Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A1 Glencoe Algebra 1
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
3
Gle
ncoe A
lgeb
ra 1
An
tici
pati
on
Gu
ide
Rad
ical
Exp
ressio
ns a
nd
Tri
an
gle
s
Befo
re y
ou
beg
in C
ha
pte
r 1
0
•
R
ead
each
sta
tem
ent.
•
D
ecid
e w
het
her
you
Agre
e (A
) or
Dis
agre
e (D
) w
ith
th
e st
ate
men
t.
•
W
rite
A o
r D
in
th
e fi
rst
colu
mn
OR
if
you
are
not
su
re w
het
her
you
agre
e or
d
isagre
e, w
rite
NS
(N
ot S
ure
).
ST
EP
1A
, D
, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
An
exp
ress
ion
th
at
con
tain
s a s
qu
are
roo
t is
call
ed a
ra
dic
al
exp
ress
ion
.A
2.
It i
s alw
ays
tru
e th
at
√ �
xy w
ill
equ
al
√ � x
· √
� y .A
3.
1
−
√ �
3
is
in s
imp
lest
for
m b
ecau
se √
�
3 i
s n
ot a
wh
ole
nu
mber
.D
4.
Th
e su
m o
f 3
√ �
3
an
d 2
√ �
3
wil
l eq
ual
5 √
�
3 .
A
5.
Bef
ore
mu
ltip
lyin
g t
wo
rad
ical
exp
ress
ion
s w
ith
dif
fere
nt
rad
ican
ds
the
squ
are
roo
ts m
ust
be
evalu
ate
d.
D
6.
Wh
en s
olvin
g r
ad
ical
equ
ati
ons
by s
qu
ari
ng e
ach
sid
e of
th
e eq
uati
on,
it i
s p
ossi
ble
to
obta
in s
olu
tion
s th
at
are
not
so
luti
ons
to t
he
orig
inal
equ
ati
on.
A
7.
Th
e lo
nges
t si
de
of a
ny t
rian
gle
is
call
ed t
he
hyp
oten
use
.D
8.
Bec
au
se 5
2 =
42 +
32,
a t
rian
gle
wh
ose
sid
es h
ave
len
gth
s 3,
4,
an
d 5
wil
l be
a r
igh
t tr
ian
gle
.A
9.
On
a c
oord
inate
pla
ne,
th
e d
ista
nce
bet
wee
n a
ny t
wo
poi
nts
ca
n b
e fo
un
d u
sin
g t
he
Pyth
agor
ean
Th
eore
m.
A
10.
Th
e D
ista
nce
For
mu
la c
an
not
be
use
d t
o fi
nd
th
e d
ista
nce
bet
wee
n t
wo
poi
nts
on
th
e sa
me
ver
tica
l li
ne.
D
11.
Tw
o tr
ian
gle
s are
sim
ilar
only
if
thei
r co
rres
pon
din
g a
ngle
s are
con
gru
ent
an
d t
he
mea
sure
s of
thei
r co
rres
pon
din
g s
ides
are
in
pro
por
tion
.A
12.
All
rig
ht
tria
ngle
s are
sim
ilar.
D
A
fter y
ou
com
ple
te C
ha
pte
r 1
0
•
R
erea
d e
ach
sta
tem
ent
an
d c
omp
lete
th
e la
st c
olu
mn
by e
nte
rin
g a
n A
or
a D
.
•
D
id a
ny o
f you
r op
inio
ns
abou
t th
e st
ate
men
ts c
han
ge
from
th
e fi
rst
colu
mn
?
•
F
or t
hos
e st
ate
men
ts t
hat
you
mark
wit
h a
D,
use
a p
iece
of
pap
er t
o w
rite
an
ex
am
ple
of
wh
y y
ou d
isagre
e.
10 Ste
p 1
Ste
p 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-1
Ch
ap
ter
10
5
Gle
ncoe A
lgeb
ra 1
Dilati
on
s o
f R
ad
ical
Fu
nct
ion
s A
sq
ua
re r
oo
t fu
ncti
on
con
tain
s th
e sq
uare
roo
t of
a v
ari
able
. S
qu
are
roo
t fu
nct
ion
s are
a t
yp
e of
ra
dic
al
fun
cti
on
.
In o
rder
for
a s
qu
are
roo
t to
be
a r
eal
nu
mber
, th
e ra
dic
an
d,
or t
he
exp
ress
ion
un
der
th
e ra
dic
al
sign
, ca
nn
ot b
e n
egati
ve.
Valu
es t
hat
mak
e th
e ra
dic
an
t n
egati
ve
are
not
in
clu
ded
in
th
e d
omain
.
Sq
uare
Ro
ot
Fu
ncti
on
Pare
nt
function:
f(x)
= √
� x
Type o
f gra
ph:
curv
e
Dom
ain
: {x
|x ≥
0}
Range:
{y|
y ≥
0}
G
ra
ph
y =
3 √
�x .
Sta
te t
he d
om
ain
an
d r
an
ge.
Ste
p 1
Mak
e a t
able
. C
hoo
se n
onn
egati
ve
S
tep
2 P
lot
poi
nts
an
d d
raw
a
valu
es f
or x
.
smoo
th c
urv
e.
xy
00
0.5
≈ 2
.12
13
2≈
4.2
4
46
6≈
7.3
5
y
x
y=
3 x
Th
e d
omain
is
{x|
x ≥
0}
an
d t
he
ran
ge
is {
y|
y ≥
0}.
Exerc
ises
Gra
ph
ea
ch
fu
ncti
on
, a
nd
co
mp
are t
o t
he p
aren
t g
ra
ph
. S
tate
th
e d
om
ain
an
d r
an
ge.
1. y =
3
−
2 √
� x 2. y =
4 √
� x
3. y =
5
−
2 √
� x
y
x
y
x
y
x
D
ilati
on
of
y =
√ " x ;
D
ilati
on
of
y =
√ " x ;
D
ilati
on
of
y =
√ " x ;
D
= {
x |
x ≥
0};
D
= {
x |
x ≥
0};
D
= {
x |
x ≥
0};
R
= {
y |
y ≥
0}
R
= {
y |
y ≥
0}
R =
{y |
y ≥
0}
10-1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Sq
uare
Ro
ot
Fu
ncti
on
s
Exam
ple
y
x
y=
x
Answers (Anticipation Guide and Lesson 10-1)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
6
Gle
ncoe A
lgeb
ra 1
Refle
ctio
ns a
nd
Tran
sla
tio
ns o
f R
ad
ical
Fu
nctio
ns
Rad
ical
fun
ctio
ns,
lik
e
qu
ad
rati
c fu
nct
ion
s, c
an
be t
ran
slate
d h
ori
zon
tall
y a
nd
vert
icall
y,
as
well
as
refl
ect
ed
acr
oss
the x
-axis
. T
o d
raw
th
e g
rap
h o
f y =
a √ """
x +
h ,
foll
ow
th
ese
ste
ps.
Gra
ph
s o
f S
qu
are
Ro
ot
Fu
ncti
on
s
Ste
p 1
D
raw
th
e g
rap
h o
f y =
+c √ x .
Th
e g
rap
h s
tart
s at
the
ori
gin
an
d p
ass
es
thro
ugh
th
e p
oin
t at
(1,
a).
If
a > 0
, th
e
gra
ph
is
in t
he 1
st q
uad
ran
t. I
f a
< 0
, th
e g
rap
h i
s re
flect
ed
acr
oss
th
e x
-axis
an
d i
s in
th
e 4
th q
uad
ran
t.
Ste
p 2
T
ran
slate
th
e g
rap
h
c u
nit
s u
p i
f c
is p
osi
tive a
nd
dow
n
if c
is
negati
ve.
Ste
p 3
T
ran
slate
th
e g
rap
h
h
un
its
left
if
h i
s p
osi
tive a
nd
rig
ht
if h
is
negati
ve.
G
ra
ph
y =
- √ """
x + 1
an
d c
om
pa
re t
o t
he p
aren
t g
ra
ph
. S
tate
th
e
do
ma
in a
nd
ra
ng
e.
Ste
p 1
M
ak
e a
table
of
valu
es.
x-
1
01
3
8
y 0
-1
-1.4
1-
2-
3
Ste
p 2
T
his
is
a h
ori
zon
tal
tran
slati
on
1 u
nit
to t
he l
eft
of
the p
are
nt
fun
ctio
n a
nd
refl
ect
ed
acr
oss
th
e x
-axis
. T
he d
om
ain
is {x
| x ≥
0}
an
d t
he r
an
ge i
s {y
| y ≤
0}.
Exerc
ises
Gra
ph
ea
ch
fu
ncti
on
, a
nd
co
mp
are t
o t
he p
aren
t g
ra
ph
. S
tate
th
e d
om
ain
an
d r
an
ge.
1. y =
√ " x +
3
2.
y = √ """
x -
1
3.
y =
- √ """
x -
1
y
x
y
x
y
x
10-1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Sq
uare
Ro
ot
Fu
ncti
on
s
Exam
ple
y
x
y=
x
y= -
x+
1
tran
sla
tio
n o
f y =
√ "
x
up
3 u
nit
s;
D =
{x |
x ≥
0};
R =
{y |
y ≥
3}
tran
sla
tio
n o
f y =
√ "
x
rig
ht
1 u
nit
;D
= {
x |
x ≥
1};
R =
{y |
y ≥
0}
tran
sla
tio
n o
f y =
√ "
x
rig
ht
1 u
nit
an
d r
efl
ecte
d
acro
ss t
he x
-axis
;D
= {
x |
x ≥
1}
R = {
y |
y ≤
0}
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-1
Ch
ap
ter
10
7
Gle
ncoe A
lgeb
ra 1
Gra
ph
ea
ch
fu
ncti
on
, a
nd
co
mp
are t
o t
he p
aren
t g
ra
ph
. S
tate
th
e d
om
ain
an
d r
an
ge.
1. y =
2 √ " x
2. y =
1 −
2 √ " x
3. y =
5 √ " x
dilati
on
of
y =
√ x ;
dil
ati
on
of
y =
√ x ;
dil
ati
on
of
y =
√ x ;
D =
{x |
x ≥
0},
R =
{ y
| y
≥ 0
}
D
= {
x |
x ≥
0},
R =
{ y
| y
≥ 0
}
D =
{x |
x ≥
0},
R =
{ y
| y
≥ 0
}
4. y =
√ " x +
1
5. y =
√ " x - 4
6. y =
√ """
x - 1
tran
sla
tio
n o
f
tran
sla
tio
n o
f t
ran
sla
tio
n o
f
y =
√ " x
up
1 u
nit
; y
= √ x
do
wn
4 u
nit
s;
y =
√ x
rig
ht
1 u
nit
;
D =
{x |
x ≥
0},
R =
{ y
| y
≥ 1
}
D =
{x |
x ≥
0},
R =
{ y
| y
≥ -
4}
D =
{x |
x ≥
1},
R =
{ y
| y
≥ 0
}
7. y =
- √ """
x -
3
8. y =
√ """
x -
2 + 3
9. y =
- 1
−
2 √ """
x - 4
+ 1
tran
sla
tio
n o
f y =
√ " x ;
tr
an
sla
tio
n o
f y =
√ x
dia
lati
on
of
y =
√ " x
refl
ecte
d
rig
ht
3 u
nit
s r
efl
ecte
d a
cro
ss
rig
ht
2 u
nit
s a
nd
up
a
cro
ss t
he x
-axis
the x
-axis
; D
= {
x |
x ≥
3},
3 u
nit
s;
D =
{x |
x ≥
2},
tran
sla
ted
rig
ht
4 u
nit
s u
p
R
= {
y |
y ≤
0}
R =
{y |
y ≥
3}
1 u
nit
s;
D =
{x |
x ≥
4},
R
= {
y |
y ≤
1}
10-1
Sk
ills
Pra
ctic
e
Sq
uare
Ro
ot
Fu
ncti
on
s
y
x
y
x
y
x
12 8 4
−2
24
y
x
y
x
y
x
y
x
y
x
y
x
Answers (Lesson 10-1)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
8
Gle
ncoe A
lgeb
ra 1
Gra
ph
ea
ch
fu
ncti
on
, a
nd
co
mp
are t
o t
he p
aren
t g
ra
ph
. S
tate
th
e d
om
ain
an
d r
an
ge.
1. y =
4 −
3 √ # x
2. y =
√ # x +
2
3. y =
√ ###
x - 3
y
x
y
x
y
x
4. y =
- √ # x +
1
5. y =
2 √
x - 1
+ 1
6. y =
- √
x -
2 +
2
y
x
y
x
y
x
7. O
HM
’S L
AW
In
ele
ctri
cal
en
gin
eeri
ng,
the r
esi
stan
ce o
f a c
ircu
it
can
be f
ou
nd
by t
he e
qu
ati
on
I =
√
P −
R , w
here
I i
s th
e c
urr
en
t in
am
pere
s, P
is
the p
ow
er
in w
att
s, a
nd
R i
s th
e r
esi
stan
ce o
f
the c
ircu
it i
n o
hm
s. G
rap
h t
his
fu
nct
ion
for
a c
ircu
it w
ith
a
resi
stan
ce o
f 4 o
hm
s.
10-1
Practi
ce
Sq
uare
Ro
ot
Fu
ncti
on
s
Current (amperes)
23 1 020
45
Pow
er (
wat
ts)
40
60
80
100
dilati
on
of
y =
√ "
x ;
D =
{x |
x ≥
0},
R =
{y |
y ≥
0}
tran
sla
tio
n o
f y =
√ "
x
up
2 u
nit
;D
= {
x |
x ≥
0},
R
= {
y |
y ≥
2}
tran
sla
tio
n o
f y =
√ "
x
left
3 u
nit
s;
D = {
x |
x ≥
-3},
R
= {
y |
y ≥
0}
tran
sla
tio
n o
f y =
√ "
x
up
1 u
nit
refl
ecte
d
in t
he x
-axis
; D
= {
x |
x ≥
0},
R =
{y |
y ≤
1}
dilati
on
of
y = √ "
x
tran
sla
ted
up
1 u
nit
an
d r
igh
t 1 u
nit
;D
= {
x |
x ≥
1},
R =
{y |
y ≥
1}
tran
sla
tio
n o
f y =
√ "
x ;
u
p 2
un
its a
nd
rig
ht
2 u
nit
s,
refl
ecte
d
in t
he x
-axis
; D
= {
x |
x ≥
2},
R =
{y |
y ≤
2}
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-1
Ch
ap
ter
10
9
Gle
ncoe A
lgeb
ra 1
10-1
Wo
rd
Pro
ble
m P
racti
ce
Sq
uare
Ro
ot
Fu
ncti
on
s
1. PEN
DU
LU
M M
OTIO
N T
he p
eri
od
T o
f
a p
en
du
lum
in
seco
nd
s, w
hic
h i
s th
e t
ime
for
the p
en
du
lum
to r
etu
rn t
o t
he p
oin
t
of
rele
ase
, is
giv
en
by t
he e
qu
ati
on
T=
1.1
1 √# L
. T
he l
en
gth
of
the
pen
du
lum
in
feet
is g
iven
by L
. G
rap
h
this
fu
nct
ion
.
2. EM
PIR
E S
TA
TE B
UIL
DIN
G T
he r
oof
of
the E
mp
ire S
tate
Bu
ild
ing i
s 1250 f
eet
above t
he g
rou
nd
. T
he v
elo
city
of
an
obje
ct d
rop
ped
fro
m a
heig
ht
of
h m
ete
rs
is g
iven
by t
he f
un
ctio
n V
= √ ##
2gh
,
wh
ere
g i
s th
e g
ravit
ati
on
al
con
stan
t,
32.2
feet
per
seco
nd
squ
are
d.
If a
n o
bje
ct
is d
rop
ped
fro
m t
he r
oof
of
the b
uil
din
g,
how
fast
is
it t
raveli
ng w
hen
it
hit
s th
e
stre
et
belo
w?
ap
pro
xim
ate
ly 2
84 f
t/s
3. ER
RO
R A
NA
LY
SIS
G
regory
is
dra
win
g
the g
rap
h o
f y =
-5 √ ###
x +
1 .
He d
esc
ribes
the r
an
ge a
nd
dom
ain
as
{x %
x ≥ -
1},
{y %
y ≥ 0
}. E
xp
lain
an
d c
orr
ect
th
e
mis
tak
e t
hat
Gre
gory
mad
e.
T
he d
om
ain
is a
ctu
ally {
y %
y ≤
0}
becau
se t
he g
rap
h h
as b
een
re
flecte
d a
cro
ss t
he x
-axis
.
4. C
APA
CIT
OR
S A
cap
aci
tor
is a
set
of
pla
tes
that
can
sto
re e
nerg
y i
n a
n
ele
ctri
c fi
eld
. T
he v
olt
age V
requ
ired
to
store
E j
ou
les
of
en
erg
y i
n a
cap
aci
tor
wit
h a
cap
aci
tan
ce o
f C
fara
ds
is g
iven
by V=√
2
E− C
.
a
. R
ew
rite
an
d s
imp
lify
th
e e
qu
ati
on
for
the c
ase
of
a 0
.0002 f
ara
d c
ap
aci
tor.
V =
100 √
E
b
. G
raph
th
e e
qu
ati
on
you
fou
nd i
n p
art
a.
Voltage (volts)
100
150
50 0
2
200
250
300
350
Ener
gy (
joule
s)
46
810
c.
How
wou
ld t
he g
rap
h d
iffe
r if
you
wis
hed
to s
tore
E +
1 j
ou
les
of
en
erg
y
in t
he c
ap
aci
tor
inst
ead
?
tran
sla
tio
n o
f V=
100 √" E
o
ne u
nit
to
th
e l
eft
d
. H
ow
wou
ld t
he g
rap
h d
iffe
r if
you
ap
pli
ed
a v
olt
age o
f V
+ 1
volt
s
inst
ead
?
tran
sla
tio
n o
fV=
100 √" E
o
ne u
nit
do
wn
Period (sec)
23 1 04
45
Pen
dulu
m L
engt
h (
ft)
812
16
20
Answers (Lesson 10-1)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A4 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
10
Gle
ncoe A
lgeb
ra 1
A c
ub
ic r
oo
t fu
ncti
on
con
tain
s th
e c
ubic
root
of
a v
ari
able
. T
he c
ub
ic r
oo
t of
a n
um
ber
x a
re t
he n
um
bers
y t
hat
sati
sfy t
he e
qu
ati
on
y ·
y ·
y =
x (
or,
alt
ern
ati
vely
, y =
3 √ " x
).U
nli
ke s
qu
are
root
fun
ctio
ns,
cu
bic
root
fun
ctio
ns
retu
rn r
eal
nu
mbers
wh
en
th
e r
ad
ican
d
is n
egati
ve.
G
ra
ph
y =
3 √ "
x .
