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 11 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
11
3
Gle
ncoe A
lgeb
ra 1
An
tici
pati
on
Gu
ide
Rati
on
al
Exp
ressio
ns a
nd
Eq
uati
on
s
B
efo
re y
ou
beg
in C
ha
pte
r 1
1
•
R
ead
each
sta
tem
en
t.
•
D
eci
de w
heth
er
you
Agre
e (
A)
or
Dis
agre
e (
D)
wit
h t
he s
tate
men
t.
•
W
rite
A o
r D
in
th
e f
irst
colu
mn
OR
if
you
are
not
sure
wh
eth
er
you
agre
e o
r d
isagre
e,
wri
te N
S (
Not
Su
re).
Aft
er y
ou
com
ple
te C
ha
pte
r 1
1
•
R
ere
ad
each
sta
tem
en
t an
d c
om
ple
te t
he l
ast
colu
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 s
tate
men
ts c
han
ge f
rom
th
e f
irst
colu
mn
?
•
F
or
those
sta
tem
en
ts t
hat
you
mark
wit
h a
D,
use
a p
iece
of
pap
er
to w
rite
an
exam
ple
of
wh
y y
ou
dis
agre
e.
11 Ste
p 1
ST
EP
1A
, D
, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
Sin
ce a
dir
ect
vari
ati
on
can
be w
ritt
en
as
y =
kx,
an
in
vers
e
vari
ati
on
can
be w
ritt
en
as
y =
x
−
k .
D
2.
A r
ati
on
al
exp
ress
ion
is
an
alg
ebra
ic f
ract
ion
th
at
con
tain
sa r
ad
ical.
D
3.
To m
ult
iply
tw
o r
ati
on
al
exp
ress
ion
s, s
uch
as
2xy
2
−
3c
an
d 3
c 2
−
5y ,
mu
ltip
ly t
he n
um
era
tors
an
d t
he d
en
om
inato
rs.
A
4.
Wh
en
solv
ing p
roble
ms
involv
ing u
nit
s of
measu
re,
dim
en
sion
al
an
aly
sis
is t
he p
roce
ss o
f d
ete
rmin
ing t
he u
nit
s
of
the f
inal
an
swer
so t
hat
the u
nit
s ca
n b
e i
gn
ore
d w
hil
e
perf
orm
ing c
alc
ula
tion
s.D
5.
To d
ivid
e (
4x
2 +
12x)
by 2
x,
div
ide 4
x2 b
y 2
x a
nd
12x b
y 2
x.
A
6.
To f
ind
th
e s
um
of
2
a
−
(3a
- 4
) an
d
5
−
(3a
- 4
) , fi
rst
ad
d t
he
nu
mera
tors
an
d t
hen
th
e d
en
om
inato
rs.
D
7.
Th
e l
east
com
mon
den
om
inato
r of
two r
ati
on
al
exp
ress
ion
s
wil
l be t
he l
east
com
mon
mu
ltip
le o
f th
e d
en
om
inato
rs.
A
8.
A c
om
ple
x f
ract
ion
con
tain
s a f
ract
ion
in
its
nu
mera
tor
or
den
om
inato
r.A
9.
Th
e f
ract
ion
(a
−
b )
−
( c −
d ) c
an
be r
ew
ritt
en
as
ac
−
bd .
D
10.
Extr
an
eou
s so
luti
on
s are
solu
tion
s th
at
can
be e
lim
inate
d
beca
use
th
ey a
re e
xtr
em
ely
hig
h o
r lo
w.
D
Ste
p 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-1
Ch
ap
ter
11
5
Gle
ncoe A
lgeb
ra 1
Both
meth
od
s sh
ow
th
at
x2 =
8
−
3 w
hen
y =
18.
Exerc
ises
Dete
rm
ine w
heth
er e
ach
ta
ble
or e
qu
ati
on
rep
resen
ts a
n i
nverse o
r a
dir
ect
va
ria
tio
n.
Ex
pla
in.
1.
xy
36
510
816
12
24
2.
y =
6x
3.
xy =
15
Assu
me t
ha
t y v
arie
s i
nv
ersely
as x
. W
rit
e a
n i
nv
erse v
aria
tio
n e
qu
ati
on
th
at
rela
tes x
an
d y
. T
hen
so
lve.
4. If
y =
10 w
hen
x =
5,
5. I
f y =
8 w
hen
x =
-2,
fi
nd
y w
hen
x =
2.
xy =
50;
25
fin
d y
wh
en
x =
4.
xy =
-16; -
4
6. If
y =
100 w
hen
x =
120,
7. I
f y =
-16 w
hen
x =
4,
fin
d x
wh
en
y =
20.
xy =
12,0
00;
600
fin
d x
wh
en
y =
32.
xy =
-64;-
2
8. If
y =
-7.5
wh
en
x =
25,
fin
d y
wh
en
x =
5.
xy =
-187.5
; -
37.5
9. D
RIV
ING
T
he G
era
rdi
fam
ily c
an
tra
vel
to O
shk
osh
, W
isco
nsi
n,
from
Ch
icago,
Illi
nois
, in
4 h
ou
rs i
f th
ey d
rive a
n a
vera
ge o
f 45 m
iles
per
hou
r. H
ow
lon
g w
ou
ld i
t ta
ke t
hem
if
they i
ncr
ease
d t
heir
avera
ge s
peed
to 5
0 m
iles
per
hou
r? 3.6
h
10. G
EO
METR
Y F
or
a r
ect
an
gle
wit
h g
iven
are
a,
the w
idth
of
the r
ect
an
gle
vari
es
invers
ely
as
the l
en
gth
. If
th
e w
idth
of
the r
ect
an
gle
is
40 m
ete
rs w
hen
th
e l
en
gth
is
5 m
ete
rs,
fin
d
the w
idth
of
the r
ect
an
gle
wh
en
th
e l
en
gth
is
20 m
ete
rs.
10 m
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Invers
e V
ari
ati
on
Iden
tify
an
d U
se I
nvers
e V
ari
ati
on
s A
n i
nv
erse v
aria
tio
n i
s an
equ
ati
on
in
th
e
form
of
y =
k
−
x o
r xy =
k.
If t
wo p
oin
ts (
x1,
y1)
an
d (
x2,
y2)
are
solu
tion
s of
an
in
vers
e v
ari
ati
on
,
then
x1 ∙
y1 =
k a
nd
x2 ∙
y2 =
k.
