
21��
�5x
�4
��
08.
10 �
�2x�
�5
9.�
x2�
7�
x��
�7x
�9
�
512
.5n
o s
olu
tio
n
10.4
3 �2x
�1
�1�
�2
�10
11.2
�x
�11
��
�x
�2
��
�3x
�6
�12
.�9x
�1
�1�
�x
�1
814
3,4
�3�
�3
Exer
cise
s
Lesson 7-7
Cha
pter
751
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solv
e R
adic
al In
equ
alit
ies
Ara
dic
al i
neq
ual
ity
is a
n i
neq
ual
ity
that
has
a v
aria
ble
in a
rad
ican
d. U
se t
he
foll
owin
g st
eps
to s
olve
rad
ical
in
equ
alit
ies.
Ste
p 1
If th
e in
dex
of t
he r
oot
is e
ven,
iden
tify
the
valu
es o
f th
e va
riabl
e fo
r w
hich
the
rad
ican
d is
non
nega
tive.
Ste
p 2
Sol
ve t
he in
equa
lity
alge
brai
cally
.S
tep
3Te
st v
alue
s to
che
ck y
our
solu
tion.
Sol
ve 5
��
20x
��
4�
�3.
Stud
y G
uide
and
Inte
rven
tion
(con
tinue
d)
So
lvin
g R
adic
al E
qu
atio
ns
and
Ineq
ual
itie
s
Sin
ce t
he
radi
can
d of
a s
quar
e ro
otm
ust
be
grea
ter
than
or
equ
al t
oze
ro, f
irst
sol
ve20
x�
4 �
0.20
x�
4 �
020
x�
�4
x�
�1 � 5
Now
sol
ve 5
��
20x
��
4��
�3.
5 �
�20
x�
�4�
��
3O
rigin
al in
equa
lity
�20
x�
�4�
�8
Isol
ate
the
radi
cal.
20x
�4
�64
Elim
inat
e th
e ra
dica
l by
squa
ring
each
sid
e.
20x
�60
Sub
trac
t 4
from
eac
h si
de.
x�
3D
ivid
e ea
ch s
ide
by 2
0.
It a
ppea
rs t
hat
��
x�
3 is
th
e so
luti
on. T
est
som
e va
lues
.
x�
�1
x�
0x
�4
�20
(�1
�)
�4
�is
not
a r
eal
5 �
�20
(0)
��
4�
�3,
so
the
5 �
�20
(4)
��
4�
�
4.2,
so
num
ber,
so t
he in
equa
lity
isin
equa
lity
is s
atis
fied.
th
e in
equa
lity
is n
otno
t sa
tisfie
d.sa
tisfie
d
Th
eref
ore
the
solu
tion
��
x�
3 ch
ecks
.
Sol
ve e
ach
in
equ
alit
y.
1.�
c�
2�
�4
�7
2.3�
2x�
1�
�6
15
3.�
10x
��
9��
2
5
c
11
x�
5x
4
4.5
3 �x
�2
��
8
25.
8 �
�3x
�4
��
36.
�2x
�8
��
4
2
x�
6�
x
7
x
14
7.9
��
6x�
3�
�6
8.�
49.
2�5x
�6
��
1
5
�
x
1x
8
x
�3
10.�
2x�
1�
2��
4 �
1211
.�2d
��
1��
�d�
�5
12.4
�b
�3
��
�b
�2
��
10
x
260
d
4
b
6
6 � 51 � 2
20�
��
3x�
1�4 � 3
1 � 2
1 � 5
1 � 5
Exam
ple
Exer
cise
s
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A24
Chapter 7 A25 Glencoe Algebra 2
An
swer
s
Answers (Lesson 7-7)
Cha
pter
752
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceS
olv
ing
Rad
ical
Eq
uat
ion
s an
d In
equ
alit
ies
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
1.�
x��
525
2.�
x��
3 �
716
3.5�
j��1
4.v�1 2�
�1
�0
no
so
luti
on
5.18
�3y
�1 2��
25n
o s
olu
tio
n6.
3 �2w�
�4
32
7.�
b�
5�
�4
218.
�3n
��
1��
58
9.3 �
3r�
6�
�3
1110
.2 �
�3p
��
7��
63
11.�
k�
4�
�1
�5
4012
.(2
d�
3)�1 3�
�2
13.(
t�
3)�1 3�
�2
1114
.4 �
(1 �
7u)�1 3�
�0
�9
15.�
3z�
2�
��
z�
4�
no
so
luti
on
16.�
g�
1�
��
2g�
�7�
8
17.�
x�
1�
�4�
x�
1�
no
so
luti
on
18.5
��
s�
3�
�6
3
s
4
19.�
2 �
�3x
�3
�
7�
1
x�
2620
.��
2a�
�4�
��
6�
2
a
16
21.2
�4r
�3
�
10r
7
22.4
��
3x�
1�
3
�
x�
0
23.�
y�
4�
�3
�3
y
3224
.�3�
11r
��
3��
�15
�
r
23 � 11
1 � 3
5 � 2
1 � 25
Lesson 7-7
Cha
pter
753
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
1.�
x��
864
2.4
��
x��
31
3.�
2p��
3 �
104.