Ste
p 1
Mak
e a
table
. S
tep
2 P
lot
poin
ts a
nd
dra
w a
sm
ooth
cu
rve.
xy
−5
−1.7
1
−3
−1.4
4
−1
−1
00
11
31.4
4
51.7
1
y
x
Exerc
ises
Gra
ph
ea
ch
fu
ncti
on
, a
nd
co
mp
are t
o t
he p
aren
t g
ra
ph
.
1. y =
2 3
√ " x
2. y =
3 √ " x +
1
3. y =
3 √ """
x +
1
y
x
y
x
y
x
d
ilati
on
of
y =
3 √ " x
tra
nsla
tio
n o
f t
ran
sla
tio
n o
f
y
=
3 √ " x
up
1 u
nit
y
=
3 √ " x
left
1 u
nit
4. y =
3 √ """
x -
1 +
2
5. y = 3
3 √ """
x -
2
6. y = - 3
√ " x +
3
y
x
y
x
y
x
tr
an
sla
tio
n o
f y =
3 √ " x
dilati
on
of
refl
ecti
on
of
y =
3 √ " x
u
p 2
un
its a
nd
y
= 3 √ " x
tran
sla
ted
a
cro
ss t
he x
-axis
r
igh
t 1 u
nit
r
igh
t 2 u
nit
s
tra
nsla
ted
up
3 u
nit
s
10-1
En
rich
men
t
Cu
bic
Ro
ot
Fu
ncti
on
s
Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-2
Ch
ap
ter
10
11
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Sim
plify
ing
Rad
ical
Exp
ressio
ns
Pro
du
ct P
rop
ert
y o
f Sq
uare
Ro
ots
T
he P
ro
du
ct
Pro
perty
of
Sq
ua
re R
oo
ts a
nd
p
rim
e f
act
ori
zati
on
can
be u
sed
to s
imp
lify
exp
ress
ion
s in
volv
ing i
rrati
on
al
squ
are
roots
. W
hen
you
sim
pli
fy r
ad
ical
exp
ress
ion
s w
ith
vari
able
s, u
se a
bso
lute
valu
e t
o e
nsu
re
non
negati
ve r
esu
lts.
S
imp
lify
√ ""
180 .
√ ""
180 =
√ """"""
2 #
2 #
3 #
3 #
5
Prim
e f
acto
rization o
f 180
= √ "
22 #
√ "
32 #
√ "
5
Pro
duct
Pro
pert
y o
f S
quare
Roots
= 2
# 3
# √ "
5
Sim
plif
y.
= 6
√ "
5
Sim
plif
y.
S
imp
lify
√ """"""
120
a2 ·
b5 ·
c4 .
√ """"""
120
a2 #
b5 #
c4
=
√ """"""""
23 #
3 #
5 #
a2 #
b5 #
c4
=
√ "
22 #
√ "
2 #
√ "
3 #
√ "
5 #
√ "
a2 #
√ """
b4 #
b #
√ "
c4
=
2 #
√ "
2 #
√ "
3 #
√ "
5 #
a #
b2 #
√ "
b #
c2
=
2 a b
2c2
√ ""
30b
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
1. √ ""
28
2. √ ""
68
3. √ ""
60
4. √ ""
75
2 √ "
7
2 √ ""
17
2 √ ""
15
5 √ "
3
5. √ ""
162
6. √ "
3 ·
√ "
6
7. √ "
2 ·
√ "
5
8. √ "
5 ·
√ ""
10
9 √ "
2
3 √ "
2
√ ""
10
5 √ "
2
9. √ ""
4a
2
10. √ ""
9x
4
11. √ """
300
a4
12. √ """
128
c6
2 a
3x
2
10
a2 √ "
3
8 c
3 √ "
2
13. 4 √ ""
10 #
3 √ "
6
14. √ ""
3x
2 #
3 √ ""
3x
4
15. √ """
20
a2b
4
16. √ """
100
x3y
24 √ ""
15
9 x
3
2 a
b2 √ "
5
10
x √ "
xy
17. √ """
24
a4b
2
18. √ """
81
x4y
2
19. √ """"
150
a2b
2c
2a
2 b
√ "
6
9x
2 y
5 a
b √ ""
6c
20. √ """"
72
a6b
3c2
21. √ """"
45
x2y
5z8
22. √ """"
98
x4y
6z2
6 a
3b
c √ ""
2b
3
x y
2z
4 √ ""
5y
7x
2 y
3z √ "
2
10-2
Pro
du
ct
Pro
pert
y o
f S
qu
are
Ro
ots
For
any n
um
bers
a a
nd b
, w
here
a ≥
0 a
nd b
≥ 0
, √ ""
ab =
√ " a # √ "
b .
Exam
ple
1
Exam
ple
2
Answers (Lesson 10-1 and Lesson 10-2)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
12
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Sim
plify
ing
Rad
ical
Exp
ress
ion
s
Qu
oti
en
t Pro
pert
y o
f Sq
uare
Ro
ots
A
fra
ctio
n c
on
tain
ing r
ad
icals
is
in s
imp
lest
fo
rm i
f n
o r
ad
icals
are
left
in
th
e d
en
om
inato
r. T
he Q
uo
tien
t P
ro
perty
of
Sq
ua
re R
oo
ts
an
d r
ati
on
ali
zin
g t
he d
en
om
ina
tor c
an
be u
sed
to s
imp
lify
rad
ical
exp
ress
ion
s th
at
involv
e d
ivis
ion
. W
hen
you
rati
on
ali
ze t
he d
en
om
inato
r, y
ou
mu
ltip
ly t
he n
um
era
tor
an
d
den
om
inato
r by a
rad
ical
exp
ress
ion
th
at
giv
es
a r
ati
on
al
nu
mber
in t
he d
en
om
inato
r.
S
imp
lify
√ �
�
56
−
45 .
√ ��
56
−
45 =
√ �
��
4 "
14
−
9 "
5
=
2 "
√ �
�
14
−
3 "
√ �
�
15
Sim
plif
y t
he n
um
era
tor
and d
enom
inato
r.
=
2 √
��
14
−
3 √
�
5
" √
�
5
−
√ �
5
Multip
ly b
y √
�
5
−
√ �
5 t
o r
ationaliz
e t
he d
enom
inato
r.
=
2 √
��
70
−
15
P
roduct
Pro
pert
y o
f S
quare
Roots
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
1. √
�
9
−
√ �
18
√
�
2
−
2
2. √
�
8
−
√ �
24
√
� 3
−
3
3. √
��
100
−
√ �
�
121
1
0
−
11
4. √
�
75
−
√ �
3
5
5. 8
√ �
2
−
2 √
�
8
2
6. √ �
2
−
5 "
√ �
6
−
5
2
√ � 3
−
5
7. √ �
3
−
4 "
√ �
5
−
2
√
��
30
−
4
8. √ �
5
−
7 "
√ �
2
−
5
√
��
14
−
7
9. √ �
�
3a
2
−
10b
6
|a
| √ ��
30
−
10| b
3 |
10. √ �
x
6
−
y4
x3
−
y2
11. √ �
�
100a
4
−
144b
8
5
a2
−
6b
4
12. √ �
��
75b
3c6
−
a
2
5
bc
3 √
��
3b
−
a
13.
√ �
4
−
3 -
√ �
5
3
+ √
�
5
−
2
14.
√ �
8
−
2 +
√ �
3
4 √
�
2 -
2 √
� 6
15.
√ �
5
−
5 +
√ �
5
5 -
2 √
�
5
16.
√ �
8
−
2 √
�
7 +
4 √
�
10
4
√ �
5 -
√ ��
14
−
33
10-2
Qu
oti
en
t P
rop
ert
y o
f S
qu
are
Ro
ots
For
any n
um
bers
a a
nd b
, w
here
a ≥
0 a
nd b
> 0
, √ �
a
−
b =
√
�
a
−
√ �
b
.
Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-2
Ch
ap
ter
10
13
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Sim
plify
ing
Rad
ical
Exp
ressio
ns
Sim
pli
fy e
ach
ex
pressio
n.
1.
√ �
�
28
2 √
�
7
2.
√ �
�
40
2 √
��
10
3.
√ �
�
72
6 √
�
2
4.
√ �
�
99
3 √
��
11
5.
√ �
2 ·
√ �
�
10
2 √
�
5
6.
√ �
5 ·
√ �
�
60
10 √
�
3
7.
3 √
�
5 ·
√ �
5
15
8.
√ �
6 ·
4 √
��
24
48
9.
2 √
�
3 ·
3 √
��
15
18 √
�
5
10.
√ �
�
16
b4
4
b2
11.
√ �
��
81
a2d
4
9| a
|d2
12.
√ �
��
40
x4y
6
2x
2 y
3 √
��
10
13.
√ �
��
75
m5P
2
5
m2| P
| √ �
�
3m
14.
√ �
5
−
3
√
��
15
−
3
15.
√ �
1
−
6
√
�
6
−
6
16.
√ �
6
−
7 ·
√ �
1
−
3
√
��
14
−
7
17.
√ ��
q
−
12
√
��
3q
−
6
18.
√ ��
4h
−
5
2
√ �
�
5h
−
5
19.
√ ��
12
−
b2
2
√ �
3
−
| b |
20.
√ ��
45
−
4m
4
3
√ �
5
−
2m
2
21.
2
−
4 +
√ �
5
8
- 2
√ �
5
−
11
22.
3
−
2 -
√ �
3
6 +
3 √
�
3
23.
5
−
7 +
√ �
7
3
5 -
5 √
�
7
−
42
24.
4
−
3 -
√ �
2 1
2 +
4 √
�
2
−
7
10-2
Answers (Lesson 10-2)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A6 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
14
Gle
ncoe A
lgeb
ra 1
Practi
ce
Sim
plify
ing
Rad
ical
Exp
ressio
ns
Sim
pli
fy.
1.
√ �
24
2 √
� 6
2.
√ �
60
2 √
��
15
3. √
��
108 6
√ � 3
4. √
�
8 !
√ �
6 4
√ � 3
5. √
�
7 !
√ �
14 7 √
�
2
6. 3
√ �
12 !
5 √
�
6 9
0 √
�
2
7. 4 √
�
3 !
3 √
�
18 3
6 √
� 6
8. √
��
�
27tu
3
3 u
√ �
�
3tu
9. √
��
50p
5 5
p2 √
��
2p
10. √
��
��
108x
6y
4z5
6
x3 y
2z
2 √
��
3z
11. √
��
��
56m
2n
4p
5 2
m n
2p
2 √
��
14
p
12. √
�
8
−
√ �
6
2
√ �
3
−
3
13. √ �
2
−
10
√ �
5
−
5
14. √ �
5
−
32
√
��
10
−
8
15. √ �
3
−
4 !
√ �
4
−
5
√
��
15
−
5
16. √ �
1
−
7 !
√ �
7
−
11
√
��
11
−
11
17. √
�
3k
−
√ �
8
√
��
6k
−
4
18. √ �
1
8
−
x3
3
√ ��
2x
−
x2
19. √ �
�
4y
−
3y
2
20. √ �
�
9ab
−
4ab
4
3
√ �
b
−
2
b2
21.
3
−
5 -
√ �
2
15 +
3 √
�
2
−
23
22.
8
−
3 +
√ �
3
1
2 -
4 √
�
3
−
3
23.
5
−
√ �
7 +
√ �
3
5
√ �
7 -
5 √
�
3
−
4
24.
3 √
�
7
−
-1 -
√ �
27
3
√ �
7 -
9 √
��
21
−
26
25. S
KY
DIV
ING
W
hen
a s
kyd
iver
jum
ps
from
an
air
pla
ne,
the t
ime t
it
tak
es
to f
ree f
all
a
giv
en
dis
tan
ce c
an
be e
stim
ate
d b
y t
he f
orm
ula
t =
√ �
�
2s
−
9.8
, w
here
t i
s in
seco
nd
s an
d s
is
in
mete
rs.
If J
uli
e j
um
ps
from
an
air
pla
ne,
how
lon
g w
ill
it t
ak
e h
er
to f
ree f
all
750
mete
rs?
26. M
ET
EO
RO
LO
GY
T
o e
stim
ate
how
lon
g a
th
un
ders
torm
wil
l la
st,
mete
oro
logis
ts c
an
use
the f
orm
ula
t =
√ �
�
d3
−
216 ,
wh
ere
t i
s th
e t
ime i
n h
ou
rs a
nd
d i
s th
e d
iam
ete
r of
the s
torm
in
m
iles.
a
. A
th
un
ders
torm
is
8 m
iles
in d
iam
ete
r. E
stim
ate
how
lon
g t
he s
torm
wil
l la
st.
Giv
e y
ou
r an
swer
in s
imp
lifi
ed
form
an
d a
s a d
eci
mal.
b
. W
ill
a t
hu
nd
ers
torm
tw
ice t
his
dia
mete
r la
st t
wic
e a
s lo
ng?
Exp
lain
.
N
o;
it w
ill
last
ab
ou
t 4.4
h,
or
nearl
y 3
tim
es a
s l
on
g.
10-2
ab
ou
t 12.4
s
8
√ �
3
−
9
h ≈
1.5
h
2 √
��
3y
−
3 y
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-2
Ch
ap
ter
10
15
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Sim
plify
ing
Rad
ical
Exp
ressio
ns
1. S
PO
RT
S Jasm
ine c
alc
ula
ted
th
e h
eig
ht
of
her
team
’s s
occ
er
goal
to b
e
15− √
3 f
eet.
S
imp
lify
th
e e
xp
ress
ion
.
5 √
�
3
2. N
AT
UR
E In
2004,
an
eart
hqu
ak
e b
elo
w
the o
cean
flo
or
init
iate
d a
devast
ati
ng
tsu
nam
i in
th
e I
nd
ian
Oce
an
. S
cien
tist
s ca
n a
pp
roxim
ate
th
e v
elo
city
(in
feet
per
seco
nd
) of
a t
sun
am
i in
wate
r of
dep
th d
(in
feet)
wit
h t
he f
orm
ula
V =
√ ##
16d
. D
ete
rmin
e t
he v
elo
city
of
a t
sun
am
i in
300 f
eet
of
wate
r. W
rite
you
r an
swer
in
sim
pli
fied
rad
ical
form
.
40 √
�
3 f
t/s
3. A
UT
OM
OB
ILE
S T
he f
oll
ow
ing f
orm
ula
ca
n b
e u
sed
to f
ind
th
e “
zero
to s
ixty
” ti
me f
or
a c
ar,
or
the t
ime i
t ta
kes
for
a
car
to a
ccele
rate
fro
m a
sto
p t
o s
ixty
m
iles
per
hou
r. V =
√ ##
2P
T −
M
V
is
the v
elo
city
(in
mete
rs p
er
seco
nd
).P
is
the c
ar’
s avera
ge p
ow
er
(in
watt
s).
M i
s th
e m
ass
of
the c
ar
(in
kil
ogra
ms)
.T
is
the t
ime (
in s
eco
nd
s).
F
ind
th
e t
ime i
t ta
kes
for
a 9
00-k
ilogra
m
car
wit
h a
n a
vera
ge 6
0,0
00 w
att
s of
pow
er
to a
ccele
rate
fro
m s
top
to 2
6.8
2
mete
rs p
er
seco
nd
(60 m
iles
per
hou
r).
Rou
nd
you
r an
swer
to t
he n
eare
st t
en
th.
ab
ou
t 5.4
s
4. P
HY
SIC
AL S
CIE
NC
E W
hen
a s
ubst
an
ce
such
as
wate
r vap
or
is i
n i
ts g
ase
ou
s st
ate
, th
e v
olu
me a
nd
th
e v
elo
city
of
its
mole
cule
s in
crease
as
tem
pera
ture
in
crease
s. T
he a
vera
ge v
elo
city
V o
f a
mole
cule
wit
h m
ass
m a
t te
mp
era
ture
T
is g
iven
by t
he f
orm
ula
V= √##
3kT−
m.
Solv
e t
he e
qu
ati
on
for
k.
k
=m
V 2
− 3T
5. G
EO
ME
TR
Y
Su
pp
ose
Em
ery
vil
le
Hosp
ital
wan
ts t
o b
uil
d a
new
h
eli
pad
on
wh
ich
med
ic r
esc
ue
heli
cop
ters
can
lan
d.
Th
e
heli
pad
wil
l be c
ircu
lar
an
d
mad
e o
f fi
re r
esi
stan
t ru
bber.
a
. If
th
e a
rea o
f th
e h
eli
pad
is
A,
wri
te a
n
equ
ati
on
for
the r
ad
ius
r.
r
= √
�
A
−
π
b
. W
rite
an
exp
ress
ion
in
sim
pli
fied
ra
dic
al
form
for
the r
ad
ius
of
a h
eli
pad
w
ith
an
are
a o
f 288 s
qu
are
mete
rs.
r
= 1
2 √
��
2π
−
π
c.
Usi
ng y
ou
r ca
lcu
lato
r, f
ind
a d
eci
mal
ap
pro
xim
ati
on
for
the r
ad
ius.
Rou
nd
you
r an
swer
to t
he n
eare
st h
un
dre
dth
.
9.5
7 m
r
10-2
Answers (Lesson 10-2)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A7 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
16
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
Sq
uare
s a
nd
Sq
uare
Ro
ots
Fro
m a
Gra
ph
Th
e g
rap
h o
f y =
x2 c
an
be u
sed
to f
ind
th
e s
qu
are
s an
d s
qu
are
ro
ots
of
nu
mbers
.
To f
ind
th
e s
qu
are
of
3,
loca
te 3
on
th
e x
-axis
. T
hen
fin
d i
ts
corr
esp
on
din
g v
alu
e o
n t
he y
-axis
.
Th
e a
rrow
s sh
ow
th
at
32 =
9.
To f
ind
th
e s
qu
are
root
of
4,
firs
t lo
cate
4 o
n t
he y
-axis
. T
hen
fin
d
its
corr
esp
on
din
g v
alu
e o
n t
he x
-axis
. F
oll
ow
ing t
he a
rrow
s on
th
e
gra
ph
, you
can
see t
hat
√
4 =
2.
A s
mall
part
of
the g
rap
h a
t y =
x2 i
s sh
ow
n b
elo
w.
A 1
:10 r
ati
o
for
un
it l
en
gth
on
th
e y
-axis
to u
nit
len
gth
on
th
e x
-axis
is
use
d.
F
ind
√ �
�
11 .
Th
e a
rrow
s sh
ow
th
at
√
11 =
3.3
to
th
e n
eare
st t
en
th.
Exerc
ises
Use t
he g
ra
ph
ab
ov
e t
o f
ind
ea
ch
of
the f
oll
ow
ing
to
th
e n
ea
rest
wh
ole
nu
mb
er.
1. 1.5
2 2
2. 2.7
2 7
3. 0.9
2 1
4. 3.6
2 13
5. 4.2
2 18
6. 3.9
2 15
Use t
he g
ra
ph
ab
ov
e t
o f
ind
ea
ch
of
the f
oll
ow
ing
to
th
e n
ea
rest
ten
th.