Pro
du
ct
Ru
le f
or
Invers
e V
ari
ati
on
x1 ∙
y1 =
x2 ∙
y2
Fro
m t
he p
rod
uct
ru
le,
you
can
form
th
e p
rop
ort
ion
x1
−
x2
= y
1
−
y2
.
If
y v
arie
s i
nv
ersely
as x
an
d y
= 1
2 w
hen
x =
4,
fin
d x
wh
en
y =
18.
Meth
od
1 U
se t
he p
rod
uct
ru
le.
x1 ∙
y1 =
x2 ∙
y2
Pro
duct
rule
for
invers
e v
ariation
4 ∙
12
= x
2 ∙
18
x
1 =
4,
y1 =
12,
y2 =
18
4
8
−
18 =
x 2
Div
ide e
ach s
ide b
y 1
8.
8
−
3 =
x 2
Sim
plif
y.
Meth
od
2 U
se a
pro
port
ion
.
x
1
−
x 2 =
y 2
−
y 1
Pro
port
ion f
or
invers
e v
ariation
4
−
x 2 =
18
−
12
x1 =
4,
y1 =
12,
y2 =
18
48 =
18x
2
Cro
ss m
ultip
ly.
8
−
3 =
x2
Sim
plif
y.
11-1
Exam
ple
dir
ect
vari
ati
on
; o
f th
e f
orm
y =
kx
dir
ect
vari
ati
on
; o
f th
e f
orm
y =
kx
invers
e
vari
ati
on
; o
f th
e
form
xy =
k
Answers (Anticipation Guide and Lesson 11-1)
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 11 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
11
6
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Invers
e V
ari
ati
on
Gra
ph
In
vers
e V
ari
ati
on
s S
itu
ati
on
s in
wh
ich
th
e v
alu
es
of
y d
ecr
ease
as
the v
alu
es
of
x i
ncr
ease
are
exam
ple
s of
inv
erse v
aria
tio
n.
We s
ay t
hat
y v
ari
es
invers
ely
as
x,
or
y i
s in
vers
ely
pro
port
ion
al
to x
.
S
up
po
se y
ou
driv
e
200 m
iles w
ith
ou
t sto
pp
ing
. T
he t
ime
it t
ak
es t
o t
ra
vel
a d
ista
nce v
arie
s
inv
ersely
as t
he r
ate
at
wh
ich
yo
u
tra
vel.
Let
x =
sp
eed
in
mil
es p
er h
ou
r
an
d y
= t
ime i
n h
ou
rs.
Gra
ph
th
e
va
ria
tio
n.
Th
e e
qu
ati
on
xy =
200 c
an
be u
sed
to
rep
rese
nt
the s
itu
ati
on
. U
se v
ari
ou
s sp
eed
s to
mak
e a
table
.
x
y O20
40
60
30
20
10
G
ra
ph
an
in
verse
va
ria
tio
n i
n w
hic
h y
va
rie
s i
nv
ersely
as
x a
nd
y =
3 w
hen
x =
12.
Solv
e f
or
k.
xy =
k
Invers
e v
ariation e
quation
12(3
) =
k
x =
12 a
nd y
= 3
36 =
k
Sim
plif
y.
Ch
oose
valu
es
for
x a
nd
y,
wh
ich
have a
p
rod
uct
of
36.
x
y O12
24
24
12
Exerc
ises
Gra
ph
ea
ch
va
ria
tio
n i
f y v
arie
s i
nv
ersely
as x
.
1. y =
9 w
hen
x =
-3
2. y =
12 w
hen
x =
4
3. y =
-25 w
hen
x =
5
x
y
O24
12
-12
-24
-12
-24
12
24
x
y
O32
16
-16
-32
-16
-32
16
32
x
y
O50
-50
-100
100
100
50
-50
-100
4. y =
4 w
hen
x =
5
5. y =
-18 w
hen
x =
-9
6. y =
4.8
wh
en
x =
5.4
x
y
O20
10
-10
-20
-10
-20
10
20
x
y
O36
18
-18
-36
-18
-36
18
36
x
y
O
7.2
3.6
-3.6
-7.2
-3.6
-7.2
3.6
7.2
11-1
Exam
ple
1Exam
ple
2
xy
10
20
20
10
30
6.7
40
5
50
4
60
3.3
xy
−
6−
6
−
3−
12
−
2−
18
218
312
66
Invers
e V
ari
ati
on
Eq
uati
on
an e
quation o
f th
e f
orm
xy =
k,
where
k ≠
0
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-1
Ch
ap
ter
11
7
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Invers
e V
ari
ati
on
Dete
rm
ine w
heth
er e
ach
ta
ble
or e
qu
ati
on
rep
resen
ts a
n i
nverse o
r a
dir
ect
va
ria
tio
n. E
xp
lain
.
1.
xy
0.5
8
14
22
41
2.
xy =
2 −
3
3.
-2
x +
y =
0
Assu
me t
ha
t y v
arie
s i
nv
ersely
as x
. W
rit
e a
n i
nv
erse v
aria
tio
n e
qu
ati
on
th
at
rela
tes x
an
d y
. T
hen
gra
ph
th
e e
qu
ati
on
.
4. y
= 2
wh
en
x =
5
5. y
= -
6 w
hen
x =
-6
6. y
= -
4 w
hen
x =
-12
7. y
= 1
5 w
hen
x =
3
So
lve.
Assu
me t
ha
t y v
arie
s i
nv
ersely
as x
.
8. If
y =
4 w
hen
x =
8,
9. If
y =
-7 w
hen
x =
3,
fin
d y
wh
en
x =
2.
xy =
32;
16
fi
nd
y w
hen
x =
-3.
xy =
-21;
7
10. If
y =
-6 w
hen
x =
-2,
11. If
y =
-24 w
hen
x =
-3,
fi
nd
y w
hen
x =
4.
xy =
12;
3
fi
nd
x w
hen
y =
-6.
xy =
72; -
12
12. If
y =
15 w
hen
x =
1,
13. If
y =
48 w
hen
x =
-4,
fi
nd
x w
hen
y =
-3.
xy =
15; -
5
fi
nd
y w
hen
x =
6.
xy =
-192; -
32
14. If
y =
-4 w
hen
x =
1
−
2 ,
fin
d x
wh
en
y =
2.
xy =
-2; -
1
11-1
x
y
O8
-8
-16
16
16 8
-8
-16
x
y
O8
-8
-16
16
16 8
-8
-16
x
y
O10
-10
-20
20
20
10
-10
-20
x
y
O4
-4
-8
8
8 4
-4
-8
invers
e,
xy =
4
invers
e,
xy =
2 −
3
dir
ect,
y =
2x
xy =
10
xy =
36
xy =
48
xy =
45
Answers (Lesson 11-1)
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 11 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-1
Ch
ap
ter
11
9
Gle
ncoe A
lgeb
ra 1
1.PH
YSIC
AL S
CIE
NC
E T
he
illu
min
ati
on I
pro
du
ced
by a
lig
ht
sou
rce
vari
es
inver
sely
as
the
squ
are
of
the
dis
tan
ce d
from
th
e so
urc
e. T
he
illu
min
ati
on
pro
du
ced
5 f
eet
from
th
e li
gh
t so
urc
e is
80 f
oot-
can
dle
s.