4�3h�
�2
�0
5.c�1 2�
�6
�9
96.
18 �
7h�1 2�
�12
no
so
luti
on
7.3 �
d�
2�
�7
341
8.5 �
w�
7�
�1
8
9.6
�3 �
q�
4�
�9
3110
.4 �
y�
9�
�4
�0
no
so
luti
on
11.�
2m�
�6�
�16
�0
131
12.
3 �4m
��
1��
2 �
2
13. �
8n�
�5�
�1
�2
14.�
1 �
4�
t��8
��
6�
15.�
2t�
5�
�3
�3
16.(
7v�
2)�1 4�
�12
�7
no
so
luti
on
17.(
3g�
1)�1 2�
�6
�4
3318
.(6u
�5)
�1 3��
2 �
�3
�20
19.�
2d�
�5�
��
d�
1�
420
.�4r
�6
��
�r�
2
21.�
6x�
4�
��
2x�
1�
0�22
.�2x
�5
��
�2x
�1
�n
o s
olu
tio
n
23.3
�a�
�12
a
1624
.�z
�5
��
4 �
13�
5
z
76
25.8
��
2q��
5n
o s
olu
tio
n26
.�2a
��
3�
5
a�
14
27.9
��
c�
4�
�6
c
528
.3 �
x�
1�
�
2x
��
7
29.S
TATI
STIC
SS
tati
stic
ian
s u
se t
he
form
ula
��
�v�
to c
alcu
late
a s
tan
dard
dev
iati
on �
,w
her
e v
is t
he
vari
ance
of
a da
ta s
et. F
ind
the
vari
ance
wh
en t
he
stan
dard
dev
iati
on
is 1
5.22
5
30.G
RA
VIT
ATI
ON
Hel
ena
drop
s a
ball
fro
m 2
5 fe
et a
bove
a l
ake.
Th
e fo
rmu
la
t�
�25
��
h�de
scri
bes
the
tim
e t
in s
econ
ds t
hat
th
e ba
ll i
s h
feet
abo
ve t
he
wat
er.
How
man
y fe
et a
bove
th
e w
ater
wil
l th
e ba
ll b
e af
ter
1 se
con
d?9
ft
1 � 4
3 � 2
7 � 2
41 � 2
3 � 47 � 4
63 � 4
1 � 1249 � 2
Prac
tice
S
olv
ing
Rad
ical
Eq
uat
ion
s an
d In
equ
alit
ies
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A25
Chapter 7 A26 Glencoe Algebra 2
Answers (Lesson 7-7)
Cha
pter
754
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.SI
GN
SA
sign
pai
nte
r m
ust
spe
nd
$8n
�2 3��
400
to
mak
e n
sign
s.
How
man
ysi
gns
can
th
e pa
inte
r m
ake
for
$120
0?10
00
2.LA
TER
AL
AR
EAT
he
late
ral
area
of
aco
ne
wit
h b
ase
radi
us
ran
d h
eigh
t h
isgi
ven
by
the
form
ula
L�
�r�
r2�
h�
2 �.
Aco
ne
has
a l
ater
al a
rea
of 6
5�sq
uar
eu
nit
s an
d a
base
rad
ius
of 5
un
its.
Wh
at i
s th
e h
eigh
t of
th
e co
ne?
12 u
nit
s
3.O
RIG
AM
IG
eorg
ia w
ants
to
fold
asq
uar
e pi
ece
of p
aper
in
to a
n e
quil
ater
altr
ian
gle.
Sh
e w
ants
to
loca
te t
he
dist
ance
xu
p th
e si
de o
f th
e sq
uar
ew
her
e sh
e ca
n m
ake
the
fold
in
dica
ted
by t
he
dash
ed l
ine
in t
he
figu
re s
o th
at
a�
b. F
rom
geo
met
ry c
lass
, sh
e kn
ows
that
a�
�1
�x2
�an
d b
��
2�(1
�x)
. S
o th
e eq
uat
ion
sh
e m
ust
sol
ve i
s �
1 �
x2�
��
2�(1
�x)
. Wh
at i
s x?
2 �
�3�
4.TE
THER
SA
teth
er i
s be
ing
atta
ched
to
a 2
5-fo
ot p
ole
in s
uch
a w
ay t
hat
x
�y
�50
. By
the
Pyt
hag
orea
nT
heo
rem
, th
e di
stan
ce y
��
x2�
2�
52 �.