7. √
15 3.9
8. √
8 2.8
9. √
3 1.7
10. √
5 2.2
11. √
14 3.7
12. √
17 4.1
12
1110
20
34
3.3
Ox
y
x
y O
10-2
Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-3
Ch
ap
ter
10
17
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Op
era
tio
ns w
ith
Rad
ical
Exp
ressio
ns
Ad
d o
r Su
btr
act
Rad
ical
Exp
ress
ion
s W
hen
ad
din
g o
r su
btr
act
ing r
ad
ical
exp
ress
ion
s, u
se t
he A
ssoci
ati
ve a
nd
Dis
trib
uti
ve P
rop
ert
ies
to s
imp
lify
th
e e
xp
ress
ion
s.
If r
ad
ical
exp
ress
ion
s are
not
in s
imp
lest
form
, si
mp
lify
th
em
.
S
imp
lify
10 √
�
6 -
5 √
�
3 +
6 √
�
3 -
4 √
�
6 .
10 √ #
6 -
5 √ #
3 +
6 √ #
3 -
4 √ #
6 =
(10 -
4) √ #
6 +
(-
5 +
6) √ #
3
Associa
tive a
nd D
istr
ibutive P
ropert
ies
= 6
√ #
6 +
√ #
3
Sim
plif
y.
S
imp
lify
3 √
��
12 +
5 √
��
75 .
3 √ ##
12 +
5 √ ##
75 =
3 √ ###
22 ·
3 +
5 √ ###
52 ·
3
Sim
plif
y.
= 3
· 2
√ #
3 +
5 ·
5 √ #
3
Sim
plif
y.
= 6
√ #
3 +
25 √ #
3
Sim
plif
y.
= 3
1 √ #
3
Dis
trib
utive P
ropert
y
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
1. 2 √ #
5 +
4 √ #
5 6 √
�
5
2. √ #
6 -
4 √ #
6 -
3 √
�
6
3. √ #
8 -
√ #
2 √
�
2
4. 3 √ #
75 +
2 √ #
5 1
5 √
�
3 +
2 √
�
5
5. √ #
20 +
2 √ #
5 -
3 √ #
5 √
�
5
6. 2 √ #
3 +
√ #
6 -
5 √ #
3 -
3 √
�
3 +
√ �
6
7. √ #
12 +
2 √ #
3 -
5 √ #
3 -
√ �
3
8. 3 √ #
6 +
3 √ #
2 -
√ #
50 +
√ #
24 5
√ �
6 -
2 √
�
2
9. √ #
8a -
√ #
2a +
5 √ #
2a 6
√ �
�
2a
10. √ #
54 +
√ #
24 5
√ �
6
11. √ #
3 +
√ # 1 −
3
4
√ �
3
−
3
12. √ #
12 +
√ # 1 −
3
7
√ �
3
−
3
13. √ #
54 -
√ # 1 −
6
1
7 √
�
6
−
6
14. √ #
80 -
√ #
20 +
√ ##
180 8
√ �
5
15. √ #
50 +
√ #
18 -
√ #
75 +
√ #
27 8
√ �
2 -
2 √
�
3
16. 2 √ #
3 -
4 √ #
45 +
2 √ #
1 −
3
8
√ �
3
−
3
- 1
2 √
�
5
17. √ ##
125 -
2 √ #
1 −
5 +
√ # 1 −
3
2
3 √
�
5
−
5
+ √
�
3
−
3
18. √ #
2 −
3 +
3 √ #
3 -
4 √ #
1 −
12
√
�
6 +
7 √
�
3
−
3
10-3
Exam
ple
1
Exam
ple
2
Answers (Lesson 10-2 and Lesson 10-3)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
18
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Op
era
tio
ns w
ith
Rad
ical
Exp
ressio
ns
Mu
ltip
ly R
ad
ical
Exp
ress
ion
s M
ult
iply
ing t
wo r
ad
ical
exp
ress
ion
s w
ith
dif
fere
nt
rad
ican
ds
is s
imil
ar
to m
ult
iply
ing b
inom
ials
.
M
ult
iply
(3 √
�
2 -
2 √
�
5 )(
4 √
��
20 +
√ �
8 ).
Use
th
e F
OIL
meth
od
.
(3 √
�
2 -
2 √
�
5 )(
4 √
��
20 +
√ �
8 ) =
(3 √
�
2 )(
4 √
��
20 ) +
(3 √
�
2 )(
√ �
8 ) +
(-2 √
�
5 )(
4 √
��
20 ) +
(-2 √
�
5 )(
√ �
8 )
= 1
2 √
��
40 +
3 √
��
16 -
8 √
��
100 -
2 √
��
40
Multip
ly.
= 1
2 √
��
�
22 ·
10 +
3 ·
4 -
8 ·
10 -
2 √
��
�
22 ·
10
Sim
plif
y.
= 2
4 √
��
10 +
12 -
80 -
4 √
��
10
Sim
plif
y.
= 2
0 √
��
10 -
68
Com
bin
e lik
e t
erm
s.
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
1. 2( √
�
3 +
4 √
�
5 )
2
√ �
3 +
8 √
�
5
2. √
�
6 ( √
�
3 -
2 √
�
6 )
3 √
�
2 -
12
3. √
�
5 ( √
�
5 -
√ �
2 )
5 -
√ �
�
10
4. √
�
2 (3
√ �
7 +
2 √
�
5 )
3 √
��
14 +
2 √
��
10
5. (2
- 4
√ �
2 )(
2 +
4 √
�
2 )
-
28
6. (3
+ √
�
6 ) 2
1
5 +
6 √
�
6
7. (2
- 2
√ �
5 ) 2
24 -
8 √
�
5
8. 3 √
�
2 ( √
�
8 +
√ �
24 )
12 +
12
√ �
3
9. √
�
8 ( √
�
2 +
5 √
�
8 )
44
10. ( √
�
5 -
3 √
�
2 )(
√ �
5 +
3 √
�
2 )
-13
11. ( √
�
3 +
√ �
6 ) 2
9 +
6 √
�
2
12. ( √
�
2 -
2 √
�
3 ) 2
1
4 -
4 √
�
6
13. ( √
�
5 -
√ �
2 )(
√ �
2 +
√ �
6 )
14. ( √
�
8 -
√ �
2 )(
√ �
3 +
√ �
6 )
√
��
10 -
2 +
√ ��
30 -
2 √
�
3
√
�
6 +
2 √
�
3
15. ( √
�
5 -
√ �
18 )(
7 √
�
5 +
√ �
3 )
16. (2
√ �
3 -
√ �
45 )(
√ �
12 +
2 √
�
6 )
35 +
√ ��
15 -
21 √
��
10 -
3 √
�
6
12 -
6 √
��
15 +
12 √
�
2 -
6 √
��
30
17. (2
√ �
5 -
2 √
�
3 )(
√ �
10 +
√ �
6 )
18. ( √
�
2 +
3 √
�
3 )(
√ �
12 -
4 √
�
8 )
4 √
�
2
2 -
22 √
�
6
10-3
Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-3
Ch
ap
ter
10
19
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Op
era
tio
ns w
ith
Rad
ical
Exp
ressio
ns
10-3
Sim
pli
fy e
ach
ex
pressio
n.
1. 7 √
�
7 -
2 √
�
7
5 √
�
7
2. 3 √
��
13 +
7 √
��
13
10 √
��
13
3. 6 √
�
5 -
2 √
�
5 +
8 √
�
5 12 √
�
5
4.
√ �
�
15 +
8 √
��
15 -
12
√ �
�
15
-3 √
��
15
5. 12 √
� r -
9 √
� r 3 √
�
r
6. 9 √
��
6a
- 1
1 √
��
6a
+ 4
√ �
�
6a
2 √
��
6a
7. √
��
44 -
√ �
�
11
√ �
�
11
8.
√ �
�
28 +
√ �
�
63
5 √
�
7
9. 4 √
�
3 +
2 √
��
12
8 √
�
3
10. 8 √
��
54 -
4 √
�
6
20 √
�
6
11. √
��
27 +
√ �
�
48 +
√ �
�
12
9 √
�
3
12.
√ �
�
72 +
√ �
�
50 -
√ �
8
9 √
�
2
13. √
��
180 -
5 √
�
5 +
√ �
�
20
3 √
�
5
14. 2 √
��
24 +
4 √
��
54 +
5 √
��
96
36 √
�
6
15. 5 √
�
8 +
2 √
��
20 -
√ �
8
16. 2 √
�
13 +
4 √
�
2 -
5 √
�
13 +
√ �
2
8 √
�
2 +
4 √
�
5
-3 √
��
13 +
5 √
�
2
17.
√ �
2 ( √
�
8 +
√ �
6 )
4 +
2 √
�
3
18.
√ �
5 ( √
�
10 -
√ �
3 )
5 √
�
2 -
√ �
�
15
19.
√ �
6 (3
√ �
2 -
2 √
�
3 )
6 √
�
3 -
6 √
�
2
20. 3 √
�
3 (2
√ �
6 +
4 √
�
10 )
18 √
�
2 +
12 √
��
30
21.
( 4 +
√ �
3 ) (
4 -
√ �
3 )
13
22. (2
- √
�
6 )2
10 -
4 √
�
6
23.
( √ �
8 +
√ �
2 ) (
√ �
5 +
√ �
3 )
24. ( √
�
6 +
4 √
�
5 )(
4 √
�
3 -
√ �
10 )
3 √
��
10 +
3 √
�
6
-8 √
�
2 +
14 √
��
15
Answers (Lesson 10-3)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A9 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
20
Gle
ncoe A
lgeb
ra 1
Practi
ce
Op
era
tio
ns w
ith
Rad
ical
Exp
ressio
ns
Sim
pli
fy e
ach
ex
pressio
n.
1. 8 √
�
30 -
4 √
�
30 4
√ �
�
30
2. 2 √
�
5 -
7 √
�
5 -
5 √
�
5 -
10
√ �
5
3. 7 √
��
13x -
14 √
��
13x +
2 √
��
13x -
5 √
��
13
x
4. 2 √
��
45 +
4 √
�
20 1
4 √
�
5
5. √
�
40 -
√ �
10 +
√ �
90 4
√ �
�
10
6. 2 √
�
32 +
3 √
�
50 -
3 √
�
18 14
√ �
2
7. √
�
27 +
√ �
18 +
√ �
�
300 3
√ �
2 +
13
√ �
3
8. 5 √
�
8 +
3 √
�
20 -
√ �
32 6
√ �
2 +
6 √
�
5
9. √
�
14 -
√ �
2
−
7
6
√ �
�
14
−
7
10. √
�
50 +
√ �
32 -
√ �
1
−
2
1
7 √
�
2
−
2
11. 5 √
�
19 +
4 √
�
28 -
8 √
�
19 +
√ �
63
12. 3 √
�
10 +
√ �
75 -
2 √
�
40 -
4 √
�
12
-
3 √
��
19 +
11 √
�
7
-
√ �
�
10 -
3 √
�
3
13. √
�
6 ( √
�
10 +
√ �
15 )
2
√ �
�
15 +
3 √
��
10
14. √
�
5 (5
√ �
2 -
4 √
�
8 )
-3
√ �
�
10
15. 2 √
�
7 (3
√ �
12 +
5 √
�
8 )
12
√ �
�
21 +
20
√ �
�
14
16. (5
- √
�
15 ) 2
40 -
10
√ �
�
15
17. ( √
�
10 +
√ �
6 )
( √ �
30 -
√ �
18 )
4 √
�
3
18. ( √
�
8 +
√ �
12 )
( √ �
48 +
√ �
18 )
36 +
14
√ �
6
19. ( √
�
2 +
2 √
�
8 )(
3 √
�
6 -
√ �
5 )
20. (4
√ �
3 -
2 √
�
5 )(
3 √
�
10 +
5 √
�
6 )
3
0 √
�
3 -
5 √
��
10
2 √
��
30 +
30
√ �
2
21. S
OU
ND
T
he s
peed
of
sou
nd
V i
n m
ete
rs p
er
seco
nd
near
Eart
h’s
su
rface
is
giv
en
by
V
= 2
0 √
��
�
t +
273 ,
wh
ere
t i
s th
e s
urf
ace
tem
pera
ture
in
degre
es
Cels
ius.
a
. W
hat
is t
he s
peed
of
sou
nd
near
Eart
h’s
su
rface
at
15°C
an
d a
t 2°C
in
sim
ple
st f
orm
?
240 √
�
2 m
/s,
100 √
��
11 m
/s
b
. H
ow
mu
ch f
ast
er
is t
he s
peed
of
sou
nd
at
15°C
th
an
at
2°C
?
240 √
�
2 -
100 √
��
11 ≈
7.7
5 m
/s
22. G
EO
ME
TR
Y A
rect
an
gle
is
5 √
�
7 +
2 √
�
3 m
ete
rs l
on
g a
nd
6 √
�
7 -
3 √
�
3 m
ete
rs w
ide.
a
. F
ind
th
e p
eri
mete
r of
the r
ect
an
gle
in
sim
ple
st f
orm
. 22 √
�
7 -
2 √
�
3 m
b
. F
ind
th
e a
rea o
f th
e r
ect
an
gle
in
sim
ple
st f
orm
. 190 -
3 √
��
21 m
2
10-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-3
Ch
ap
ter
10
21
Gle
ncoe A
lgeb
ra 1
-5
-1
0
5
5
10
10
15
20
Ski slo
pe
y
xO
Wo
rd
Pro
ble
m P
racti
ce
Op
era
tio
ns w
ith
Rad
ical
Exp
ressio
ns
1. A
RC
HIT
EC
TU
RE
T
he P
en
tagon
is
the
bu
ild
ing t
hat
hou
ses
the U
.S.
Dep
art
men
t of
Defe
nse
. F
ind
th
e
ap
pro
xim
ate
peri
mete
r of
the b
uil
din
g,
wh
ich
is
a r
egu
lar
pen
tagon
. L
eave y
ou
r an
swer
as
a r
ad
ical
exp
ress
ion
.
115 √
��
149 m
2. E
AR
TH
T
he s
urf
ace
are
a o
f a s
ph
ere
w
ith
rad
ius
r i
s giv
en
by t
he f
orm
ula
4π
r2.
Ass
um
ing t
hat
Eart
h i
s cl
ose
to
sph
eri
cal
in s
hap
e a
nd
has
a s
urf
ace
are
a
of
abou
t 5.1
× 1
08 s
qu
are
kil
om
ete
rs,
wh
at
is t
he r
ad
ius
of
Eart
h t
o t
he
neare
st t
en
kil
om
ete
rs?
6370 k
m
3. G
EO
ME
TR
Y T
he a
rea o
f a t
rap
ezoid
is
fou
nd
by m
ult
iply
ing i
ts h
eig
ht
by t
he
avera
ge l
en
gth
of
its
base
s. F
ind
th
e a
rea
of
deck
att
ach
ed
to M
r. W
ilso
n’s
hou
se.
Giv
e y
ou
r an
swer
as
a s
imp
lifi
ed
rad
ical
exp
ress
ion
.
6
3 √ �
�
15 ft
2
4. R
EC
RE
AT
ION
C
arm
en
su
rveyed
a s
ki
slop
e u
sin
g a
dig
ital
devic
e c
on
nect
ed
to
a c
om
pu
ter.
Th
e c
om
pu
ter
mod
el
ass
ign
ed
coord
inate
s to
th
e t
op
an
d
bott
om
poin
ts o
f th
e h
ill
as
show
n i
n t
he
dia
gra
m.
Wri
te a
sim
pli
fied
rad
ical
exp
ress
ion
th
at
rep
rese
nts
th
e s
lop
e o
f th
e h
ill.
5. FR
EE
FA
LL
S
up
pose
a b
all
is
dro
pp
ed
fr
om
a b
uil
din
g w
ind
ow
800 f
eet
in t
he
air
. A
noth
er
ball
is
dro
pp
ed
fro
m a
low
er
win
dow
288 f
eet
hig
h.
Both
ball
s are
re
lease
d a
t th
e s
am
e t
ime.
Ass
um
e a
ir
resi
stan
ce i
s n
ot
a f
act
or
an
d u
se t
he
foll
ow
ing f
orm
ula
to f
ind
how
man
y
seco
nd
s t
it w
ill
tak
e a
ball
to f
all
h f
eet.
t
= 1
−
4
√ �
h
a.
How
mu
ch t
ime w
ill
pass
betw
een
w
hen
th
e f
irst
ball
hit
s th
e g
rou
nd
an
d w
hen
th
e s
eco
nd
ball
hit
s th
e
gro
un
d?
Giv
e y
ou
r an
swer
as
a
sim
pli
fied
rad
ical
exp
ress
ion
.
b.
Wh
ich
ball
lan
ds
firs
t? T
he b
all
dro
pp
ed
fro
m 2
88 f
eet
lan
ds
firs
t.
c.
Fin
d a
deci
mal
ap
pro
xim
ati
on
of
the
an
swer
for
part
a.
Rou
nd
you
r an
swer
to t
he n
eare
st t
en
th.
( 7r+
12
) ˚
Ho
use
De
ck
h =
7 √
� 5 ft
12 √
�
3 f
t
6 √
�
3 f
t
A (
2 √
��
14 ,
5 √
�
7 )
23 √
��
149 m
B (-
2 √
��
14 ,
7 √
�
7 )
10-3
ab
ou
t 2.8
s
2 √
�
2 s
Answers (Lesson 10-3)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A10 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
22
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
Th
e W
heel
of T
heo
do
ru
s
Th
e G
reek
math
em
ati
cian
s w
ere
in
trig
ued
by p
roble
ms
of
re
pre
sen
tin
g d
iffe
ren
t n
um
bers
an
d e
xp
ress
ion
s u
sin
g
geom
etr
ic c
on
stru
ctio
ns.
Th
eod
oru
s, a
Gre
ek
ph
iloso
ph
er
wh
o l
ived
abou
t 425 B
.C., i
s sa
id t
o h
ave d
isco
vere
d a
way t
o c
on
stru
ct t
he s
equ
en
ce
√ �
1 ,
√ �
2 ,
√ �
3 ,
√ �
4 ,
. .
..
Th
e b
egin
nin
g o
f h
is c
on
stru
ctio
n i
s sh
ow
n.
You
sta
rt w
ith
an
is
osc
ele
s ri
gh
t tr
ian
gle
wit
h s
ides
1 u
nit
lon
g.
Use t
he f
igu
re a
bo
ve.
Writ
e e
ach
len
gth
as a
ra
dic
al
ex
pressio
n i
n s
imp
lest
form
.
1. li
ne s
egm
en
t A
O √
�
1
2.
lin
e s
egm
en
t B
O
√ �
2
3. li
ne s
egm
en
t C
O
√ �
3
4.
lin
e s
egm
en
t D
O
√ �
4
5. D
esc
ribe h
ow
each
new
tri
an
gle
is
ad
ded
to t
he f
igu
re.