Id2=
k
80(5
)2=
k
2000=
k
Fin
d t
he
illu
min
ati
on p
rod
uce
d 8
fee
t fr
om t
he
sam
e so
urc
e.
31.2
5 f
oo
t-can
dle
s
2. M
ON
EY
A f
orm
ula
call
ed t
he
Ru
le o
f 72 a
pp
roxim
ate
s h
ow f
ast
mon
ey w
ill
dou
ble
in
a s
avin
gs
acc
oun
t. I
t is
base
d
on t
he
rela
tion
th
at
the
nu
mber
of
yea
rs
it t
ak
es f
or m
oney
to
dou
ble
vari
es
inver
sely
as
the
an
nu
al
inte
rest
rate
. U
se t
he
info
rmati
on i
n t
he
table
to
wri
te
the
Ru
le o
f 72 f
orm
ula
. y
r =
72
3. ELEC
TR
ICIT
Y T
he
resi
stan
ce,
in o
hm
s,
of a
cer
tain
len
gth
of
elec
tric
wir
e vari
es
inver
sely
as
the
squ
are
of
the
dia
met
er
of t
he
wir
e. I
f a w
ire
0.0
4 c
enti
met
er i
n
dia
met
er h
as
a r
esis
tan
ce o
f 0.6
0 o
hm
, w
hat
is t
he
resi
stan
ce o
f a w
ire
of t
he
sam
e le
ngth
an
d m
ate
rial
that
is 0
.08
cen
tim
eter
s in
dia
met
er?
0.1
5 o
hm
4.B
USIN
ESS
In
th
e m
an
ufa
ctu
rin
g o
f a
cert
ain
dig
ital
cam
era,
the
cost
of
pro
du
cin
g t
he
cam
era v
ari
es i
nver
sely
as
the
nu
mber
pro
du
ced
. If
15,0
00 c
am
eras
are
pro
du
ced
, th
e co
st i
s $80 p
er u
nit
. G
rap
h t
he
rela
tion
ship
an
d l
abel
th
e p
oin
t th
at
rep
rese
nts
th
e co
st p
er u
nit
to
pro
du
ce 2
5,0
00 c
am
eras.
$48
5. SO
UN
D T
he
sou
nd
pro
du
ced
by a
str
ing
insi
de
a p
ian
o d
epen
ds
on i
ts l
ength
. T
he
freq
uen
cy o
f a v
ibra
tin
g s
trin
g v
ari
es
inver
sely
as
its
len
gth
.
a.
Wri
te a
n e
qu
ati
on t
hat
rep
rese
nts
th
e re
lati
onsh
ip b
etw
een
fre
qu
ency
f
an
d l
ength
.
Use
k f
or t
he
con
stan
t of
vari
ati
on.
b.
If y
ou h
ave
two
dif
fere
nt
len
gth
st
rin
gs,
wh
ich
on
e vib
rate
s m
ore
qu
ick
ly (
that
is,
wh
ich
str
ing h
as
a
gre
ate
r fr
equ
ency
)?
T
he s
ho
rter
str
ing
vib
rate
s
mo
re q
uic
kly
th
an
th
e l
on
ger
str
ing
.
c.
Su
pp
ose
a p
ian
o st
rin
g 2
fee
t lo
ng
vib
rate
s 300 c
ycl
es p
er s
econ
d.
Wh
at
wou
ld b
e th
e fr
equ
ency
of
a s
trin
g
4 f
eet
lon
g?
150 c
ycle
s p
er
seco
nd
Wo
rd
Pro
ble
m P
racti
ce
Invers
e V
ari
ati
on
11-1
Years
to D
ou
ble
Mo
ney
An
nu
al
Inte
rest
Rate
(perc
en
t)
18
4
14.4
5
12
6
10.2
97
Price per Unit ($)
200
300
100 0
Un
its
Pro
du
ced
(th
ou
san
ds)
10
20
30
y
x
25,000,48
f ×
ℓ =
k o
r f =
k
−
�
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
11
8
Gle
ncoe A
lgeb
ra 1
Practi
ce
Invers
e V
ari
ati
on
Dete
rm
ine w
heth
er e
ach
ta
ble
or e
qu
ati
on
rep
resen
ts a
n i
nverse o
r a
dir
ect
va
ria
tio
n.
Ex
pla
in.
1.
xy
0.2
540
0.5
20
25
81.2
5
2.
xy
-2
8
00
2-
8
4-
16
3.
y
−
x =
-3
4. y =
7
−
x
Asssu
me t
ha
t y v
arie
s i
nv
ersely
as x
. W
rit
e a
n i
nv
erse v
aria
tio
n e
qu
ati
on
th
at
rela
tes x
an
d y
. T
hen
gra
ph
th
e e
qu
ati
on
.
5. y =
-2 w
hen
x =
-12
6. y =
-6 w
hen
x =
-5
7.
y =
2.5
wh
en x
= 2
Writ
e a
n i
nv
erse v
aria
tio
n e
qu
ati
on
th
at
rela
tes x
an
d y
. A
ssu
me t
ha
t y v
arie
s
inv
ersely
as x
. T
hen
so
lve.
8. If
y =
124 w
hen
x =
12,
fin
d y
wh
en x
= -
24.
xy =
1488; -
62
9. If
y =
-8.5
wh
en x
= 6
, fi
nd
y w
hen
x =
-2.5
. xy =
-51;
20.4
10. If
y =
3.2
wh
en x
= -
5.5
, fi
nd
y w
hen
x =
6.4
. xy =
-17.6
; -
2.7
5
11. If
y =
0.6
wh
en x
= 7
.5,
fin
d y
wh
en x
= -
1.2
5.
xy =
4.5
; -
3.6
12. E
MPLO
YM
EN
T T
he
man
ager
of
a l
um
ber
sto
re s
ched
ule
s 6 e
mp
loyee
s to
tak
e in
ven
tory
in
an
8-h
our
wor
k p
erio
d.