Wh
at m
ust
xbe
?
18.7
5 ft
RA
NG
E F
or E
xerc
ises
5 a
nd
6, u
se t
he
foll
owin
g in
form
atio
n.
An
ast
eroi
d is
pas
sin
g n
ear
Ear
th. I
f E
arth
is l
ocat
ed a
t th
e or
igin
of
a co
ordi
nat
epl
ane,
th
e pa
th t
hat
th
e as
tero
id w
ill
trac
e
out
is g
iven
by
y�
, x
0.
On
e u
nit
corr
espo
nds
to o
ne m
illi
on m
iles
. Car
l le
arns
that
he
wil
l be
abl
e to
see
the
ast
eroi
d w
ith
his
tele
scop
e w
hen
the
aste
roid
is
wit
hin
mil
lion
mil
es o
f E
arth
.
5.W
rite
an
exp
ress
ion
th
at g
ives
th
edi
stan
ce o
f th
e as
tero
id f
rom
Ear
th a
s a
fun
ctio
n o
f x.
�11
11�x2 �
6.F
or w
hat
val
ues
of
xw
ill
the
aste
roid
be
in r
ange
of
Car
l’s t
eles
cope
?
x
12
17 � 12
289
� x2
145
� 12
17 � x
25 ft
y
x
b
xa 1
45˚
h
r
Wor
d Pr
oble
m P
ract
ice
Rat
ion
al E
qu
atio
ns
and
Ineq
ual
itie
s
Exam
ple
Lesson 7-7
Cha
pter
755
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
Tru
th T
able
sIn
mat
hem
atic
s, t
he
basi
c op
erat
ion
s ar
e ad
diti
on, s
ubt
ract
ion
, mu
ltip
lica
tion
, di
visi
on, f
indi
ng
a ro
ot, a
nd
rais
ing
to a
pow
er. I
n l
ogic
, th
e ba
sic
oper
atio
ns
are
the
foll
owin
g: n
ot(�
), a
nd
(�
), o
r (
), a
nd
impl
ies
(→).
If p
and
qar
e st
atem
ents
, th
en �
pm
ean
s n
ot p
; �q
mea
ns
not
q; p
� q
mea
ns
pan
d q;
p
qm
ean
s p
or q
; an
d p
→ q
mea
ns
pim
plie
s q.
Th
e op
erat
ion
s ar
e de
fin
ed b
y tr
uth
tab
les.
On
th
e le
ft b
elow
is
the
tru
th t
able
for
th
e st
atem
ent
�p.
Not
ice
that
th
ere
are
two
poss
ible
con
diti
ons
for
p, t
rue
(T)
or f
alse
(F
). I
f p
is t
rue,
�p
is f
alse
; if
pis
fal
se, �
pis
tru
e. A
lso
show
n a
re t
he
tru
th t
able
s fo
r p
� q
, p
q, a
nd
p →
q.
p�
pp
qp
� q
pq
p
qp
qp
→ q
TF
TT
TT
TT
TT
TF
TT
FF
TF
TT
FF
FT
FF
TT
FT
TF
FF
FF
FF
FT
You
can
use
th
is i
nfo
rmat
ion
to
fin
d ou
t u
nde
r w
hat
con
diti
ons
a co
mpl
ex
stat
emen
t is
tru
e.
Un
der
wh
at c
ond
itio
ns
is �
p
qtr
ue?
Cre
ate
the
tru
th t
able
for
th
e st
atem
ent.
Use
th
e in
form
atio
n f
rom
th
e tr
uth
ta
ble
abov
e fo
r p
q
to c
ompl
ete
the
last
col
um
n.
pq
�p
�p
q
TT
FT
Wh
en o
ne
stat
emen
t is
T
FF
Ftr
ue
and
on
e is
fal
se,
FT
TT
the
con
jun
ctio
n is
tru
e.F
FT
T
The
tru
th t
able
indi
cate
s th
at �
p
qis
tru
e in
all
case
s ex
cept
whe
re p
is t
rue
and
qis
fal
se.
Use
tru
th t
able
s to
det
erm
ine
the
con
dit
ion
s u
nd
er w
hic
h e
ach
sta
tem
ent
is t
rue.
1.�
p
�q
2.�
p →
(p →
q)
all e
xcep
t w
her
e b
oth
all
pan
d q
are
tru
e3.
(p
q)
(�p
� �
q)4.
(p →
q)
(q
→ p
)al
lal
l
5.(p
→ q
)�
(q →
p)
6.(�
p �
�q)
→ �
(p
q)b
oth
pan
d q
are
tru
e;al
lb
oth
pan
d q
are
fals
e
A2-A26 A2-07-873977 5/22/06 9:41 AM Page A26