Dra
w a
new
sid
e o
f le
ng
th
1 a
t ri
gh
t an
gle
s t
o t
he l
ast
hyp
ote
nu
se.
Th
en
dra
w t
he n
ew
hyp
ote
nu
se.
6. T
he l
en
gth
of
the h
yp
ote
nu
se o
f th
e f
irst
tri
an
gle
is
√ �
2 .
For
the s
eco
nd
tri
an
gle
, th
e
len
gth
is
√ �
3 .
Wri
te a
n e
xp
ress
ion
for
the l
en
gth
of
the h
yp
ote
nu
se o
f th
e n
th t
rian
gle
.
√ �
��
n +
1
7. S
how
th
at
the m
eth
od
of
con
stru
ctio
n w
ill
alw
ays
pro
du
ce t
he n
ext
nu
mber
in t
he
sequ
en
ce.
(Hin
t: F
ind
an
exp
ress
ion
for
the h
yp
ote
nu
se o
f th
e (
n +
1)t
h t
rian
gle
.)
√ �
��
��
( √ �
n
)2 +
(1)2
or
√ �
��
n +
1
8. In
th
e s
pace
belo
w,
con
stru
ct a
Wh
eel
of
Th
eod
oru
s. S
tart
wit
h a
lin
e s
egm
en
t 1 c
en
tim
ete
r lo
ng.
Wh
en
does
the W
heel
start
to o
verl
ap
?
aft
er
len
gth
√ �
�
18
1
1
1
1
OAB
CD
10-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-4
Ch
ap
ter
10
23
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Rad
ical
Eq
uati
on
s
Rad
ical
Eq
uati
on
s E
qu
ati
on
s co
nta
inin
g r
ad
icals
wit
h v
ari
able
s in
th
e r
ad
ican
d a
re
call
ed
ra
dic
al
eq
ua
tio
ns.
Th
ese
can
be s
olv
ed
by f
irst
usi
ng t
he f
oll
ow
ing s
tep
s.
S
olv
e 1
6 =
√ �
x
−
2
fo
r x
.
16 =
√ �
x
−
2
O
rigin
al equation
2(1
6)
= 2( √
�
x
−
2 )
Multip
ly e
ach s
ide b
y 2
.
32 =
√ �
x
Sim
plif
y.
(3
2)2
= (
√ �
x )
2
Square
each s
ide.
1024 =
x
Sim
plif
y.
Th
e s
olu
tion
is
1024,
wh
ich
ch
eck
s in
th
e o
rigin
al
equ
ati
on
.
S
olv
e √
��
�
4x -
7 +
2 =
7.
√
��
�
4x -
7 +
2 =
7
Origin
al equation
√ �
��
4x -
7 +
2 -
2 =
7 -
2
Subtr
act
2 f
rom
each s
ide.
√
��
�
4x -
7 =
5
Sim
plif
y.
( √
��
�
4x -
7 )2
= 5
2
Square
each s
ide.
4
x -
7 =
25
Sim
plif
y.
4x -
7 +
7 =
25 +
7
Add 7
to e
ach s
ide.
4
x =
32
Sim
plif
y.
x =
8
Div
ide e
ach s
ide b
y 4
.
Th
e s
olu
tion
is
8,
wh
ich
ch
eck
s in
th
e o
rigin
al
equ
ati
on
.
Exerc
ises
So
lve e
ach
eq
ua
tio
n.
Ch
eck
yo
ur s
olu
tio
n.
1. √
�
a =
8
64
2. √
�
a +
6 =
32 676
3. 2 √
�
x =
8 16
4. 7 =
√ �
��
26 -
n
-23
5. √
��
-a
= 6
-
36
6. √
��
3r2
= 3
±
√ �
3 ±
√ �
7. 2 √
�
3 =
√ �
y 12
8. 2 √
��
3a
- 2
= 7
6 3
−
4
9. √
��
�
x -
4 =
6 40
10. √
��
�
2m
+ 3
= 5
11
11. √
��
�
3b
- 2
+ 1
9 =
24 9
12. √
��
�
4x -
1 =
3 5
−
2
13. √
��
�
3r
+ 2
= 2
√ �
3
10
−
3
14. √ �
x
−
2 =
1
−
2
1
−
2
15. √ �
x
−
8 =
4 128
16. √
��
��
6x
2 +
5x =
2 1
−
2 ,
- 4
−
3
17. √ �
x
−
3 +
6 =
8 12
18. 2 √ �
�
3x
−
5
+ 3
= 1
1 26 2
−
3
10-4
Exam
ple
1Exam
ple
2
Ste
p 1
Is
ola
te t
he r
ad
ical
on
on
e s
ide o
f th
e e
qu
ati
on
.
Ste
p 2
S
qu
are
each
sid
e o
f th
e e
qu
ati
on
to e
lim
inate
th
e r
ad
ical.
Answers (Lesson 10-3 and Lesson 10-4)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
24
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n(c
on
tin
ued
)
Rad
ical
Eq
uati
on
s
Extran
eo
us S
olu
tio
ns
To s
olv
e a
rad
ical
equ
ati
on
wit
h a
vari
able
on
both
sid
es,
you
n
eed
to s
qu
are
each
sid
e o
f th
e e
qu
ati
on
. S
qu
ari
ng e
ach
sid
e o
f an
equ
ati
on
som
eti
mes
pro
du
ces
ex
tra
neo
us s
olu
tio
ns,
or
solu
tion
s th
at
are
not
solu
tion
s of
the o
rigin
al
equ
ati
on
. T
here
fore
, it
is
very
im
port
an
t th
at
you
ch
eck
each
solu
tion
.
S
olv
e √
��
�
x +
3 =
x -
3.
√
��
�
x +
3 =
x -
3
Origin
al equation
( √ �
��
x +
3 )2
= (
x -
3)2
S
quare
each s
ide.
x +
3 =
x2 -
6x +
9
Sim
plif
y.
0 =
x2 -
7x +
6
Subtr
act
x a
nd 3
fro
m e
ach s
ide.
0 =
(x -
1)(
x -
6)
Facto
r.
x -
1 =
0 or
x -
6 =
0
Zero
Pro
duct
Pro
pert
y
x =
1
x =
6
Solv
e.
CH
EC
K √
��
�
x +
3
= x
- 3
√
��
�
x +
3 =
x -
3
√
��
�
1 +
3
! 1
- 3
√
��
�
6 +
3 !
6 -
3
√ �
4 !
-2
√ �
9 !
3
2 ≠
-2
3 =
3 #
Sin
ce x
= 1
does
not
sati
sfy t
he o
rigin
al
equ
ati
on
, x =
6 i
s th
e o
nly
solu
tion
.
Exerc
ises
So
lve e
ach
eq
ua
tio
n.
Ch
eck
yo
ur s
olu
tio
n.
1. √
�
a =
a 0,
1
2. √
��
�
a +
6 =
a 3
3. 2 √
�
x =
x 0,
4
4. n
= √
��
�
2 -
n 1
5. √
��
-a
= a
0
6. √
��
��
10 -
6k +
3 =
k
!
7. √
��
�
y -
1 =
y -
1 1,
2
8. √
��
�
3a
- 2
= a
1,
2
9. √
��
�
x +
2 =
x 2
10. √
��
�
2b
+ 5
= b
- 5
10
11. √
��
�
3b
+ 6
= b
+ 2
1
12. √
��
�
4x -
4 =
x 2
13. r
+ √
��
�
2 -
r =
2 1,
2
14. √
��
��
x2 +
10x =
x +
4 8
15.
-2 √ �
x
−
8 =
15
!
16. √
��
��
6x
2 -
4x =
x +
2
17. √
��
��
2y
2 -
64
= y
18. √
��
��
��
3
x2 +
12
x +
1 =
x +
5
- 2
−
5 ,
2
8
-4,
3
10-4
Exam
ple
1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-4
Ch
ap
ter
10
25
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Rad
ical
Eq
uati
on
s
So
lve e
ach
eq
ua
tio
n.
Ch
eck
yo
ur s
olu
tio
n.
1. √
� f =
7 49
2. √
��
-x =
5
-25
3. √
��
5p
= 1
0 20
4. √
�
4y =
6 9
5. 2 √
�
2 =
√ �
u
8
6. 3 √
�
5 =
√ �
�
-n
-
45
7. √
�
g -
6 =
3 81
8. √
��
5a
+ 2
= 0
ø
9. √
��
�
2t
- 1
= 5
13
10. √
��
�
3k -
2 =
4 6
11. √
��
�
x +
4 -
2 =
1 5
12. √
��
�
4x -
4 -
4 =
0 5
13. √
�
d
−
3 =
4 144
14. √ �
m
−
3
= 3
27
15. x =
√ �
��
x +
2 2
16. d
= √
��
�
12 -
d 3
17. √
��
�
6x -
9 =
x 3
18. √
��
�
6p
- 8
= p
2,
4
19. √
��
�
x +
5 =
x -
1 4
20. √
��
�
8 -
d =
d -
8 8
21. √
��
�
r -
3 +
5 =
r 7
22. √
��
�
y -
1 +
3 =
y 5
23. √
��
�
5n
+ 4
= n
+ 2
1,
0
24. √
��
�
3z
- 6
= z
- 2
5,
2
10-4
Answers (Lesson 10-4)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A12 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
26
Gle
ncoe A
lgeb
ra 1
Practi
ce
Rad
ical
Eq
uati
on
sS
olv
e e
ach
eq
ua
tio
n.
Ch
eck
yo
ur s
olu
tio
n.
1. √
��
-b =
8 -
64
2
. 4 √
�
3 =
√ � x
48
3. 2 √
�
4r +
3 =
11 4
4. 6 -
√ �
2
y =
-2 32
5. √
��
�
k +
2 -
3 =
7 98
6. √
��
�
m -
5 =
4 √
�
3 53
7. √
��
�
6t
+ 1
2 =
8 √
�
6 62
8. √
��
�
3j
- 1
1 +
2 =
9 20
9. √
��
��
2x +
15
+ 5
= 1
8 77
10. √ �
3
d
−
5
- 4
= 2
60
11. 6 √ �
�
3x
−
3
- 3
= 0
1
−
4
12. 6 +
√ �
5
r −
6
= -
2 "
13. y
= √
��
�
y +
6 3
14. √
��
��
15 -
2x =
x 3
15. √
��
�
w +
4 =
w +
4 -
4, -
3
16. √
��
�
17 -
k =
k -
5 8
17. √
��
��
5m
- 1
6 =
m -
2 4,
5
18. √
��
��
24 +
8q =
q +
3 -
3,
5
19. √
��
��
4t
+ 1
7 -
t -
3 =
0 2
20. 4 -
√ �
��
�
3m
+ 2
8 =
m -
1
21. √
��
��
10
p +
61
- 7
= p
-
6,
2
22. √
��
�
2x
2 -
9 =
x 3
23. E
LE
CT
RIC
ITY
T
he v
olt
age V
in
a c
ircu
it i
s giv
en
by V
= √
��
PR
, w
here
P i
s th
e p
ow
er
in
watt
s an
d R
is
the r
esi
stan
ce i
n o
hm
s.
a
. If
th
e v
olt
age i
n a
cir
cuit
is
120 v
olt
s an
d t
he c
ircu
it p
rod
uce
s 1500 w
att
s of
pow
er,
w
hat
is t
he r
esi
stan
ce i
n t
he c
ircu
it?
b
. S
up
pose
an
ele
ctri
cian
desi
gn
s a c
ircu
it w
ith
110 v
olt
s an
d a
resi
stan
ce o
f 10 o
hm
s.
How
mu
ch p
ow
er
wil
l th
e c
ircu
it p
rod
uce
?
24. FR
EE
FA
LL
A
ssu
min
g n
o a
ir r
esi
stan
ce,
the t
ime t
in
seco
nd
s th
at
it t
ak
es
an
obje
ct t
o
fall
h f
eet
can
be d
ete
rmin
ed
by t
he e
qu
ati
on
t =
√ �
h
−
4 .
a
. If
a s
kyd
iver
jum
ps
from
an
air
pla
ne a
nd
fre
e f
all
s fo
r 10 s
eco
nd
s befo
re o
pen
ing t
he
para
chu
te,
how
man
y f
eet
does
the s
kyd
iver
fall
?
b
. S
up
pose
a s
eco
nd
sk
yd
iver
jum
ps
an
d f
ree f
all
s fo
r 6 s
eco
nd
s. H
ow
man
y f
eet
does
the
seco
nd
sk
yd
iver
fall
?
10-4
1600 f
t
9.6
oh
ms
1210 w
att
s
576 f
t
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-4
Ch
ap
ter
10
27
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Rad
ical
Eq
uati
on
s
1. S
UB
MA
RIN
ES
T
he d
ista
nce
in
mil
es
that
the l
ook
ou
t of
a s
ubm
ari
ne c
an
see
is a
pp
roxim
ate
ly d
= 1
.22 √
�
h ,
wh
ere
h i
s th
e h
eig
ht
in f
eet
above t
he s
urf
ace
of
the w
ate
r. H
ow
far
wou
ld a
su
bm
ari
ne
peri
scop
e h
ave t
o b
e a
bove t
he w
ate
r to
lo
cate
a s
hip
6 m
iles
aw
ay?
Rou
nd
you
r an
swer
to t
he n
eare
st t
en
th.
2. P
ET
S F
ind
th
e v
alu
e o
f x i
f th
e p
eri
mete
r of
a t
rian
gu
lar
dog p
en
is
25 m
ete
rs.
x =
8
3. LO
GG
ING
D
oyle
’s l
og r
ule
est
imate
s th
e
am
ou
nt
of
usa
ble
lu
mber
(in
board
feet)
th
at
can
be m
ille
d f
rom
a s
hip
men
t of
logs.
It
is r
ep
rese
nte
d b
y t
he e
qu
ati
on
B =
L ( d
- 4
−
4
) 2
, w
here
d i
s th
e l
og
d
iam
ete
r (i
n i
nch
es)
an
d L
is
the l
og
len
gth
(in
feet)
. S
up
pose
th
e t
ruck
ca
rrie
s 20 l
ogs,
each
25 f
eet
lon
g,
an
d
that
the s
hip
men
t yie
lds
a t
ota
l of
6000
board
feet
of
lum
ber.
Est
imate
th
e
dia
mete
r of
the l
ogs
to t
he n
eare
st i
nch
. A
ssu
me t
hat
all
th
e l
ogs
have u
nif
orm
le
ngth
an
d d
iam
ete
r.
18 i
n.
4. FIR
EFIG
HT
ING
F
ire f
igh
ters
calc
ula
te
the f
low
rate
of
wate
r ou
t of
a p
art
icu
lar
hyd
ran
t by u
sin
g t
he f
oll
ow
ing f
orm
ula
.
F =
26.9
d2 √
�
p
F
is
the f
low
rate
(in
gall
on
s p
er
min
ute
),
p i
s th
e n
ozzle
pre
ssu
re (
in p
ou
nd
s p
er
squ
are
in
ch),
an
d d
is
the d
iam
ete
r of
the
hose
(in
in
ches)
. In
ord
er
to e
ffect
ively
fi
gh
t a f
ire,
the c
om
bin
ed
flo
w r
ate
of
two
hose
s n
eed
s to
be a
bou
t 2430 g
all
on
s p
er
min
ute
. T
he d
iam
ete
r of
each
of
the
hose
s is
3 i
nch
es,
bu
t th
e n
ozzle
pre
ssu
re
of
on
e h
ose
is
4 t
imes
that
of
the s
eco
nd
h
ose
. W
hat
are
th
e n
ozzle
pre
ssu
res
for
each
hose
? R
ou
nd
you
r an
swers
to t
he
neare
st t
en
th.
11.2
psi
an
d 4
4.8
psi
5. G
EO
ME
TR
Y T
he l
ate
ral
surf
ace
are
a s
of
a r
igh
t ci
rcu
lar
con
e,
not
incl
ud
ing t
he
base
, is
rep
rese
nte
d b
y t
he e
qu
ati
on
s =
πr
√ �
��
r2 +
h2 ,
wh
ere
r i
s th
e r
ad
ius
of
the c
ircu
lar
base
an
d h
is
the h
eig
ht
of
the c
on
e.
a.
If t
he l
ate
ral
surf
ace
are
a o
f a f
un
nel
is 1
27.5
4 s
qu
are
cen
tim
ete
rs a
nd
its
ra
diu
s is
3.5
cen
tim
ete
rs,
fin
d i
ts
heig
ht
to t
he n
eare
st t
en
th o
f a
cen
tim
ete
r.
b.
Wh
at
is t
he a
rea o
f th
e o
pen
ing (
i.e.,
the b
ase
) of
the f
un
nel?
x+ 1
m
12
m 1
0 m
10-4
11.1
cm
38.5
cm
2
24.2
ft
Answers (Lesson 10-4)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A13 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
28
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
Mo
re T
han
On
e S
qu
are
Ro
ot
You
have l
earn
ed
th
at
to r
em
ove t
he s
qu
are
root
in a
n e
qu
ati
on
, you
fir
st n
eed
to i
sola
te t
he
squ
are
root,
th
en
squ
are
both
sid
es
of
the e
qu
ati
on
, an
d f
inall
y,
solv
e t
he r
esu
ltin
g e
qu
ati
on
. H
ow
ever,
th
ere
are
equ
ati
on
s th
at
con
tain
more
th
at
on
e s
qu
are
root
an
d s
imp
ly s
qu
ari
ng
on
ce i
s n
ot
en
ou
gh
to r
em
ove a
ll o
f th
e r
ad
icals
.
S
olv
e √
��
�
x +
7 =
√ �
x
+ 1
.
√
��
�
x +
7 =
√ �
x +
1
One o
f th
e s
quare
roots
is a
lready isola
ted.
( √ �
��
x +
7 ) 2
= (
√ �
x +
1 ) 2
S
quare
both
sid
es t
o r
em
ove t
he s
quare
root.
x
+ 7
= x
+ 2
√ �
x +
1
Sim
plif
y.
Use t
he F
OIL
meth
od t
o s
quare
rig
ht
sid
e.
x +
7 -
x -
1 =
2 √
�
x
Sim
plif
y.
6 =
2 √
�
x
Sim
plif
y.
Isola
te t
he s
quare
root
term
again
.
3 =
√ �
x
Div
ide b
oth
sid
es b
y 2
.
9 =
x
Square
both
sid
es t
o r
em
ove t
he s
quare
root.
Ch
eck
: S
ubst
itu
te i
nto
th
e o
rigin
al
equ
ati
on
to m
ak
e s
ure
you
r so
luti
on
is
vali
d.
√ �
��
9 +
7 =
√ �
9 +
1
Repla
ce x
with 9
.
√
��
16 =
3 +
1
S
impify.
4 =
4 !