Th
e m
an
ager
ass
um
es a
ll e
mp
loyee
s w
ork
at
the
sam
e ra
te.
a.
Su
pp
ose
2 e
mp
loyee
s ca
ll i
n s
ick
. H
ow m
an
y h
ours
wil
l 4 e
mp
loyee
s n
eed
to
tak
e in
ven
tory
? 12 h
b.
If t
he
dis
tric
t su
per
vis
or c
all
s in
an
d s
ays
she
nee
ds
the
inven
tory
fin
ish
ed i
n 6
hou
rs,
how
man
y e
mp
loyee
s sh
ould
th
e m
an
ager
ass
ign
to
tak
e in
ven
tory
? 8
13. TR
AV
EL J
esse
an
d J
oaqu
in c
an
dri
ve
to t
hei
r gra
nd
pare
nts
’ h
ome
in 3
hou
rs i
f th
ey
aver
age
50 m
iles
per
hou
r. S
ince
th
e ro
ad
bet
wee
n t
he
hom
es i
s w
ind
ing a
nd
m
oun
tain
ous,
th
eir
pare
nts
pre
fer
they
aver
age
bet
wee
n 4
0 a
nd
45 m
iles
per
hou
r.
How
lon
g w
ill
it t
ak
e to
dri
ve
to t
he
gra
nd
pare
nts
’ h
ome
at
the
red
uce
d s
pee
d?
betw
een
3 h
20 m
in a
nd
3 h
45 m
in
11-1
x
y
O24
12
-12
-24
-24
-12
12
24
x
y
Ox
y
O16 8
-8
-16
-8
-16
816
invers
e;
xy =
kd
irect;
y =
kx
dir
ect;
y =
kx
invers
e;
xy =
k
xy =
24
xy =
30
xy =
5
Answers (Lesson 11-1)
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 11 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
11
10
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
Dir
ect
or
Ind
irect
Vari
ati
on
Fil
l in
ea
ch
ta
ble
belo
w.
Th
en
writ
e i
nversely
, o
r d
irectl
y t
o c
om
ple
te e
ach
co
nclu
sio
n.
1.
�2
48
16
32
W4
44
4
4
A8
16
32
64
128
2.
Ho
urs
24
56
Sp
eed
55
55
55
55
Dis
tan
ce
110
220
275
330
F
or a
set
of
rect
an
gle
s w
ith
a w
idth
F
or a
car
travel
ing a
t 55 m
i/h
, th
e
of
4,
the
are
a v
ari
es
d
ista
nce
cov
ered
vari
es
as
the
len
gth
. as
the
hou
rs d
riven
.
3.
Oat
Bra
n 1
−
3 c
up
2
−
3 c
up
1 c
up
Wate
r1 c
up
2 c
up
3 c
up
Serv
ing
s1
23
4.
Ho
urs
of
Wo
rk128
128
128
Peo
ple
Wo
rkin
g
24
8
Serv
ing
s64
32
16
T
he
nu
mber
of
serv
ings
of o
at
bra
n
A
job
req
uir
es 1
28 h
ours
of
wor
k.
Th
e
vari
es
as
the
nu
mber
n
um
ber
of
hou
rs e
ach
per
son
wor
ks
of
cu
ps
of o
at
bra
n.
vari
es
as
the
nu
mber
of
peo
ple
wor
kin
g.
5.
Miles
100
100
100
100
Rate
20
25
50
100
Ho
urs
5
42
1
6.
b3
45
6
h10
10
10
10
A15
20
25
30
F
or a
100-m
ile
car
trip
, th
e ti
me
the
F
or a
set
of
righ
t tr
ian
gle
s w
ith
a h
eigh
t
tr
ip t
ak
es v
ari
es
as
the
of
10,
the
are
a v
ari
es
aver
age
rate
of
spee
d t
he
car
travel
s.
as
the
base
.
Use t
he t
ab
le a
t th
e r
igh
t.
7. x v
ari
es
as
y.
8. z v
ari
es
as
y.
9. x v
ari
es
as
z.
invers
ely
11-1
dir
ectl
yd
irectl
y
dir
ectl
y
dir
ectl
yinvers
ely
x1
1.5
22.5
3
y2
34
56
z60
40
30
24
20
invers
ely
invers
ely
dir
ectl
y
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-2
Ch
ap
ter
11
11
Gle
ncoe A
lgeb
ra 1
Iden
tify
Excl
ud
ed
Valu
es
Th
e fu
nct
ion
y =
10
−
x
is a
n e
xam
ple
of
a r
ati
on
al
fun
cti
on
.
Bec
au
se d
ivis
ion
by z
ero
is u
nd
efin
ed,
an
y v
alu
e of
a v
ari
able
th
at
resu
lts
in a
den
omin
ato
r
of z
ero
mu
st b
e ex
clu
ded
fro
m t
he
dom
ain
of
that
vari
able
. T
hes
e are
call
ed e
xclu
ded
va
lues o
f th
e ra
tion
al
fun
ctio
n.
S
tate
th
e e
xclu
ded
va
lue f
or e
ach
fu
ncti
on
.
Exerc
ises
Sta
te t
he e
xclu
ded
va
lue f
or e
ach
fu
ncti
on
.
1. y =
2
−
x x =
0
2. y =
1
−
x -
4 x =
4
3. y =
x -
3
−
x +
1 x =
-1
4. y =
4
−
x -
2 x =
2
5. y =
x
−
2x -
4 x =
2
6. y =
-
5
−
3x x =
0
7. y =
3x -
2
−
x +
3
x =
-3
8. y =
x -
1
−
5x +
10 x =
-2
9. y =
x +
1
−
x
x =
0
10. y =
x -
7
−
2x +
8 x =
-4
11. y =
x -
5
−
6x
x =
0
12. y =
x -
2
−
x +
11 x =
-11
13. y =
7
−
3x +
21 x =
-7
14. y =
3x -
4
−
x +
4
x =
-4
15. y =
x
−
7x -
35 x =
5
16. D
ININ
G M
ya a
nd
her
fri
end
s are
eati
ng a
t a r
esta
ura
nt.