The e
quation is t
rue,
so x
= 9
is t
he s
olu
tion.
Exerc
ises
So
lve e
ach
eq
ua
tio
n.
1.
√ �
��
x +
13 -
2 =
√ �
��
x +
1
3
2.
√ �
��
x +
11 =
√ �
��
x +
3 +
2
-2
3.
√ �
��
x +
9 -
3 =
√ �
��
x -
6
7
4.
√ �
��
x +
21 =
√ �
x +
3 4
5.
√ �
��
x +
9 +
3 =
√ �
��
x +
20 +
2 16
6.
√ �
��
x -
6 +
6 =
√ �
��
x +
1 +
5 15
10-4
Exam
ple
Lesson 10-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
29
Gle
ncoe A
lgeb
ra 1
Gra
ph
ing C
alc
ula
tor
Act
ivit
y
Rad
ical
Ineq
ualiti
es
Th
e g
rap
hs
of
rad
ical
equ
ati
on
s ca
n b
e u
sed
to d
ete
rmin
e t
he s
olu
tion
s of
rad
ical
inequ
ali
ties
thro
ugh
th
e C
AL
C m
en
u.
S
olv
e e
ach
in
eq
ua
lity
.
a.
√ �
��
x +
4 ≤
3
En
ter
√ �
��
x +
4 i
n Y
1 a
nd
3 i
n Y
2 a
nd
gra
ph
. E
xam
ine t
he g
rap
hs.
Use
TR
AC
E t
o f
ind
th
e e
nd
poin
t of
the
gra
ph
of
the r
ad
ical
equ
ati
on
. U
se
CA
LC
to d
ete
rmin
e t
he i
nte
rsect
ion
of
the g
rap
hs.
Th
is i
nte
rval,
-4 t
o 5
,
wh
ere
th
e g
rap
h o
f y =
√ �
��
x +
4
is
belo
w t
he g
rap
h o
f y =
3,
rep
rese
nts
the s
olu
tion
to t
he i
nequ
ali
ty.
Th
us,
the s
olu
tion
is
-4 ≤
x ≤
5.
b.
√ �
��
2x
- 5
> x
- 4
Gra
ph
each
sid
e o
f th
e i
nequ
ali
ty.
Fin
d
the i
nte
rsect
ion
an
d t
race
to t
he e
nd
poin
t of
the r
ad
ical
gra
ph
.
Th
e g
rap
h o
f y =
√ �
��
2x -
5 i
s above t
he
gra
ph
of
y =
x -
4 f
rom
2.5
up
to 7
. T
hu
s,
the s
olu
tion
is
2.5
< x
< 7
.
Exerc
ises
So
lve e
ach
in
eq
ua
lity
.
1. 6 -
√ �
��
2x +
1 <
3
2.
√ �
��
4x -
5 ≤
7
3.
√ �
��
5x -
4 ≥
4
x
> 4
5
−
4 ≤
x ≤
27
−
2
x ≥
4
4.
-4 >
√ �
��
3x -
2
5.
√ �
��
3x -
6 +
5 ≥
-3
6.
√ �
��
6 -
3x <
x +
16
n
o s
olu
tio
n
x
≥ 2
-10
< x
< 2
[-1
0,
10
] sc
l:1
by
[-1
0,
10
] sc
l:1
[-1
0,
10
] sc
l:1
by
[-1
0,
10
] sc
l:1
[-1
0,
10
] sc
l:1
by
[-1
0,
10
] sc
l:1
[-1
0,
10
] sc
l:1
by
[-1
0,
10
] sc
l:1
10-4
Exam
ple
Answers (Lesson 10-4)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A14 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
30
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Th
e P
yth
ag
ore
an
Th
eo
rem
Th
e P
yth
ag
ore
an
Th
eo
rem
T
he s
ide o
pp
osi
te t
he r
igh
t an
gle
in
a r
igh
t tr
ian
gle
is
call
ed
th
e h
yp
ote
nu
se
. T
his
sid
e i
s alw
ays
the l
on
gest
sid
e o
f a r
igh
t tr
ian
gle
. T
he o
ther
two s
ides
are
call
ed
th
e l
eg
s o
f th
e t
rian
gle
. T
o f
ind
th
e l
en
gth
of
an
y s
ide o
f a r
igh
t
tria
ngle
, giv
en
th
e l
en
gth
s of
the o
ther
two s
ides,
you
can
use
th
e P
yth
ag
orea
n T
heo
rem
.
Pyth
ag
ore
an
Th
eo
rem
If a
and b
are
the m
easure
s o
f th
e legs o
f a r
ight
tria
ngle
and c
is t
he m
easure
of
the h
ypote
nuse,
then c
2 =
a2 +
b2.
CB
Ab
ac
F
ind
th
e l
en
gth
of
the m
issin
g s
ide.
c2 =
a2 +
b2
Pyth
agore
an T
heore
m
c2 =
52 +
12
2
a =
5 a
nd b
= 1
2
c2 =
169
Sim
plif
y.
c =
√ ""
169
Take t
he s
quare
root
of
each s
ide.
c =
13
Th
e l
en
gth
of
the h
yp
ote
nu
se i
s 13.
Exerc
ises
Fin
d t
he l
en
gth
of
ea
ch
mis
sin
g s
ide.
If n
ecessa
ry
, ro
un
d t
o t
he
nea
rest
hu
nd
red
th.
1.
2.
3.
5
0
45.8
3
35.3
625
25
c
100
110
a
40
30
c
10-5
12
5
14
8
415
89
5
Exam
ple
4.
5.
6.
16.1
2
5.5
7
8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-5
Ch
ap
ter
10
31
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n(c
on
tin
ued
)
Th
e P
yth
ag
ore
an
Th
eo
rem
Rig
ht
Tri
an
gle
s If
a a
nd
b a
re t
he m
easu
res
of
the s
hort
er
sid
es
of
a t
rian
gle
, c i
s th
e
measu
re o
f th
e l
on
gest
sid
e,
an
d c
2 =
a2 +
b2,
then
th
e t
rian
gle
is
a r
igh
t tr
ian
gle
.
D
ete
rm
ine w
heth
er t
he f
oll
ow
ing
sid
e m
ea
su
res f
orm
rig
ht
tria
ng
les.
a.
10,
12,
14
Sin
ce t
he m
easu
re o
f th
e l
on
gest
sid
e i
s 14,
let
c =
14,
a =
10,
an
d b
= 1
2.
c
2 =
a2 +
b2
Pyth
agore
an T
heore
m
14
2 #
10
2 +
12
2
a =
10,
b =
12,
c =
14
196 #
100 +
144
Multip
ly.
196 ≠
244
Add.
Sin
ce c
2 ≠
a2 +
b2,
the t
rian
gle
is
not
a r
igh
t tr
ian
gle
.
b.
7,
24,
25
Sin
ce t
he m
easu
re o
f th
e l
on
gest
sid
e i
s 25,
let
c =
25,
a =
7,
an
d b
= 2
4.
c
2 =
a2 +
b2
Pyth
agore
an T
heore
m
25
2 #
72 +
24
2
a =
7,
b =
24,
c =
25
625 #
49
+ 5
76
Multip
ly.
625 =
625
Add.
Sin
ce c
2 =
a2 +
b2,
the t
rian
gle
is
a r
igh
t tr
ian
gle
.
Exerc
ises
Dete
rm
ine w
heth
er e
ach
set
of
mea
su
res c
an
be s
ides o
f a
rig
ht
tria
ng
le.
Th
en
dete
rm
ine w
heth
er t
hey
fo
rm
a P
yth
ag
orea
n t
rip
le.
1. 14,
48,
50 yes;
yes
2. 6,
8,
10 yes;
yes
3. 8,
8,
10 n
o;
no
4. 90,
120,
150 yes;
yes
5. 15,
20,
25 yes;
yes
6. 4,
8,
4 √ "
5 yes;
no
7. 2,
2,
√ "
8 yes;
no
8. 4,
4,
√ ""
20 n
o;
no
9. 25,
30,
35 n
o;
no
10. 24,
36,
48 n
o;
no
11. 18,
80,
82 yes;
yes
12. 150,
200,
250 yes;
yes
13. 100,
200,
300 n
o;
no
14. 500,
1200,
1300 yes;
yes
15. 700,
1000,
1300 n
o;
no
10-5
Exam
ple
Answers (Lesson 10-5)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A15 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
32
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Th
e P
yth
ag
ore
an
Th
eo
rem
Fin
d t
he l
en
gth
of
ea
ch
mis
sin
g s
ide.
If n
ecessa
ry
, ro
un
d t
o t
he n
ea
rest
hu
nd
red
th.
1.
2.
75
36
3.
4.
30
15.7
5
5.
6.
9.8
5
70
Dete
rm
ine w
heth
er e
ach
set
of
mea
su
res c
an
be s
ides o
f a
rig
ht
tria
ng
le.
Th
en
dete
rm
ine w
heth
er t
hey
fo
rm
a P
yth
ag
orea
n t
rip
le.
7.
7,
24,
25 yes;
yes
8.
15,
30,
34 n
o;
no
9.
16,
28,
32 n
o;
no
10.
18,
24,
30 yes;
yes
11.
15,
36,
39 yes;
yes
12.
5,
7,
√ �
�
74 yes;
no
13.
4,
5,
6 n
o;
no
14.
10,
11,
√ �
�
221 yes;
no
250240
a4
9
c
29
33
b
16
34
b
15
39
a
21
72
c
10-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 10-5
Ch
ap
ter
10
33
Gle
ncoe A
lgeb
ra 1
Practi
ce
Th
e P
yth
ag
ore
an
Th
eo
rem
Fin
d t
he l
en
gth
of
ea
ch
mis
sin
g s
ide.
If n
ecessa
ry
, ro
un
d t
o t
he
nea
rest
hu
nd
red
th.
1.
2.
3.
68
15.4
9
11.3
1
Dete
rm
ine w
heth
er e
ach
set
of
mea
su
res c
an
be s
ides o
f rig
ht
tria
ng
le.
Th
en
dete
rm
ine w
heth
er t
hey
fo
rm
a P
yth
ag
orea
n t
rip
le.
4. 11,
18,
21
5. 21,
72,
75
n
o;
no
y
es;
yes
6. 7,
8,
11
7. 9,
10,
√ �
�
161
n
o;
yes
no
; n
o
8. 9,
2 √
��
10 ,
11
9.
√ �
7 ,
2 √
�
2 ,
√ �
�
15
y
es;
no
yes;
no
10. S
TO
RA
GE
T
he s
hed
in
Ste
ph
an
’s b
ack
yard
has
a d
oor
that
measu
res
6 f
eet
hig
h a
nd
3 f
eet
wid
e.
Ste
ph
an
wou
ld l
ike t
o s
tore
a s
qu
are
th
eate
r p
rop
th
at
is 7
feet
on
a s
ide.
Wil
l it
fit
th
rou
gh
th
e d
oor
dia
gon
all
y?
Exp
lain
. N
o;
the g
reate
st
len
gth
th
at
will
fit
thro
ug
h t
he d
oo
r is
√ �
�
45 ≈
6.7
1 f
t.
11. S
CR
EE
N S
IZE
S T
he s
ize o
f a t
ele
vis
ion
is
measu
red
by t
he l
en
gth
of
the s
creen
’s
dia
gon
al.
a.
If a
tele
vis
ion
scr
een
measu
res
24 i
nch
es
hig
h a
nd
18 i
nch
es
wid
e,
wh
at
size
tele
vis
ion
is
it?
30-i
n.
tele
vis
ion
b.
Darl
a t
old
Tri
th
at
she h
as
a 3
5-i
nch
tele
vis
ion
. T
he h
eig
ht
of
the s
creen
is
21 i
nch
es.
Wh
at
is i
ts w
idth
? 28 i
n.
c.
Tri
told
Darl
a t
hat
he h
as
a 5
-in
ch h
an
dh
eld
tele
vis
ion
an
d t
hat
the s
creen
measu
res
2 i
nch
es
by 3
in
ches.
Is
this
a r
easo
nable
measu
re f
or
the s
creen
siz
e?
Exp
lain
. N
o;
if t
he s
cre
en
measu
res 2
in
. b
y 3
in
., t
hen
its
dia
go
nal
is o
nly
ab
ou
t 3.6
1 i
n.
12
4
b19
11
a
60
32
c
10-5
Answers (Lesson 10-5)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A16 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
34
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Pyth
ag
ore
an
Th
eo
rem
1. B
AS
EB
ALL
A
base
ball
dia
mon
d i
s a
squ
are
. E
ach
base
path
is
90 f
eet
lon
g.
Aft
er
a p
itch
, th
e c
atc
her
qu
ick
ly t
hro
ws
the b
all
fro
m h
om
e p
late
to a
team
mate
st
an
din
g b
y s
eco
nd
base
. F
ind
th
e
dis
tan
ce t
he b
all
tra
vels
. R
ou
nd
you
r an
swer
to t
he n
eare
st t
en
th.
127.3
ft
2. T
RIA
NG
LE
S E
ach
stu
den
t in
Mrs
. K
ell
y’s
geom
etr
y c
lass
con
stru
cted
a
un
iqu
e r
igh
t tr
ian
gle
fro
m d
rin
kin
g
stra
ws.
Mrs
. K
ell
y m
ad
e a
ch
art
wit
h t
he
dim
en
sion
s of
each
tri
an
gle
. H
ow
ever,
M
rs.
Kell
y m
ad
e a
mis
tak
e w
hen
re
cord
ing t
heir
resu
lts.
Wh
ich
resu
lt w
as
reco
rded
in
corr
ect
ly?
3. M
AP
S F
ind
th
e d
ista
nce
betw
een
Maco
n
an
d B
err
yvil
le.
Rou
nd
you
r an
swer
to t
he
neare
st t
en
th.
76.2
mi
4. T
ELE
VIS
ION
T
ele
vis
ion
s are
id
en
tifi
ed
by t
he d
iagon
al
measu
rem
en
t of
the
vie
win
g s
creen
. F
or
exam
ple
, a 2
7-i
nch
te
levis
ion
has
a d
iagon
al
scre
en
m
easu
rem
en
t of
27 i
nch
es.
Com
ple
te t
he c
hart
to f
ind
th
e s
creen
h
eig
ht
of
each
tele
vis
ion
giv
en
its
siz
e
an
d s
creen
wid
th.
Rou
nd
you
r an
swers
to
the n
eare
st w
hole
nu
mber.
So
urc
e:
Best
Buy
5. M
AN
UFA
CTU
RIN
G K
arl
work
s fo
r a
com
pan
y t
hat
man
ufa
ctu
res
car
part
s.
His
job i
s to
dri
ll a
hole
in
sp
heri
cal
steel
ball
s. T
he b
all
s an
d t
he h
ole
s h
ave t
he
dim
en
sion
s sh
ow
n o
n t
he d
iagra
m.
a.
How
deep
is
the h
ole
? 12 c
m
b.
Wh
at
wou
ld b
e t
he r
ad
ius
of
a b
all
w
ith
a s
imil
ar
hole
7 c
en
tim
ete
rs w
ide
an
d 2
4 c
en
tim
ete
rs d
eep
? 12.5
cm
d
Seco
nd
Base
Ho
me P
late
90
ft
x c
m
13
cm
5 c
m
Sid
e L
en
gth
s
S
tud
en
t a
b
c
Stu
den
t a
b
c
A
my
3
4
5
Fra
n
8
14
16
B
elin
da
7
24
25
Gus
5
12
13
E
mory
9
12
15
27
in
.
1 02345678
12
34
56
78
910
tens of miles
ten
s o
f m
iles
Cart
er
Cit
y
Maco
nH
am
ilto
n
Berr
yville
10-5
TV
siz
ew
idth
(in
.)h
eig
ht
(in
.)
19-inch
15
12
25-inch
21
14
32-inch
25
20
50-inch
40
30
Fra
n’s
Lesson 10-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
35
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Pyth
ag
ore
an
Tri
ple
sR
eca
ll t
he P
yth
agore
an
Th
eore
m:
In a
rig
ht
tria
ngle
, th
e s
qu
are
of
the l
en
gth
of
the h
yp
ote
nu
se
is e
qu
al
to t
he s
um
of
the s
qu
are
s of
the l
en
gth
s of
the l
egs.
a
2 +
b2 =
c2
N
ote
th
at
c i
s th
e l
en
gth
of
the h
yp
ote
nu
se.
Th
e i
nte
gers
3,
4,
an
d 5
sati
sfy t
he
32 +
42 =
52
Pyth
agore
an
Th
eore
m a
nd
can
be t
he
9 +
16
= 2
5le
ngth
s of
the s
ides
of
a r
igh
t tr
ian
gle
. 25 =
25
Fu
rth
erm
ore
, fo
r an
y p
osi
tive i
nte
ger
n,
F
or
n =
2:
6
2 +
82 =
10
2
the n
um
bers
3n
, 4n
, an
d 5
n s
ati
sfy t
he
36 +
64 =
10
0P
yth
agore
an
Th
eore
m.
100 =
100
If t
hre
e n
um
bers
sati
sfy t
he P
yth
agore
an
Th
eore
m,
they a
re c
all
ed
a
Py
tha
go
rea
n t
rip
le.
Here
is
an
easy
way t
o f
ind
oth
er
Pyth
agore
an
tri
ple
s.
Th
e n
um
bers
a,
b,
an
d c
are
a P
yth
agore
an
tri
ple
if
a =
m2 -
n2,
b =
2m
n,
an
d c
= m
2 +
n2,
wh
ere
m a
nd
n a
re r
ela
tively
pri
me p
osi
tive i
nte
gers
an
d m
> n
.
C
ho
ose m
= 5
an
d n
= 2
.
a =
m2 -
n2
b =
2m
n
c =
m2 +
n2
Ch
eck
20
2 +
21
2
29
2
=
52 -
22
= 2
(5)(
2)
= 5
2 +
22
400 +
441
84
1
=
25
- 4
=
20
= 2
5 +
4
841 =
841
=
21
=
29
Exerc
ises
Use t
he f
oll
ow
ing
va
lues o
f m
an
d n
to
fin
d P
yth
ag
orea
n t
rip
les.
1. m
= 3
an
d n
= 2
2. m
= 4
an
d n
= 1
3. m
= 5
an
d n
= 3
5
, 12,
13
8,
15,
17
16,
30,
34
4. m
= 6
an
d n
= 5
5. m
= 1
0 a
nd
n =
7
6. m
= 8
an
d n
= 5
1
1,
60,
61
51,
140,
149
39,
80,
89
ACB a
c b
10-5
Exam
ple
Answers (Lesson 10-5)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A17 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
36
Gle
ncoe A
lgeb
ra 1
Sp
read
sheet
Act
ivit
y
Pyth
ag
ore
an
Tri
ple
sA
Py
tha
go
rea
n t
rip
le i
s a s
et
of
thre
e w
hole
nu
mbers
th
at
sati
sfie
s th
e
equ
ati
on a
2 +
b2 =
c2, w
her
e c
is t
he
gre
ate
st n
um
ber
. Y
ou
can
use
a s
pre
adsh
eet
to i
nvest
igate
th
e p
att
ern
s in
Pyth
agore
an
tri
ple
s. A
prim
itiv
e P
yth
ag
orea
n
trip
le i
s a P
yth
agore
an
tri
ple
in
wh
ich
th
e n
um
bers
have n
o c
om
mon
fact
ors
oth
er
than
1.