Th
e to
tal
bil
l of
$36 i
s sp
lit
am
ong x
fri
end
s. T
he
am
oun
t ea
ch p
erso
n p
ays
y i
s giv
en b
y y
= 3
6
−
x ,
wh
ere
x i
s th
e n
um
ber
of
peo
ple
. G
rap
h t
he
fun
ctio
n.
11-2
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Rati
on
al
Fu
ncti
on
s
Exam
ple
a
. y =
3
−
x
Th
e d
enom
inato
r ca
nn
ot e
qu
al
zero
. T
he
excl
ud
ed v
alu
e is
x =
0.
b.
y =
4
−
x -
5
x -
5 =
0
Set
the d
enom
inato
r equal to
0.
x =
5
Add 5
to e
ach s
ide.
Th
e ex
clu
ded
valu
e is
x =
5.
Bill per Person ($)
4 08
12
16
20
24
28
32
36
Num
ber
of
Peo
ple
12
34
56
78
Answers (Lesson 11-1 and Lesson 11-2)
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 11 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
11
12
Gle
ncoe A
lgeb
ra 1
Iden
tify
an
d U
se A
sym
pto
tes
Beca
use
excl
ud
ed
vale
s are
un
defi
ned
, th
ey a
ffect
the g
rap
h o
f th
e f
un
ctio
n.
An
asy
mp
tote
is
a l
ine t
hat
the g
rap
h o
f a f
un
ctio
n a
pp
roach
es.
A r
ati
on
al
fun
ctio
n i
n t
he f
orm
y =
a −
x - b
+ c
has
a v
ert
ical
asy
mp
tote
at
the x
-valu
e t
hat
mak
es
the d
en
om
inato
r equ
al
zero
, x =
b.
It h
as
a h
ori
zon
tal
asy
mp
tote
at
y =
c.
Iden
tify
th
e a
sy
mp
tote
s o
f y =
1 −
x - 1
+ 2
. T
hen
gra
ph
th
e f
un
cti
on
.
Ste
p 1
Id
en
tify
an
d g
rap
h t
he a
sym
pto
tes
usi
ng d
ash
ed
lin
es.
vert
ical
asy
mp
tote
: x =
1
h
ori
zon
tal
asy
mp
tote
: y =
2
Ste
p 2
M
ak
e a
table
of
valu
es
an
d p
lot
the p
oin
ts.
Th
en
con
nect
th
em
.
x–1
02
3
y1.5
13
2.5
Exerc
ises
Iden
tify
th
e a
sy
mp
tote
s o
f ea
ch
fu
ncti
on
. T
hen
gra
ph
th
e f
un
cti
on
.
1. y = 3
−
x x =
0;
y =
0
2. y = -
2 −
x x =
0;
y =
0
3. y = 4
−
x +
1 x =
0;
y =
1
4. y = 2
−
x -
3 x =
0;
y =
3
5. y =
2 −
x +
1 x =
1;
y =
0
6. y = -
2 −
x - 3
x =
3;
y =
0
11-2
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Rati
on
al
Fu
ncti
on
s
Exam
ple
y
x
y=
+2
y=
2
x=
1
1
x-1
y
x
y
x
y
x
y
x
y
x
y
x
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-2
Ch
ap
ter
11
13
Gle
ncoe A
lgeb
ra 1
Sta
te t
he e
xclu
ded
va
lue f
or e
ach
fu
ncti
on
.
1. y =
6 −
x x =
0
2. y =
2 −
x - 2
x =
2
3. y =
x −
x + 6
x =
-6
4. y =
x - 3 −
x + 4
x =
-4
5. y =
3x - 5 −
x + 8
x =
-8
6. y =
-5 −
2x - 1
4 x =
7
7. y =
x −
3x
+ 2
1 x =
-7
8. y =
x - 1 −
9x
- 3
6 x =
4
9. y =
9 −
5x
+ 40
x =
-8
Iden
tify
th
e a
sy
mp
tote
s o
f ea
ch
fu
ncti
on
. T
hen
gra
ph
th
e f
un
cti
on
.
10.
y = 1
−
x
11. y = 3
−
x
12. y =
2 −
x +
1
x =
0,
y =
0
x =
0,
y =
0
x =
-1,
y =
0
13.
y =
3 −
x - 2
14. y =
2 −
x +
1 -
1
15. y =
1 −
x -
2 +
3
x =
2,
y =
0
x =
-1,
y =
-1
x =
2,
y =
3
11-2
Sk
ills
Pra
ctic
e
Rati
on
al
Fu
ncti
on
s
y
x
y
x
y
x
y
x
y
x
y
x
Answers (Lesson 11-2)
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 11 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
11
14
Gle
ncoe A
lgeb
ra 1
Sta
te t
he e
xclu
ded
va
lue f
or e
ach
fu
ncti
on
.
1. y =
-1
−
x x =
0
2. y =
3
−
x +
5 x =
-5
3. y =
2
x
−
x -
5 x =
5
4. y =
x -
1
−
12x +
36 x =
-3
5. y =
x +
1
−
2x +
3 x =
- 3
−
2
6. y =
1
−
5x -
2
x =
2
−
5
Iden
tify
th
e a
sy
mp
tote
s o
f ea
ch
fu
ncti
on
. T
hen
gra
ph
th
e f
un
cti
on
.
7. y =
1
−
x
8. y
= 3
−
x
9.
y =
2
−
x -
1
x
= 0
, y =
0
x =
0,
y =
0
x =
1,
y =
0
10. y =
2
−
x +
2
11. y =
1
−
x -
3 +
2
12. y =
2
−
x +
1 -
1
x =
-2,
y =
0
x =
3,
y =
2
x =
-1,
y =
-1
13. A
IR T
RA
VEL D
enver
, C
olor
ad
o, i
s lo
cate
d a
pp
roxim
ate
ly
1000 m
iles
fro
m I
nd
ian
ap
olis
, In
dia
na.
Th
e aver
age
spee
d o
f a
pla
ne
travel
ing b
etw
een
th
e tw
o ci
ties
is
giv
en b
y y
= 1
000
−
x
,
wh
ere
x i
s th
e to
tal
flig
ht
tim
e. G
rap
h t
he
fun
ctio
n.