A f
am
ily
of
Py
tha
go
rea
n t
rip
les i
s a p
rim
itiv
e P
yth
agore
an
trip
le a
nd
its
wh
ole
nu
mber
mu
ltip
les.
Th
e s
prea
dsh
eet
at
the r
igh
t p
ro
du
ces a
fa
mil
y o
f P
yth
ag
orea
n t
rip
les.
Ste
p 1
E
nte
r a P
yth
agore
an
tri
ple
in
to c
ell
s A
1,
A2,
an
d A
3.
Ste
p 2
U
se r
ow
s 2 t
hro
ugh
10 t
o f
ind
9
ad
dit
ion
al
Pyth
agore
an
tri
ple
s th
at
are
mu
ltip
les
of
the p
rim
itiv
e t
rip
le.
Form
at
the r
ow
s so
th
at
row
2 m
ult
ipli
es
the
nu
mbers
in
row
1 b
y 2
, ro
w 3
mu
ltip
lies
the n
um
bers
in
row
1 b
y 3
, an
d s
o o
n.
Exerc
ises
Use t
he s
prea
dsh
eet
of
fam
ilie
s o
f P
yth
ag
orea
n t
rip
les.
1. C
hoose
on
e o
f th
e t
rip
les
oth
er
than
(3,
4,
5)
from
th
e s
pre
ad
sheet.
Veri
fy
that
it i
s a P
yth
agore
an
tri
ple
. S
am
ple
an
sw
er:
Fo
r (6
, 8,
10),
62 +
82 =
36 +
64 o
r 100 =
10
2.
2. T
wo p
oly
gon
s are
sim
ila
r i
f th
ey a
re t
he s
am
e s
hap
e,
bu
t n
ot
nece
ssari
ly
the s
am
e s
ize.
For
tria
ngle
s, i
f tw
o t
rian
gle
s h
ave a
ngle
s w
ith
th
e s
am
e
measu
res
then
th
ey a
re s
imil
ar.
Use
a c
en
tim
ete
r ru
ler
to d
raw
tri
an
gle
s w
ith
measu
res
from
th
e s
pre
ad
sheet.
Do t
he t
rian
gle
s ap
pear
to b
e s
imil
ar?
See s
tud
en
ts’
wo
rk.;
yes
Ea
ch
of
the f
oll
ow
ing
is a
prim
itiv
e P
yth
ag
orea
n t
rip
le.
Use t
he
sp
rea
dsh
eet
to f
ind
tw
o P
yth
ag
orea
n t
rip
les i
n t
heir
fa
mil
ies.
3
. (5
, 12,
13)
Sam
ple
an
sw
er:
(10,
24,
26),
(15,
36,
39)
4.
(9,
40,
41)
Sam
ple
an
sw
er:
(18,
80,
82),
(27,
120,
123)
5
. (2
0,
21,
29)
Sam
ple
an
sw
er:
(40,
42,
58),
(60,
63,
87)
Tri
ple
s.x
ls
A
1 3 4 5 62 8 9 10
117
BC
3 6 9
12
15
18
21
24
27
30
4 8
12
16
20
24
28
32
36
40
5
10
15
20
25
30
35
40
45
50
The form
ula
in c
ell A
10 is
A1 *
10.
Sh
eet
1S
heet
2S
I
10-5
Lesson 10-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
37
Gle
ncoe A
lgeb
ra 1
F
ind
th
e d
ista
nce b
etw
een
th
e
po
ints
at
(-5,
2)
an
d (
4,
5).
d =
√ """""""""
(x2 -
x1)2
+ (y
2 -
y1)2
D
ista
nce F
orm
ula
=
√ """""""""
(4 -
(-
5))
2 +
(5 -
2)2
(x
1,
y1) =
(-
5,
2),
(x
2,
y2) =
(4,
5)
=
√ """
92 +
32
Sim
plif
y.
=
√ """
81 +
9
Evalu
ate
square
s a
nd s
implif
y.
=
√ ""
90
Th
e d
ista
nce
is
√ ""
90 ,
or
abou
t 9.4
9 u
nit
s.
Exam
ple
1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Th
e D
ista
nce a
nd
Mid
po
int
Fo
rmu
las
Dis
tan
ce F
orm
ula
T
he P
yth
agore
an
Th
eore
m c
an
be u
sed
to d
eri
ve t
he D
ista
nce
Fo
rm
ula
sh
ow
n b
elo
w.
Th
e D
ista
nce
Form
ula
can
th
en
be u
sed
to f
ind
th
e d
ista
nce
betw
een
an
y t
wo p
oin
ts i
n t
he c
oord
inate
pla
ne.
Dis
tan
ce F
orm
ula
The d
ista
nce b
etw
een a
ny t
wo p
oin
ts w
ith c
oord
inate
s (
x1,
y1)
and (
x2,
y2)
is
giv
en b
y d
= √ """"""""
(x2 - x
1)2
+ (
y2 -
y1)2
J
ill
dra
ws a
lin
e
seg
men
t fr
om
po
int
(1,
4)
on
her
co
mp
ute
r s
creen
to
po
int
(98,
49).
H
ow
lo
ng
is t
he s
eg
men
t?
d =
√ """""""""
(x2 -
x1)2
+ (y
2 -
y1)2
=
√ """""""""
(98 -
1)2
+ (
49 -
4)2
=
√ """"
97
2 +
45
2
=
√ """"""
9409 +
2025
=
√ """
11,4
34
Th
e s
egm
en
t is
abou
t 106.9
3 u
nit
s lo
ng.
Exerc
ises
Fin
d t
he d
ista
nce b
etw
een
th
e p
oin
ts w
ith
th
e g
iven
co
ord
ina
tes.
1. (1
, 5),
(3,
1)
2. (0
, 0),
(6,
8)
3. (-
2, -
8),
(7, -
3)
2
√ "
5 ;
4.4
7
10
√ ""
106 ;
10.3
0
4. (6
, -
7),
(-
2,
8)
5. (1
, 5),
(-
8,
4)
6. (3
, -
4),
(-
4, -
4)
1
7
√ ""
82 ;
9.0
6
7
7. (-
1,
4),
(3,
2)
8. (0
, 0),
(-
3,
5)
9. (2
, -
6),
(-
7,
1)
2
√ "
5 ;
4.4
7
√ ""
34 ;
5.8
3
√ ""
130 ;
11.4
0
10. (-
2, -
5),
(0,
8)
11. (3
, 4),
(0,
0)
12. (3
, -
4),
(-
4, -
16)
√ ""
173 ;
13.1
5
5
√ ""
193 ;
13.8
9
Fin
d t
he p
ossib
le v
alu
es o
f a
if
the p
oin
ts w
ith
th
e g
iven
co
ord
ina
tes a
re t
he
ind
ica
ted
dis
tan
ce a
pa
rt.
13. (1
, a
), (
3, -
2);
d =
√ "
5
14. (0
, 0),
(a
, 4);
d =
5
15. (2
, -
1),
(a
, 3);
d =
5
-
1 o
r -
3
3 o
r -
3
-1 o
r 5
16. (1
, -
3),
(a
, 21);
d =
25
17. (1
, a
), (-
2,
4);
d =
3
18. (3
, -
4),
(-
4, a
); d
= √ ""
65
-
6 o
r 8
4
-8 o
r 0
10-6
Exam
ple
2
Answers (Lesson 10-5 and Lesson 10-6)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A18 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
38
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n(continued)
Th
e D
ista
nce a
nd
Mid
po
int
Fo
rmu
las
Mid
po
int
Fo
rmu
la
Th
e p
oin
t th
at
is e
qu
idis
tan
ce f
rom
both
of
the e
nd
poin
ts i
s ca
lled
th
e m
idp
oin
t. Y
ou
can
fin
d t
he c
oord
inate
s of
the m
idp
oin
t by u
sin
g t
he M
idp
oin
t F
orm
ula
.
Mid
po
int
Fo
rmu
la
The m
idpoin
t M
of
a lin
e s
egm
ent
with e
ndpoin
ts a
t (x
1,
y1)
and (
x2,
y2)
is
giv
en b
y M
( x1 +
x2
−
2
, y
1 +
y2
−
2
) .
F
ind
th
e c
oo
rd
ina
tes o
f th
e m
idp
oin
t o
f th
e s
eg
men
t w
ith
en
dp
oin
ts
at
(–2,
5)
an
d (
4,
9).
M ( x
1 +
x2 −
2
, y
1 +
y2 −
2
) M
idpoin
t F
orm
ula
=
M ( -
2 +
4 −
2
, 5
+ 9 −
2
) (x
1,
y1) =
(-
2,
5)
and (
x2,
y2) =
(4,
9)
=
M ( 2
−
2 ,
14 −
2 )
Sim
plif
y t
he n
um
era
tors
.
=
M (
1,
3)
Sim
plif
y.
Exerc
ises
Fin
d t
he c
oo
rd
ina
tes o
f th
e m
idp
oin
t o
f th
e s
eg
men
t w
ith
th
e g
iven
en
dp
oin
ts.
1. (1
, 6),
(3,
10)
2. (4
, -
2),
(0,
6)
3. (7
, 2),
(13, -
4)
(
2,
8)
(2,
2)
(10, -
1)
4. (-
1,
2),
(1,
0)
5. (-
3, -
3),
(5, -
11)
6. (0
, 8),
(-
6,
0)
(
1,
0)
(1, -
7)
(-
3,
4)
7. (4
, -
3),
(-
2,
3)
8. (9
, -
1),
(3, -
7)
9. (2
, -
1),
(8,
7)
(
1,
0)
(6, -
4)
(5,
3)
10. (1
, 4),
(-
3,
12)
11. (4
, 0),
(-
2,
6)
12. (1
, 9),
(7,
1)
(-
1,
8)
(1,
3)
(4,
5)
13. (1
2,
0),
(2, -
6)
14. (1
, 1),
(9, -
9)
15. (4
, 5),
(-
2, -
1)
(
7, -
3)
(5, -
4)
(1,
2)
16. (1
, -
14),
(-
5,
0)
17. (2
, 2),
(6,
8)
18. (-
7,
3),
(5, -
3)
(-
2, -
7)
(4,
5)
(-
1,
0)
10-6
Exam
ple
1
Lesson 10-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
39
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Th
e D
ista
nce a
nd
Mid
po
int
Fo
rmu
las
Fin
d t
he d
ista
nce b
etw
een
th
e p
oin
ts w
ith
th
e g
iven
co
ord
ina
tes.
1. (9
, 7),
(1,
1)
10
2
. (5
, 2),
(8, -
2)
5
3. (1
, -
3),
(1,
4)
7
4. (7
, 2),
(-
5,
7)
13
5. (-
6,
3),
(10,
3)
16
6. (3
, 3),
(-
2,
3)
5
7. (-
1, -
4),
(-
6,
0)
√ ""
41 ≈
6.4
0
8. (-
2,
4),
(5,
8)
√ ""
65 ≈
8.0
6
Fin
d t
he p
ossib
le v
alu
es o
f a
if
the p
oin
ts w
ith
th
e g
iven
co
ord
ina
tes a
re t
he
ind
ica
ted
dis
tan
ce a
pa
rt.
9. (-
2, -
5),
(a
, 7);
d =
13
a =
-7 o
r 3
10. (8
, -
2),
(5, a
); d
= 3
a
= -
2
11. (4
, a
), (
1,
6);
d =
5 a =
2 o
r 10
12. (a
, 3),
(5, -
1);
d =
5 a
= 2
or
8
13. (1
, 1),
(a
, 1);
d =
4 a =
-3 o
r 5
14. (2
, a
), (
2,
3);
d =
10
a =
-7 o
r 13
15. (a
, 2),
(-
3,
3);
d =
√ #
2 a
= -
4 o
r -
2
16. (-
5,
3),
(-
3, a
); d
= √ #
5 a
= 2
or
4
Fin
d t
he c
oo
rd
ina
tes o
f th
e m
idp
oin
t o
f th
e s
eg
men
t w
ith
th
e g
iven
en
dp
oin
ts.
17. (-
3,
4),
(-
2,
8)
(-2.5
, 6)
18. (5
, -
6),
(7, -
9)
(6, -
7.5
)
19. (4
, 2),
(8,
6)
(6,
4)
20. (5
, 2),
(3,
10)
(4,
6)
21. (1
2, -
1),
(4, -
11)
(8, -
6)
22. (-
3, -
1),
(-
11,
3)
(-7,
1)
23. (9
, 3),
(6, -
6)
(7.5
, -
1.5
) 24. (0
, -
4),
(8,
4)
(4,
0)
10-6
Answers (Lesson 10-6)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A19 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
40
Gle
ncoe A
lgeb
ra 1
Practi
ce
Th
e D
ista
nce a
nd
Mid
po
int
Fo
rmu
las
Fin
d t
he d
ista
nce b
etw
een
th
e p
oin
ts w
ith
th
e g
iven
co
ord
ina
tes.
1. (4
, 7),
(1,
3)
5
2. (0
, 9),
(-
7,
-2)
√ �
�
170 ≈
13.0
4
3. (6
, 2),
+ (4
, 1
−
2 )
5
−
2 o
r 2.5
0
4. (-
1,
7),
+ ( 1
−
3 , 6
) 5
−
3 ≈
1.6
7
5.
( √ #
3 ,
3) ,
( 2 √
#
3 ,
5)
√ �
7 ≈
2.6
5
6.
( 2 √
#
2 ,
-1
) , ( 3
√ #
2 ,
3)
3 √
�
2 ≈
4.2
4
Fin
d t
he p
ossib
le v
alu
es o
f a
if
the p
oin
ts w
ith
th
e g
iven
co
ord
ina
tes a
re t
he
ind
ica
ted
dis
tan
ce a
pa
rt.
7. (4
, -
1),
(a
, 5);
d =
10
a =
-4 o
r 12
8
. (2
, -
5),
(a
, 7);
d =
15
a =
-7 o
r 11
9. (6
, -
7),
(a
, -
4);
d =
√ #
#
18 a
= 3
or
9
10. (-
4,
1),
(a
, 8);
d =
√ #
#
50 a
= -
5 o
r -
3
11. (8
, -
5),
(a
, 4);
d =
√ #
#
85 a
= 6
or
10
12. (-
9,
7),
(a
, 5);
d =
√ #
#
29 a
= -
14 o
r -
4
Fin
d t
he c
oo
rd
ina
tes o
f th
e m
idp
oin
t o
f th
e s
eg
men
t w
ith
th
e g
iven
en
dp
oin
ts.
13. (4
, -
6),
(3,
-9)
(3.5
, -
7.5
) 14. (-
3,
-8),
(-
7,
2)
(-5,
-3)
15. (0
, -
4),
(3,
2)
(1.5
, -
1)
16. (-
13,
-9),
(-
1,
-5)
(-7,
-7)
17.
(2, -
1
−
2 ) ,
(1, 1
−
2 ) (
1 1
−
2 ,
0)
18. ( 2
−
3 ,
-1
) , (2,
1
−
3 ) (1
1
−
3 ,
- 1
−
3 )
19. B
ASEB
ALL T
hre
e p
layers
are
warm
ing u
p f
or
a b
ase
ball
gam
e.
Pla
yer
B s
tan
ds
9 f
eet
to t
he r
igh
t an
d 1
8 f
eet
in f
ron
t of
Pla
yer
A.
Pla
yer
C s
tan
ds
8 f
eet
to t
he l
eft
an
d 1
3 f
eet
in
fron
t of
Pla
yer
A.
a
. D
raw
a m
od
el
of
the s
itu
ati
on
on
th
e c
oord
inate
gri
d.
Ass
um
e t
hat
Pla
yer
A i
s lo
cate
d a
t (0
, 0).
b
. T
o t
he n
eare
st t
en
th,
wh
at
is t
he d
ista
nce
betw
een
Pla
yers
A
an
d B
an
d b
etw
een
Pla
yers
A a
nd
C?
c.
Wh
at
is t
he d
ista
nce
betw
een
Pla
yers
B a
nd
C?
20. M
APS
M
ari
a a
nd
Jack
son
liv
e i
n a
dja
cen
t n
eig
hborh
ood
s. I
f th
ey s
up
eri
mp
ose
a
coord
inate
gri
d o
n t
he m
ap
of
their
neig
hborh
ood
s, M
ari
a l
ives
at
(-9,
1)
an
d J
ack
son
li
ves
at
(5,
-4).
x
y
O4
8
16
12 8 4
-8
-4
10-6
ab
ou
t 1.9
6 m
i
20.1
ft;
15.3
ft
17.7
ft
Lesson 10-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
41
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Th
e D
ista
nce a
nd
Mid
po
int
Fo
rmu
las
1. C
HESS
M
arg
are
t’s
last
tw
o r
em
ain
ing
chess
pie
ces
are
loca
ted
at
the c
en
ters
of
the s
qu
are
s at
op
posi
te c
orn
ers
of
the
board
. If
th
e c
hess
board
is
a s
qu
are
wit
h
8-i
nch
sid
es,
abou
t h
ow
far
ap
art
are
th
e
pie
ces?
Rou
nd
you
r an
swer
to t
he
neare
st t
en
th.
2. EN
GIN
EER
ING
T
od
d h
as
dra
wn
a
cul-
de-s
ac
for
a r
esi
den
tial
develo
pm
en
t p
lan
. H
e u
sed
a c
om
pass
to d
raw
th
e
cul-
de-s
ac
so t
hat
it w
ou
ld b
e c
ircu
lar.
O
n h
is b
luep
rin
t, t
he c
en
ter
of
the c
ul-
de-s
ac
has
coord
inate
s (-
1,
-1)
an
d a
p
oin
t on
th
e c
ircl
e i
s (2
, 3).
Wh
at
is t
he
rad
ius
of
the c
ul-
de-s
ac?
3. LA
ND
SC
APIN
G R
an
dy p
lott
ed
a
tria
ngu
lar
pati
o o
n a
lan
dsc
ap
e p
lan
for
a c
lien
t. W
hat
is t
he l
en
gth
of
fen
cin
g h
e
wil
l n
eed
alo
ng t
he p
ati
o e
dge t
hat
bord
ers
th
e p
rop
ert
y l
ine?
Rou
nd
you
r
an
swer
to t
he n
eare
st t
en
th.
4. U
TIL
ITIE
S T
he e
lect
ric
com
pan
y i
s ru
nn
ing s
om
e w
ires
acr
oss
an
op
en
fie
ld.
Th
e w
ire c
on
nect
s a u
tili
ty p
ole
at
(2,
14)
an
d a
seco
nd
uti
lity
pole
at
(7,
-8).
If
the
ele
ctri
c co
mp
an
y w
ish
es
to p
lace
a t
hir
d
pole
at
the m
idp
oin
t of
the t
wo p
ole
s, a
t w
hat
coord
inate
s sh
ou
ld t
he p
ole
be
pla
ced
?
5. M
AR
CH
ING
BA
ND
T
he O
hio
Sta
te
Un
ivers
ity m
arc
hin
g b
an
d p
erf
orm
s a
fam
ou
s on
-fie
ld s
pell
ing o
f O
-H-I
-O c
all
ed
“S
crip
t O
hio
”. S
om
eti
mes
they m
ust
ad
just
th
e u
sual
dim
en
sion
s of
the w
ord
to
fit
it
into
th
e l
imit
ed
gu
est
ban
d
perf
orm
an
ce a
rea.
Th
e d
iagra
m b
elo
w
show
s p
art
of
the a
dju
sted
dri
ll c
hart
. E
ach
poin
t re
pre
sen
ts o
ne b
an
d m
em
ber,
an
d t
he c
oord
inate
s are
in
yard
s.
a.
How
far
is t
he d
rum
majo
r fr
om
th
e
tuba p
layer
wh
o d
ots
th
e “
i”?
b.
Caro
l is
th
e b
an
d m
em
ber
at
the t
op
le
ft o
f th
e f
irst
O i
n O
hio
. S
he i
s lo
cate
d a
t (0
, 26).
How
far
aw
ay i
s C
aro
l fr
om
th
e t
uba p
layer?
Rou
nd
you
r an
swer
to t
he n
eare
st t
en
th.
dru
m m
ajo
rtu
ba p
layer
(20
, 1
3)
(32
, 1
0)
123456789
10
23
45
67
89
meters
meters
shru
bs
property line
house
treep
ati
o
( 2,
4)
( 6,
8)
( 5,
1)
10-6
9.9
in
.
5 u
nit
s
7.1
m
(4.5
, 3)
12.4
yd
23.9
yd
Answers (Lesson 10-6)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A20 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
42
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
A S
pace-S
avin
g M
eth
od
Tw
o a
rran
gem
en
ts f
or
cook
ies
on
a 3
2 c
m b
y 4
0 c
m c
ook
ie
sheet
are
sh
ow
n a
t th
e r
igh
t. T
he c
ook
ies
have 8
-cm
dia
mete
rs
aft
er
they a
re b
ak
ed
. T
he c
en
ters
of
the c
ook
ies
are
on
th
e
vert
ices
of
squ
are
s in
th
e t
op
arr
an
gem
en
t. I
n t
he o
ther,
th
e
cen
ters
are
on
th
e v
ert
ices
of
equ
ilate
ral
tria
ngle
s. W
hic
h
arr
an
gem
en
t is
more
eco
nom
ical?
Th
e t
rian
gle
arr
an
gem
en
t is
more
eco
nom
ical,
beca
use
it
con
tain
s on
e m
ore
cook
ie.
In t
he s
qu
are
arr
an
gem
en
t, r
ow
s are
pla
ced
every
8 c
m.
At
wh
at
inte
rvals
are
row
s p
lace
d i
n t
he t
rian
gle
arr
an
gem
en
t?
Look
at
the r
igh
t tr
ian
gle
labele
d a
, b,
an
d c
. A
leg a
of
the
tr
ian
gle
is
the r
ad
ius
of
a c
ook
ie,
or
4 c
m.
Th
e h
yp
ote
nu
se c
is
the s
um
of
two r
ad
ii,
or
8 c
m.
Use
th
e P
yth
agore
an
th
eore
m t
o
fin
d b
, th
e i
nte
rval
of
the r
ow
s.
c
2 =
a2 +
b2
8
2 =
42 +
b2
64 -
16 =
b2
√ ""
48 =
b
4 √ "
3 =
b
b =
4 √ "
3 ≈
6.9
3
Th
e r
ow
s are
pla
ced
ap
pro
xim
ate
ly e
very
6.9
3 c
m.
So
lve e
ach
pro
ble
m.
1. S
up
pose
cook
ies
wit
h 1
0-c
m d
iam
ete
rs a
re a
rran
ged
in
th
e
tria
ngu
lar
patt
ern
sh
ow
n a
bove.
Wh
at
is t
he i
nte
rval
b o
f th
e r
ow
s? 8.6
6 c
m
2. F
ind
th
e d
iam
ete
r of
a c
ook
ie i
f th
e r
ow
s are
pla
ced
in
th
e
tria
ngu
lar
patt
ern
every
3 √ "
3 c
m.
6 c
m
3. D
esc
ribe o
ther
pra
ctic
al
ap
pli
cati
on
s in
wh
ich
th
is k
ind
of
tria
ngu
lar
patt
ern
can
be u
sed
to e
con
om
ize o
n s
pace
.
Sam
ple
an
sw
er:
packag
ing
can
s
{b=
?
21
co
okie
s
ca
{8
cm
20
co
okie
s
10-6
Lesson 10-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
43
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Sim
ilar
Tri
an
gle
s
Sim
ilar
Tri
an
gle
s %
RS
T i
s sim
ila
r t
o %
XY
Z.
Th
e a
ngle
s of
the
tw
o t
rian
gle
s h
ave e
qu
al
measu
re.
Th
ey a
re c
all
ed
co
rresp
on
din
g
an
gle
s.
Th
e s
ides
op
posi
te t
he c
orr
esp
on
din
g a
ngle
s are
call
ed
co
rresp
on
din
g s
ides.
30°
30°
60°
60°
S
ZX Y
RT
D
ete
rm
ine w
heth
er
the p
air
of
tria
ng
les i
s s
imil
ar.
Ju
sti
fy y
ou
r a
nsw
er.
Sin
ce c
orr
esp
on
din
g a
ngle
s d
o n
ot
have
the e
qu
al
measu
res,
th
e t
rian
gle
s are
n
ot
sim
ilar.
50°
75°
45°
89°
R
S
T
X
Y
Z
D
ete
rm
ine w
heth
er t
he p
air
of
tria
ng
les i
s s
imil
ar.
Ju
sti
fy y
ou
r
an
sw
er.
Th
e m
easu
re o
f ∠
G =
180° -
(90° +
45°)
= 4
5°.
T
he m
easu
re o
f ∠
I =
180° -
(45° +
45°)
= 9
0°.
S
ince
corr
esp
on
din
g a
ngle
s h
ave e
qu
al
measu
res,
%E
FG
∼ %
HIJ
.
90°
45°
45°
45°
F
G
H
J
I
E
Exerc
ises
Dete
rm
ine w
heth
er e
ach
pa
ir o
f tr
ian
gle
s i
s s
imil
ar.
Ju
sti
fy y
ou
r a
nsw
er.
1.
2.
3.
Y
es;
co
rresp
on
din
g
No
; co
rresp
on
din
g
Yes;
co
rresp
on
din
g
an
gle
s h
ave e
qu
al
a
ng
les d
o n
ot
have
an
gle
s h
ave e
qu
al
measu
res.
eq
ual
measu
res.
measu
res.
4.
5.
6.
Y
es;
co
rresp
on
din
g
Yes;
co
rresp
on
din
g
No
; co
rresp
on
din
g
an
gle
s h
ave e
qu
al
a
ng
les h
ave e
qu
al
an
gle
s d
o n
ot
have
measu
res.
measu
res.
eq
ual
measu
res.
20°
30°
12
0° 1
15°
45°
45°
80°
55°
40°
30°
30°
11
0°
90°
45°
60°
60°
30°
30°
30°
12
0°
10-7
Sim
ilar
Tri
an
gle
s
If t
wo t
riangle
s a
re s
imila
r, t
hen t
he
measure
s o
f th
eir c
orr
espondin
g s
ides
are
pro
port
ional and t
he m
easure
s o
f
their c
orr
espondin
g a
ngle
s a
re e
qual.
!
AB
C ∼
!D
EF
AB
−
DE =
BC
−
EF
= A
C
−
DF
A
BD
E
F
C
Exam
ple
1Exam
ple
2
Answers (Lesson 10-6 and Lesson 10-7)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A21 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
44
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n(c
on
tin
ued
)
Sim
ilar
Tri
an
gle
s
Fin
d U
nkn
ow
n M
easu
res
If s
om
e o
f th
e m
easu
rem
en
ts a
re k
now
n,
pro
port
ion
s ca
n
be u
sed
to f
ind
th
e m
easu
res
of
the o
ther
sid
es
of
sim
ilar
tria
ngle
s.
IND
IREC
T M
EA
SU
REM
EN
T
�A
BC
∼ �
AED
in
th
e f
igu
re a
t th
e r
igh
t.
Fin
d t
he h
eig
ht
of
the a
pa
rtm
en
t b
uil
din
g.
Let
BC
= x
.
ED −
BC
= A
D −
AC
=
25 −
300
ED
= 7
, A
D =
25,
AC
= 3
00
25
x =
2100
Fin
d t
he c
ross p
roducts
.
x =
84
Th
e a
part
men
t bu
ild
ing i
s 84 m
ete
rs h
igh
.
Exerc
ises
Fin
d t
he m
issin
g m
ea
su
res f
or t
he p
air
of
sim
ila
r
tria
ng
les i
f �ABC
∼ �
DEF
.
1. c =
15,
d =
8,
e =
6,
f =
10 a
= 1
2;
b =
9
2. c =
20,
a =
12,
b =
8,
f =
15
d
= 9
; e
= 6
3. a
= 8
, d
= 8
, e =
6,
f =
7 b
= 6
; c
= 7
4. a
= 2
0,
d =
10,
e =
8,
f =
10
b
= 1
6;
c =
20
5. c =
5,
d =
10,
e =
8,
f =
8 a
= 2
5 −
4 ;
b =
5
6. a
= 2
5,
b =
20,
c =
15,
f =
12 d
= 2
0;
e =
16
7. b
= 8
, d
= 8
, e =
4,
f =
10
a
= 1
6;
c =
20
8. IN
DIR
EC
T M
EA
SU
RE
ME
NT
B
ruce
lik
es
to a
mu
se
his
bro
ther
by s
hin
ing a
fla
shli
gh
t on
his
han
d a
nd
mak
ing a
sh
ad
ow
on
th
e w
all
. H
ow
far
is i
t fr
om
the f
lash
ligh
t to
th
e w
all
? 51.6
in
. o
r 4.3
ft
9. IN
DIR
EC
T M
EA
SU
RE
ME
NT
A
fore
st r
an
ger
use
s si
mil
ar
tria
ngle
s to
fin
d t
he h
eig
ht
of
a t
ree.
Fin
d t
he h
eig
ht
of
the t
ree.
60 f
t
12
ft
20
ft
x
10
0 f
t
5 in
.6 in.
x in.
4 f
t
Note: N
ot
dra
wn t
o s
cale
A
ca
be
fd
CD
F
EB
25
m
Note: N
ot
dra
wn t
o s
cale
27
5 m
7 m
ADE
CB
x
10-7
Exam
ple
7 −
x
Lesson 10-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
45
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Sim
ilar
Tri
an
gle
s
PR
Q
q
rp
SU
T
t
us
52°
52°
63°
65°
FE
H
J
K
G4
0°
40°
45°
F
EG
H
J
K
60°
60°
57°
60°
XV
W
U
Z
Y
40°
50°
A
DF
E C
B
10-7
Dete
rm
ine w
heth
er e
ach
pa
ir o
f tr
ian
gle
s i
s s
imil
ar.
Ju
sti
fy y
ou
r a
nsw
er.
1.
2.
Y
es; ∠
A =
∠D
= 9
0°;
∠B
=
No
; ∠
Y =
180° -
(60° +
60°)
= 6
0°.
180° -
(90° +
40°)
= 5
0° =
∠E
;
Sin
ce �
UV
W h
as a
57°
an
gle
, b
ut
∠F =
180° -
(90° +
50°)
= 4
0° =
�
XY
Z d
oes n
ot,
co
rresp
on
din
g
∠C
. S
ince t
he c
orr
esp
on
din
g
an
gle
s d
o n
ot
all h
ave e
qu
al
an
gle
s h
ave e
qu
al
measu
res,
m
easu
res,
an
d t
he t
rian
gle
s a
re n
ot
�A
BC
∼ �
DE
F.
sim
ilar.
3.
4.
N
o; ∠
F =
180° -
(45° +
40°)
=
Yes; ∠
G =
180° -
(65° +
52°)
= 6
3° =
95°.
Sin
ce �
HJK
has a
90°
∠
K; ∠
J =
180° -
(63° +
52°)
= 6
5° =
an
gle
, b
ut �
EFG
do
es n
ot,
∠
F; ∠
E =
∠H
= 5
2°.
Sin
ce t
he
co
rresp
on
din
g a
ng
les d
o n
ot
all
co
rresp
on
din
g a
ng
les h
ave e
qu
al
have e
qu
al
measu
res,
an
d t
he
m
easu
res, �
EFG
∼ �
HJK
.
tria
ng
les a
re n
ot
sim
ilar.
Fin
d t
he m
issin
g m
ea
su
res f
or t
he p
air
of
sim
ila
r
tria
ng
les i
f �PQR
∼ �
STU
.
5.
r =
4,
s =
6,
t =
3,
u =
2 p
= 1
2,
q =
6
6.
t =
8,
p =
21,
q =
14,
r =
7 u
= 4
, s =
12
7.
p =
15,
q =
10,
r =
5,
s =
6 t =
4,
u =
2
8.
p =
48,
s =
16,
t =
8,
u =
4 r =
12,
q =
24
9.
q =
6,
s =
2,
t =
3 −
2 ,
u =
1 −
2 r =
2,
p =
8
10.
p =
3,
q =
2,
r =
1,
u =
1 −
3 s =
1,
t =
2 −
3
11.
p =
14,
q =
7,
u =
2.5
, t =
5 r =
3.5
, s =
10
12.
r =
6,
s =
3,
t =
21 −
8 ,
u =
9 −
4 p
= 8
, q
= 7
Answers (Lesson 10-7)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A22 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
46
Gle
ncoe A
lgeb
ra 1
Practi
ce
Sim
ilar
Tri
an
gle
sD
ete
rm
ine w
heth
er e
ach
pa
ir o
f tr
ian
gle
s i
s s
imil
ar.
Ju
sti
fy y
ou
r a
nsw
er.
1.
2.
Y
es; ∠
Q =
∠T =
90°;
∠P
=
No
; ∠
C =
180° -
(47° +
80°)
= 5
3°.
180° -
(90° +
31°)
= 5
9° =
∠S
;
Sin
ce !
FG
H h
as a
56°
an
gle
, b
ut
∠U
= 1
80° -
(90° +
59°)
= 3
1° =
!
CD
E d
oes n
ot,
co
rresp
on
din
g
∠R
. S
ince t
he c
orr
esp
on
din
g
an
gle
s d
o n
ot
all h
ave e
qu
al
an
gle
s h
ave e
qu
al
measu
res,
m
easu
res,
an
d t
he t
rian
gle
s a
re n
ot
!P
QR
, !
STU
. sim
ilar.
Fin
d t
he m
issin
g m
ea
su
res f
or t
he p
air
of
sim
ila
r
tria
ng
les i
f !ABC
∼ !
DEF
.
3. c =
4, d
= 1
2, e =
16, f =
8 a
= 6
, b
= 8
4. e =
20, a
= 2
4, b
= 3
0, c =
15 d
= 1
6,
f =
10
5. a
= 1
0, b =
12, c =
6, d
= 4
e =
4.8
, f =
2.4
6. a
= 4
, d
= 6
, e =
4, f =
3 c =
2,
b =
8 −
3
7. b
= 1
5, d
= 1
6, e =
20, f =
10
a =
12,
c =
15 −
2
8. a
= 1
6, b =
22, c =
12, f =
8 d
= 3
2 −
3 ,
e =
44 −
3
9. a
= 5
−
2 , b =
3, f =
11 −
2 ,
e =
7 c
= 3
3 −
14 ,
d =
35 −
6
10. c =
4, d
= 6
, e =
5.6
25, f =
12 a
= 2
, b
= 1
.875
11. S
HA
DO
WS
S
up
pose
you
are
sta
nd
ing n
ear
a b
uil
din
g a
nd
you
wan
t to
kn
ow
its
heig
ht.
Th
e b
uil
din
g c
ast
s a 6
6-f
oot
shad
ow
. Y
ou
cast
a 3
-foot
shad
ow
. If
you
are
5 f
eet
6 i
nch
es
tall
, h
ow
tall
is
the b
uil
din
g?
12. M
OD
ELS
T
russ
bri
dges
use
tri
an
gle
s in
th
eir
su
pp
ort
beam
s. M
oll
y m
ad
e a
mod
el
of
a
tru
ss b
rid
ge i
n t
he s
cale
of
1 i
nch
= 8
feet.
If
the h
eig
ht
of
the t
rian
gle
s on
th
e m
od
el
is
4.5
in
ches,
wh
at
is t
he h
eig
ht
of
the t
rian
gle
s on
th
e a
ctu
al
bri
dge?
DF
E
e
fd
AC
B
b
ca
80°
47°
47°
56°
EH
F
GD
C
31°
59°
RQ
STU
P
10-7
121 f
t
36 f
t
Lesson 10-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
47
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Sim
ilar
Tri
an
gle
s
1. C
RA
FTS
L
ayla
is
wan
ts t
o b
uy a
set
of
sim
ilar
magn
ets
for
her
refr
igera
tor
door.
Layla
fin
ds
the m
agn
ets
belo
w f
or
sale
at
a l
oca
l sh
op
. W
hic
h t
wo a
re s
imil
ar?
B a
nd
C
2. EX
HIB
ITIO
NS
T
he w
orl
d’s
larg
est
can
dle
was
dis
pla
yed
at
the 1
897 S
tock
holm
Exh
ibit
ion
. S
up
pose
Lars
measu
red
th
e
len
gth
of
the s
had
ow
it
cast
at
11:0
0 A
.M.
an
d f
ou
nd
th
at
it w
as
12 f
eet.
Su
pp
ose
that
imm
ed
iate
ly a
fter
this
, h
e m
easu
red
to f
ind
th
at
a n
earb
y 2
5-f
oot
ten
t p
ole
cast
a s
had
ow
5 f
eet
lon
g.
How
tall
was
the w
orl
d’s
larg
est
can
dle
?
3. LA
ND
MA
RK
S T
he T
oy a
nd
Min
iatu
re
Mu
seu
m o
f K
an
sas
Cit
y d
isp
lays
a
min
iatu
re r
ep
lica
of
Georg
e W
ash
ingto
n’s
Mou
nt
Vern
on
man
sion
. T
he m
inia
ture
hou
se i
s 10 f
eet
lon
g,
6 f
eet
wid
e,
8 f
eet
tall
, an
d h
as
22 r
oom
s. T
he s
cale
of
the
mod
el
to t
he o
rigin
al
is o
ne i
nch
to o
ne
foot.