11-2
Practi
ce
Rati
on
al
Fu
ncti
on
s
Average Speed (mph)
400
600
200 0
1
800
1000
Tota
l Fl
ight
Tim
e
23
45
y=1000
x
y
x
y
x
y
x
y
x
y
x
y
x
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-2
Ch
ap
ter
11
15
Gle
ncoe A
lgeb
ra 1
1. B
ULLET T
RA
INS
Th
e S
hin
kan
sen
, or
Jap
an
ese
bu
llet
tra
in n
etw
ork
, p
rovid
es
hig
h-s
pee
d g
rou
nd
tra
nsp
orta
tion
thro
ugh
out
Jap
an
. T
rain
s re
gu
larl
y
oper
ate
at
spee
ds
in e
xce
ss o
f 200
kil
omet
ers
per
hou
r. T
he
aver
age
spee
d
of a
bu
llet
tra
in t
ravel
ing b
etw
een
Tok
yo
an
d K
yot
o is
giv
en b
y y
=515
−x
, w
her
e x i
s
the
tota
l tr
avel
tim
e in
hou
rs.
Gra
ph
the
fun
ctio
n.
2. D
RIV
ING
Pet
er i
s d
rivin
g t
o h
is
gra
nd
pare
nts
’ h
ouse
40 m
iles
aw
ay.
Du
rin
g t
he
trip
, P
eter
mak
es a
30-m
inu
te
stop
for
lu
nch
. T
he
aver
age
spee
d o
f
Pet
er’s
tri
p i
s giv
en b
y y
=
40
− x +
0.5
, w
her
e
x i
s th
e to
tal
tim
e sp
ent
in t
he
car.
Wh
at
are
th
e asy
mp
tote
s of
th
e fu
nct
ion
?
x=
-0.5
, y
= 0
3. ER
RO
R A
NA
LY
SIS
Nic
olas
is g
rap
hin
g
the
equ
ati
on y
=
20
− x +
3 -
6an
d d
raw
s a
gra
ph
wit
h a
sym
pto
tes
at
y=
3 a
nd
x=
– 6
. E
xpla
in t
he
erro
r th
at
Nic
olas
made
in h
is g
rap
h.
Th
e a
sym
pto
tes
sh
ou
ld b
e x
= 3
, y
=–6.
11-2
Wo
rd
Pro
ble
m P
racti
ce
Rati
on
al
Fu
ncti
on
s
Average Speed (km/h)
100
150
50 0
1
200
300
250
Tim
e (h
ours
)
23
4
y=
515 x
4. U
SED
CA
RS
Wh
ile
rese
arc
hin
g c
ars
to
pu
rch
ase
on
lin
e, M
s. J
aco
bs
fou
nd
th
at
the
valu
e of
a u
sed
car
is i
nver
sely
p
rop
orti
onal
to t
he
age
of t
he
car.
Th
e aver
age
pri
ce o
f a u
sed
car
is g
iven
by
y =
17,9
00
− x +
1.2
+ 1
00,
wh
ere
x i
s th
e age
of
the
car.
Wh
at
are
th
e asy
mp
tote
s of
th
e fu
nct
ion
? E
xp
lain
wh
y x
= 0
ca
nn
ot b
e an
asy
mp
tote
.x
=-
1.2
, y
= 1
00;
An
asym
pto
te a
t x
= 0
wo
uld
giv
e y
, th
e c
ost
of
the c
ar,
an
in
fin
ite v
alu
e w
hen
th
e c
ar
is b
ran
d
new
. T
he a
sym
pto
te n
eed
s t
o b
e
locate
d a
t x
=a
, w
here
a<
0.
5. FA
MIL
Y R
EU
NIO
N T
he
Gau
det
fam
ily
is h
old
ing t
hei
r an
nu
al
reu
nio
n a
t W
atk
ins
Park
. It
cos
ts $
50 t
o get
a
per
mit
to
hol
d t
he
reu
nio
n a
t th
e p
ark
, an
d t
he
fam
ily i
s sp
end
ing $
8 p
er p
erso
n
on f
ood
. T
he
Gau
det
s h
ave
agre
ed t
o sp
lit
the
cost
of
the
even
t ev
enly
am
ong
all
th
ose
att
end
ing.
a.
Wri
te a
n e
qu
ati
on s
how
ing t
he
cost
p
er p
erso
n y
if
x p
eop
le a
tten
d t
he
reu
nio
n.
b.
Wh
at
are
th
e asy
mp
tote
s of
th
e eq
uati
on?
c.
Now
ass
um
e th
at
the
fam
ily w
an
ts t
o le
t a l
ong-l
ost
cou
sin
att
end
for
fre
e.
Rew
rite
th
e eq
uati
on t
o fi
nd
th
e n
ew
cost
per
payin
g p
erso
n y
.
y=
8+
58
− x -
1
d.
Wh
at
are
th
e asy
mp
tote
s fo
r th
e n
ew
equ
ati
on?
y =
8 +
5
0
−
x
x =
0,
y =
8
x =
1,
y =
8
Answers (Lesson 11-2)
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 11 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
11
16
Gle
ncoe A
lgeb
ra 1
Inequ
ali
ties
involv
ing r
ati
on
al
fun
ctio
ns
can
be g
rap
hed
mu
ch l
ike t
hose
in
volv
ing l
inear
fun
ctio
ns.
Gra
ph
y ≥
1 −
x .
Ste
p 1
P
lot
poin
ts a
nd
dra
w a
sm
ooth
soli
d c
urv
e.
Beca
use
th
e
inequ
ali
ty i
nvolv
es
a g
reate
r th
an
or
equ
al
to s
ign
, so
luti
on
s th
at
sati
sfy y
= 1
−
x w
ill
be a
part
of
the g
rap
h.
Ste
p 2
P
lot
the a
sym
pto
tes,
x =
0 a
nd
y =
0,
as
dash
ed
lin
es.
Ste
p 3
B
egin
test
ing v
alu
es.
A v
alu
e m
ust
be t
est
ed
betw
een
each
set
of
lin
es,
in
clu
din
g a
sym
pto
tes.
Reg
ion
1
Test
(–1,
1).
Th
is r
etu
rns
a t
rue v
alu
e f
or
th
e i
nequ
ali
ty.
Reg
ion
2
Test
(–1,
–0.5
). T
his
retu
rns
a t
rue v
alu
e
for
the i
nequ
ali
ty.
Reg
ion
3
Test
(–1,
–2).
Th
is r
etu
rns
a f
als
e v
alu
e f
or
th
e i
nequ
ali
ty.
Reg
ion
4
Test
(1,
2).
Th
is r
etu
rns
a t
rue v
alu
e f
or
th
e i
nequ
ali
ty.
Reg
ion
5
Test
(1,
0.5
). T
his
retu
rns
a f
als
e v
alu
e f
or
th
e i
nequ
ali
ty.