If
the r
oof
gable
of
the m
inia
ture
has
dim
en
sion
s as
show
n o
n t
he d
iagra
m
belo
w,
wh
at
is t
he h
eig
ht
of
the r
oof
gable
on
th
e o
rigin
al
Mou
nt
Vern
on
man
sion
?
So
urce:
Mount
Vern
on
4. S
UR
VE
YIN
G S
urv
eyors
use
pro
pert
ies
of
tria
ngle
s in
clu
din
g s
imil
ari
ty a
nd
th
e
Pyth
agore
an
Th
eore
m t
o f
ind
un
kn
ow
n
dis
tan
ces.
Use
th
e d
imen
sion
s on
th
e
dia
gra
m t
o f
ind
th
e u
nk
now
n d
ista
nce
x
acr
oss
th
e l
ak
e.
80 m
5. PU
ZZLES
T
he f
igu
re b
elo
w s
how
s an
an
cien
t C
hin
ese
movable
pu
zzle
call
ed
a
tan
gra
m.
It h
as
7 p
iece
s th
at
can
be
reco
nfi
gu
red
to p
rod
uce
an
en
dle
ss
nu
mber
of
desi
gn
s an
d p
ictu
res.
Ass
um
e t
hat
the s
ide l
en
gth
of
this
tan
gra
m s
qu
are
is
√$ 2 c
m.
Leave y
ou
r
an
swers
as
sim
pli
fied
rad
ical
exp
ress
ion
s.
a
. Wh
at
are
th
e s
ide l
en
gth
s of
tria
ngle
s
1 a
nd
2?
b
. Wh
at
are
th
e s
ide l
en
gth
s of
tria
ngle
7?
√ &
2 − 2
cm
, √ &
2 − 2
cm
, 1 c
m
c.
Wh
at
are
th
e s
ide l
en
gth
s of
tria
ngle
s
3 a
nd
5?
AB
C
7cm
6cm
5cm
3cm
4cm
8cm
3 f
t
1.9
ft
1.9
ft
hei
gh
t
NP
M
x
Q
80 m
40 m
120 m
0
lake
1
2
3
4
5
67
10-7
1 −
2 c
m,
1 −
2 c
m,
√ &
2 −
2 c
m
60 f
t
14 f
t1 c
m,
1 c
m,
√ &
2 c
m
Answers (Lesson 10-7)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A23 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
48
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
A C
uri
ou
s C
on
str
ucti
on
Man
y m
ath
em
ati
cian
s h
ave b
een
in
tere
sted
in
ways
to
con
stru
ct t
he n
um
ber π
. H
ere
is
on
e s
uch
geom
etr
ic c
on
stru
ctio
n.
In t
he d
raw
ing,
tria
ngle
s A
BC
an
d A
DE
are
rig
ht
tria
ngle
s. T
he l
en
gth
of
−−−
AD
equ
als
th
e l
en
gth
of
−−
AC
an
d −−
FB
is
para
llel
to −−−
EG
.
Th
e l
en
gth
of
−−−
BG
giv
es
a d
eci
mal
ap
pro
xim
ati
on
of
the f
ract
ion
al
part
of π t
o s
ix d
eci
mal
pla
ces.
Fo
llo
w t
he s
tep
s t
o f
ind
th
e l
en
gth
of
−−
BG
. R
ou
nd
to s
ev
en
decim
al
pla
ces.
1. U
se t
he l
en
gth
of
−−−
BC
an
d t
he P
yth
agore
an
Th
eore
m t
o f
ind
th
e l
en
gth
of
−−
AC
.
A
C =
√ ""
""
1 2 +
( 7
−
8 ) 2
= 1
.3287682
2. F
ind
th
e l
en
gth
of
−−−
AD
.
A
D =
AC
= 1
.3287682
3. U
se t
he l
en
gth
of
−−−
AD
an
d t
he P
yth
agore
an
Th
eore
m t
o f
ind
th
e l
en
gth
of
−−
AE
.
A
E =
√ ""
""
""
(A
D ) 2
+ ( 1
−
2 ) 2
= 1
.4197271
4. T
he s
ides
of
the s
imil
ar
tria
ngle
s F
ED
an
d D
EA
are
in
pro
port
ion
. S
o,
FE −
0.5
= 0
.5 −
AE
.
Fin
d t
he l
en
gth
of
−−
FE
.
F
E =
1
−
4(A
E)
= 0
.1760902
5. F
ind
th
e l
en
gth
of
−−
AF
.
A
F =
AE
- F
E =
1.2
436369
6. T
he s
ides
of
the s
imil
ar
tria
ngle
s A
FB
an
d A
EG
are
in
pro
port
ion
. S
o,
AF −
AE
= A
B −
AG
.
Fin
d t
he l
en
gth
of
−−−
AG
.
A
G =
AB
· A
E
−
AF
= A
E
−
AF =
1.1
415929
7. N
ow
, fi
nd
th
e l
en
gth
of
−−−
BG
.
B
G =
AG
- A
B =
AG
- 1
= 0
.1415929
8. T
he v
alu
e o
f π
to s
even
deci
mal
pla
ces
is 3
.1415927.
Com
pare
th
e f
ract
ion
al
part
of
pi
wit
h t
he l
en
gth
of
−−−
BG
.
0
.1415929 -
0.1
415927 =
0.0
000002,
an
err
or
of
less t
han
1 p
art
in
a m
illio
n
7 – 8
1 – 2
C
E DG
BA
F
1
10-7
Lesson 10-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
49
Gle
ncoe A
lgeb
ra 1
10-8
Tri
go
no
metr
ic R
ati
os
Tri
gon
om
etr
y i
s th
e s
tud
y o
f re
lati
on
ship
s of
the a
ngle
s an
d t
he
sid
es
of
a r
igh
t tr
ian
gle
. T
he t
hre
e m
ost
com
mon
tri
gon
om
etr
ic r
ati
os
are
th
e s
ine
, co
sin
e,
an
d t
an
gen
t.
sin
e o
f ∠
A = le
g o
pposite ∠
A
−
hypote
nuse
sin
e o
f ∠
B = le
g o
pposite ∠
B
−
hypote
nuse
sin
A = a
−
c
sin
B = b
−
c
cosin
e o
f ∠
A = le
g a
dja
cent to
∠A
−−
hypote
nuse
cosin
e o
f ∠
B = le
g a
dja
cent to
∠B
−−
hypote
nuse
cos A
= b
−
c
cos B
= a
−
c
tangent
of ∠
A =
leg o
pposite ∠
A
−−
le
g a
dja
cent to
∠A
tangent
of ∠
B =
leg o
pposite ∠
B
−−
le
g a
dja
cent to
∠B
tan A
= a
−
b
tan B
= b
−
a
F
ind
th
e v
alu
es o
f th
e t
hree t
rig
on
om
etr
ic r
ati
os f
or a
ng
le A
.
Ste
p 1
U
se t
he P
yth
agore
an
Th
eore
m t
o f
ind
BC
.
a2 +
b2 = c
2
Pyth
agore
an T
heore
m
a2 +
82 = 1
02
b =
8 a
nd c
= 1
0
a
2 +
64 = 1
00
Sim
plif
y.
a2 = 3
6
Subtr
act
64 f
rom
both
sid
es.
a = 6
T
ake t
he s
quare
root
of
each s
ide.
Ste
p 2
U
se t
he s
ide l
en
gth
s to
wri
te t
he t
rigon
om
etr
ic r
ati
os.
sin
A = o
pp −
hyp =
6 −
10 =
3 −
5
co
s A
=
ad
j −
hyp =
8 −
10 =
4 −
5
tan
A = o
pp −
ad
j = 6
−
8 = 3
−
4
Exerc
ises
Fin
d t
he v
alu
es o
f th
e t
hree t
rig
on
om
etr
ic r
ati
os f
or a
ng
le A
.
1.
8
17
2.
3
5
3.
24
7
sin
A =
15 −
17 ,
co
s A
=
8 −
17 ,
sin
A =
7 −
25 ,
co
s A
= 2
4 −
25 ,
tan
A =
15 −
8
ta
n A
=
7 −
24
Use a
ca
lcu
lato
r t
o f
ind
th
e v
alu
e o
f ea
ch
trig
on
om
etr
ic r
ati
o t
o t
he n
ea
rest
ten
-th
ou
sa
nd
th.
4. s
in 4
0°
5. co
s 25°
0.9
063
6. ta
n 8
5°
11.4
301
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Tri
go
no
metr
ic R
ati
os
Exam
ple
a
10 8
0.6
428
b
a
c
sin
A =
4
−
5 ,
co
s A
= 3
−
5 ,
tan
A =
4
−
3
Answers (Lesson 10-7 and Lesson 10-8)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 10 A24 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
50
Gle
ncoe A
lgeb
ra 1
10-8
Use
Tri
go
no
metr
ic R
ati
os
Wh
en
you
fin
d a
ll o
f th
e u
nk
now
n m
easu
res
of
the s
ides
an
d a
ngle
s of
a r
igh
t tr
ian
gle
, you
are
so
lvin
g t
he t
ria
ng
le.
You
can
fin
d t
he m
issi
ng
measu
res
of
a r
igh
t tr
ian
gle
if
you
kn
ow
th
e m
easu
re o
f tw
o s
ides
of
the t
rian
gle
, or
the
measu
re o
f on
e s
ide a
nd
th
e m
easu
re o
f on
e a
cute
an
gle
.
So
lve t
he t
ria
ng
le.
Ro
un
d e
ach
sid
e l
en
gth
to
th
e n
ea
rest
ten
th.
Ste
p 1
F
ind
th
e m
easu
re o
f ∠
B.
Th
e s
um
of
the m
easu
res
of
the a
ngle
s in
a t
rian
gle
is
180.
180° −
(90° +
38°)
= 5
2°
Th
e m
easu
re o
f ∠
B i
s 52°.
Ste
p 2
F
ind
th
e m
easu
re o
f −−
AB
. B
eca
use
you
are
giv
en
th
e
measu
re o
f th
e s
ide a
dja
cen
t to
∠ A
an
d a
re f
ind
ing
the m
easu
re o
f th
e h
yp
ote
nu
se,
use
th
e c
osi
ne r
ati
o.
co
s 38° =
13 −
c
D
efinitio
n o
f cosin
e
c c
os
38° =
13
M
ultip
ly e
ach s
ide b
y c
.
c =
13 −
cos
38°
Div
ide e
ach s
ide b
y s
in 4
1°.
So t
he m
easu
re o
f −−
AB
is
abou
t 16.5
.
Ste
p 3
F
ind
th
e m
easu
re o
f −−−
BC
. B
eca
use
you
are
giv
en
th
e m
easu
re o
f th
e
sid
e a
dja
cen
t to
∠ A
an
d a
re f
ind
ing t
he m
easu
re o
f th
e s
ide o
pp
osi
te
∠ A
, u
se t
he t
an
gen
t ra
tio.
tan
38° =
a −
13
Definitio
n o
f ta
ngent
13 t
an
38° =
a
Multip
ly e
ach s
ide b
y 1
3.
10.2
≈ a
U
se a
calc
ula
tor.
So t
he m
easu
re o
f −−−
BC
is
abou
t 10.2
.
Exerc
ises
So
lve e
ach
rig
ht
tria
ng
le.
Ro
un
d e
ach
sid
e l
en
gth
to
th
e n
ea
rest
ten
th.
1.
9
ab 30°
2.
b
8c
44°
3.
16c
b
56°
∠B
= 6
0°,
AC
≈ 7
.8,
∠A
= 6
0°,
AC
≈ 7
.7,
∠B
= 3
4°,
AC
≈ 1
9.3
,B
C =
4.5
A
B ≈
11.1
A
B ≈
10.8
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Tri
go
no
metr
ic R
ati
os
Exam
ple
13
ac
38°
Lesson 10-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
51
Gle
ncoe A
lgeb
ra 1
Fin
d t
he v
alu
es o
f th
e t
hree t
rig
on
om
etr
ic r
ati
os f
or a
ng
le A
.
1.
77
85
2.
15
9
sin
A =
7
7
−
85 , c
os A
= 36
−
85 , t
an
A =
77
−
36
sin
A =
4
−
5 , c
os A
= 3
−
5 , t
an
A =
4
−
3
3.
10
24
4.
15
8
sin
A =
12
−
13 , c
os A
=
5
−
13 , t
an
A =
12
−
5
sin
A =
8
−
17 , c
os A
= 1
5
−
17 , t
an
A =
8
−
15
Use a
ca
lcu
lato
r t
o f
ind
th
e v
alu
e o
f ea
ch
trig
on
om
etr
ic r
ati
o t
o t
he
nea
rest
ten
-th
ou
sa
nd
th.
5. s
in 1
8°
0.3
090
6.
cos
68°
0.3
746
7. t
an
27°
0.5
095
8. c
os
60°
0.5
9.
tan
75°
3.7
321
10. s
in 9
° 0.1
564
So
lve e
ach
rig
ht
tria
ng
le.
Ro
un
d e
ach
sid
e l
en
gth
to
th
e n
ea
rest
ten
th.
11.
13
17°
12.
6
55°
∠A
= 7
3°,
AB
= 1
3.6
, A
C =
4.0
∠
B =
35°,
AB
= 1
0.5
, B
C =
8.6
Fin
d m
∠J
fo
r e
ach
rig
ht
tria
ng
le t
o t
he n
ea
rest
deg
ree.
13.
6
5
14.
19
11
40°
55°
10-8
Sk
ills
Pra
ctic
e
Tri
go
no
metr
ic R
ati
os
Answers (Lesson 10-8)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 10 A25 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
52
Gle
ncoe A
lgeb
ra 1
Fin
d t
he v
alu
es o
f th
e t
hree t
rig
on
om
etr
ic r
ati
os f
or a
ng
le A
.
1.
7297
2.
36
15
sin
A =
65
−
97 ,
co
s A
= 7
2
−
97 ,
tan
A =
65
−
72
sin
A =
36
−
39 ,
co
s A
= 1
5
−
39 ,
tan
A =
36
−
15
Use a
ca
lcu
lato
r t
o f
ind
th
e v
alu
e o
f ea
ch
trig
on
om
etr
ic r
ati
o t
o t
he n
ea
rest
ten
-th
ou
sa
nd
th.
3. t
an
26°
0.4
877
4. s
in 5
3°
0.7
986
5. c
os
81°
0.1
564
So
lve e
ach
rig
ht
tria
ng
le.
Ro
un
d e
ach
sid
e l
en
gth
to
th
e n
ea
rest
ten
th.
6.
67°
22
7.
9
29°
∠B
= 2
3°,
AB
= 2
3.9
, A
C =
9.3
∠
A =
61°,
AB
= 1
0.3
, B
C =
5.0
Fin
d m
∠J
fo
r e
ach
rig
ht
tria
ng
le t
o t
he n
ea
rest
deg
ree.
8.
11
5
9.
12
18
24°
42°
10. SU
RV
EY
ING
If
poin
t A
is
54 f
eet
from
th
e
tree,
an
d t
he a
ngle
betw
een
th
e g
rou
nd
at
poin
t A
an
d t
he t
op
of
the t
ree i
s 25°,
fin
d
the h
eig
ht h
of
the t
ree.
25.2
ft
10-8
Practi
ce
Tri
go
no
metr
ic R
ati
os
25°
54
ft
h
Lesson 10-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
10
53
Gle
ncoe A
lgeb
ra 1
10-8
Wo
rd
Pro
ble
m P
racti
ce
Tri
go
no
metr
ic R
ati
os
1. W
ASH
ING
TO
N M
ON
UM
EN
TJean
nie
is t
ryin
g t
o d
ete
rmin
e t
he h
eig
ht
of
the
Wash
ingto
n M
on
um
en
t. I
f p
oin
t A
is
765 f
eet
from
th
e m
on
um
en
t, a
nd
th
e
an
gle
betw
een
th
e g
rou
nd
an
d t
he t
op
of
the m
on
um
en
t at
poin
t A
is
36°,
fin
d t
he
heig
ht h
of
the m
on
um
en
t to
th
e
neare
st f
oot.
765 ft3
6°
h
2. A
IRPLA
NES
A
pil
ot
tak
es
off
fro
m a
run
way a
t an
an
gle
of
20º
an
d m
ain
tain
s
that
an
gle
un
til
it i
s at
its
cru
isin
g
alt
itu
de o
f 2500 f
eet.
Wh
at
hori
zon
tal
dis
tan
ce h
as
the p
lan
e t
ravele
d w
hen
it
reach
es
its
cru
isin
g a
ltit
ud
e?
3. TR
UC
K R
AM
PS
A
movin
g c
om
pan
y u
ses
an
11-f
oot-
lon
g r
am
p t
o u
nlo
ad
fu
rnit
ure
from
a t
ruck
. If
th
e b
ed
of
the t
ruck
is
3
feet
above t
he g
rou
nd
, w
hat
is t
he a
ngle
of
incl
ine o
f th
e r
am
p t
o t
he n
eare
st
degre
e?
4. SPEC
IAL T
RIA
NG
LES
W
hil
e
invest
igati
ng r
igh
t tr
ian
gle
KLM
,
Merc
ed
es
fin
ds
that
cos M
= s
in M
.
Wh
at
is t
he m
easu
re o
f an
gle
M?
5. TELEV
ISIO
NS
Tele
vis
ion
s are
com
mon
ly
sized
by m
easu
rin
g t
heir
dia
gon
al.
A
com
mon
siz
e f
or
wid
esc
reen
pla
sma T
Vs
is 4
2 i
nch
es.
42
’’h
h1
6 9
a
. A
wid
esc
reen
tele
vis
ion
has
a 1
6:9
asp
ect
rati
o,
that
is,
the s
creen
wid
th
is 1
6 −
9
tim
es
the s
creen
heig
ht.
Use
th
e
Pyth
agore
an
Th
eore
m t
o w
rite
an
equ
ati
on
an
d s
olv
e f
or
the h
eig
ht h
of
the t
ele
vis
ion
in
in
ches.
b
. Use
th
e i
nfo
rmati
on
fro
m p
art
a t
o
solv
e t
he r
igh
t tr
ian
gle
.
c.
Wh
at
wou
ld t
he m
easu
re o
f an
gle
A b
e
on
a s
tan
dard
tele
vis
ion
wit
h a
4:3
asp
ect
rati
o?
( 16 −
9
h) 2
+ h
2 =
42
2;
h =
20.6
in
.
wid
th =
36.6
in
., ∠
A = 2
9°,
∠B
= 6
1°
16°
45°
6869 f
t
556 f
t
37°
Answers (Lesson 10-8)
ERROR: undefined
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