Reg
ion
6
Test
(1,
–1).
Th
is r
etu
rns
a t
rue v
alu
e f
or
th
e i
nequ
ali
ty.
Ste
p 4
S
had
e t
he r
egio
ns
wh
ere
th
e i
nequ
ali
ty i
s tr
ue.
Exerc
ises
Gra
ph
ea
ch
in
eq
ua
lity
.
1. y ≤
1 −
x + 1
2. y >
2 −
x
3. y ≤
1 −
x +
1 -
1
11-2
En
rich
men
t
Ineq
ualiti
es i
nvo
lvin
g R
ati
on
al
Fu
ncti
on
s
Exam
ple
y
x
y
x
y
x
y
x
y
x
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-3
Ch
ap
ter
11
17
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Sim
plify
ing
Rati
on
al
Exp
ressio
ns
Iden
tify
Excl
ud
ed
Valu
es
Beca
use
a r
ati
on
al
exp
ress
ion
in
volv
es
div
isio
n,
the d
en
om
inato
r ca
nn
ot
equ
al
zero
. A
ny
valu
e o
f th
e d
en
om
inato
r th
at
resu
lts
in d
ivis
ion
by z
ero
is
call
ed
an
ex
clu
ded
va
lue
of
the d
en
om
inato
r.
S
tate
th
e e
xclu
ded
va
lue o
f 4
m -
8 −
m +
2 .
Excl
ud
e t
he v
alu
es
for
wh
ich
m +
2 =
0.
m
+ 2
= 0
T
he d
enom
inato
r cannot
equal 0.
m
+ 2
- 2
= 0
- 2
S
ubtr
act
2 f
rom
each s
ide.
m
= -
2
Sim
plif
y.
Th
ere
fore
, m
can
not
equ
al -
2.
S
tate
th
e e
xclu
ded
va
lues o
f x
2 +
1 −
x 2 -
9 .
Excl
ud
e t
he v
alu
es
for
wh
ich
x2 -
9 =
0.
x2 -
9 =
0
The d
enom
inato
r cannot
equal 0.
(x
+ 3
)(x -
3) =
0
Facto
r.
x +
3 =
0 or
x -
3 =
0
Zero
Pro
duct
Pro
pert
y
=
-3
= 3
Th
ere
fore
, x
can
not
equ
al -
3 o
r 3.
Exerc
ises
Sta
te t
he e
xclu
ded
va
lues f
or e
ach
ra
tio
na
l ex
pressio
n.
1.
2b −
b2 -
8
√ #
8 , -
√ #
8
2. 1
2 -
a −
32 +
a -
32
3. x
2 -
2 −
x2 +
4
2, -
2
4.
m 2 -
4 −
2m
2 -
8
2, -
2
5. 2
n -
12 −
n 2 -
4
-
2,
2
6. 2
x +
18 −
x 2 -
16 -
4,
4
7.
x 2 -
4 −
x 2 +
4x +
4 -
2
8.
a -
1 −
a 2 +
5a
+ 6
-
3, -
2
9. k
2 -
2k
+ 1 −
k 2 +
4k +
3 -
3, -
1
10.
m 2 -
1 −
2 m
2 -
m -
1 - 1
−
2 ,
1
11.
25 -
n 2 −
n 2 -
4n
- 5
-
1,
5
12.
2 x 2 +
5x +
1
−
x 2 -
10
x +
16
2,
8
13. n
2 -
2n
- 3 −
n 2 +
4n
- 5
-
5,
1
14. y
2 -
y -
2 −
3 y 2 -
12
-2,
2
15.
k 2 +
2k -
3
−
k 2 -
20
k +
64
4,
16
16.
x 2 +
4x +
4
−
4 x 2 +
11
x -
3 -
3,
1 −
4
11-3
Rati
on
al
Exp
ressio
n
an a
lgebra
ic f
raction w
ith n
um
era
tor
and
denom
inato
r th
at
are
poly
nom
ials
Exam
ple
: x
2 +
1 −
y 2
Exam
ple
2Exam
ple
1
Answers (Lesson 11-2 and Lesson 11-3)
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 11 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
11
18
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Sim
plify
ing
Rati
on
al
Exp
ressio
ns
Sim
plify
Exp
ress
ion
s F
act
ori
ng p
oly
nom
ials
is
a u
sefu
l to
ol
for
sim
pli
fyin
g r
ati
on
al
exp
ress
ion
s. T
o s
imp
lify
a r
ati
on
al
exp
ress
ion
, fi
rst
fact
or
the n
um
era
tor
an
d d
en
om
inato
r.
Th
en
div
ide e
ach
by t
he g
reate
st c
om
mon
fact
or.
S
imp
lify
54 z 3
−
24yz .
54 z 3
−
24
yz =
(6z)
(9 z 2 )
−
(6z)
(4y)
The G
CF
of
the n
um
era
tor
and t
he d
enom
inato
r is
6z.
= 1
(6z)
(9 z 2 )
−
1 (6
z)(4
y)
D
ivid
e t
he n
um
era
tor
and d
enom
inato
r by 6
z.
= 9
z 2
−
4y
S
implif
y.
S
imp
lify
3x
- 9
−
x 2 -
5x
+ 6
. S
tate
th
e e
xclu
ded
va
lues o
f x.
3x -
9
−
x 2 -
5x +
6
=
3(x
- 3
) −
(x -
2)(
x
- 3
) F
acto
r.
=
3(x
- 3
) 1
−
(x
- 2
)(x -
3) 1
Div
ide b
y t
he G
CF
, x
- 3
.
=
3
−
x -
2
Sim
plif
y.
Excl
ud
e t
he v
alu
es
for
wh
ich
x2 -
5x +
6 =
0.
x
2 -
5x +
6
= 0
(x
- 2
)(x -
3)
= 0
x =
2
or
x =
3
Th
ere
fore
, x ≠
2 a
nd
x ≠
3.
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
Sta
te t
he e
xclu
ded
va
lues o
f th
e v
aria
ble
s.
1. 1
2a
b
−
a 2 b 2
1
2
−
ab ;
a ≠
0;
b ≠
0
2.
7 n
3
−
21 n
8
1
−
3 n
5 ;
n ≠
0
3.
x +
2
−
x 2 -
4
1
−
x -
2 ;
x ≠
-2 o
r 2
4.
m 2 -
4
−
m
2 +
6m
+ 8
m
- 2
−
m +
4 ;
m ≠
-4 o
r -
2
5.
2n
- 8
−
n 2 -
16
2
−
n +
4 ;
n ≠
-4 o
r 4
6. x
2 +
2x +
1
−
x 2 -
1
x
+ 1
−
x -
1 ;
x ≠
-1 o
r 1
7.
x 2 -
4
−
x 2 +
4x +
4
x
- 2
−
x +
2 ;
x ≠
-2
8. a
2 +
3a
+ 2
−
a 2 +
5a
+ 6
a
+ 1
−
a +
3 ;
a ≠
-3 o
r -
2
9.
k 2 -
1
−
k 2 +
4k +
3
k
- 1
−
k +
3 ;
k ≠
-3 o
r -
1
10. m
2 -
2m
+ 1
−
2 m
2 -
m -
1
m
- 1
−
2m
+ 1
; m
≠ -
1
−
2 o
r 1
11.
n 2 -
25
−
n 2 -
4n
- 5
n
+ 5
−
n +
1 ;
n ≠
-1 o
r 5
12. x
2 +
x -
6
−
2 x 2 -
8
x
+ 3
−
2x +
4 ;
x ≠
-2 o
r 2
13. n
2 +
7n
+ 1
2
−
n
2 +
2n
- 8
n
+ 3
−
n -
2 ;
n ≠
-4 o
r 2
14.
y 2 -
y -
2
−
y 2 -
10
y +
16
y
+ 1
−
y -
8 ;
y ≠
2 o
r 8
11-3
Exam
ple
1
Exam
ple
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-3
Ch
ap
ter
11
19
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Sim
plify
ing
Rati
on
al
Exp
ressio
ns
Sta
te t
he e
xclu
ded
va
lues f
or e
ach
ra
tio
na
l ex
pressio
n.
1.
2p
−
p -
7 7
2.
4n
+ 1
−
n+
4 -
4
3.
k +
2
−
k 2 -
4
-2,
2
4.
3x +
15
−
x 2 -
25
-5,
5
5.
y 2 -
9
−
y 2 +
3y -
18
-6,
3
6.
b 2 -
2b -
8
−
b 2 +
7b +
10
-5,
-2
Sim
pli
fy e
ach
ex
pressio
n.
Sta
te t
he e
xclu
ded
va
lues o
f th
e v
aria
ble
s.
7.
21bc
−
28 bc 2
3
−
4c ;
0,
0
8.
12 m
2 r
−
24 m
r 3
m
−
2 r 2
; 0
, 0
9. 1
6 x 3 y 2
−
36 x 5 y 3
4
−
9 x 2 y ;
0,
0
10. 8 a
2 b 3
−
40 a
3 b
b 2
−
5a ;
0,
0
11.
n +
6
−
3n
+ 1
8
1
−
3 ; -
6
12. 4
x -
4
−
4x +
4
x
– 1
−
x +
1 ; -
1
13. y
2 -
64
−
y +
8 y -
8;
-8
14. y
2 -
7y -
18
−
y -
9
y +
2;
9
15.
z +
1
−
z 2 -
1
1
−
z -
1 ; -
1,
1
16.
x +
6
−
x 2 +
2x -
24
1
−
x –
4 ;
-6,
4
17.
2d
+ 1
0
−
d
2 -
2d
- 3
5
2
−
d -
7 ; -
5,
7
18.
3h
- 9
−
h
2 -
7h
+ 1
2
3
−
h -
4 ; 3
, 4
19. t 2
+ 5
t +
6
−
t 2 +
6t
+ 8
t
+ 3
−
t +
4 ; -
4,
-2
20. a
2 +
3a
- 4
−
a 2 +
2a
- 8
a
- 1
−
a -
2 ; -
4,
2
21. x
2 +
10x +
24
−
x 2 -
2x -
24
x
+ 6
−
x -
6 ; -
4,
6
22.
b 2 -
6b
+ 9
−
b 2 -
9b
+ 1
8
b
- 3
−
b -
6 ; 3
, 6
11-3
Answers (Lesson 11-3)
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 11 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
11
20
Gle
ncoe A
lgeb
ra 1
Practi
ce
Sim
plify
ing
Rati
on
al
Exp
ressio
ns
Sta
te t
he e
xclu
ded
va
lues f
or e
ach
ra
tio
na
l ex
pressio
n.
1. 4
n -
28 −
n 2 -
49
-7,
7
2.
p 2 -
16 −
p 2 -
13
p +
36
4,
9
3. a
2 -
2a
- 1
5
−
a 2 +
8a
+ 1
5
-5, -
3
Sim
pli
fy e
ach
ex
pressio
n.
Sta
te t
he e
xclu
ded
va
lues o
f th
e v
aria
ble
s.
4.
12a −
48 a
3
1 −
4 a 2 ;
0
5.
6xy z 3 −
3 x 2 y 2 z
2 z 2 −
xy ;
0,
0,
0
6. 3
6 k
3 n
p 2 −
20 k
2 n
p 5
9k −
5 p
3 ;
0,
0,
0
7.
5 c 3
d 4 −
40 cd
2 +
5 c 4
d 2
c 2 d
2 −
8 +
c 3 ;
c:
0, -
2,
d:
0
8. p
2 -
8p
+ 1
2
−
p -
2
p -
6;
2
9. m
2 -
4m
- 1
2
−
m -
6
m
+ 2
; 6
10. m
+ 3 −
m 2 -
9
1 −
m -
3 ; -
3,
3
11.
2b
- 1
4 −
b 2 -
9b
+ 1
4
2 −
b -
2 ;
2,
7
12. x
2 -
7x +
10
−
x 2 -
2x -
15
x -
2 −
x +
3 ; -
3,
5
13. y
2 +
6y -
16
−
y 2 -
4y +
4
y +
8 −
y - 2
; 2
14. r 2
- 7
r +
6 −
r 2 +
6r -
7
r – 6 −
r +
7 ; -
7,
1
15.
t 2 -
81 −
t 2 -
12
t +
27
t +
9 −
t -
3 ;
3,
9
16.
r 2 +
r -
6 −
r 2 +
4r -
12
r +
3 −
r +
6 ; -
6,
2
17. 2
x 2 +
18
x +
36
−
3 x 2 -
3x -
36
2(x
+ 6
) −
3(x
- 4
) ; -
3,
4
18. 2
y 2 +
9y +
4
−
4 y 2 -
4y -
3
y +
4 −
2y -
3 ; - 1
−
2 ,
3 −
2
19. EN
TER
TA
INM
EN
T F
air
fiel
d H
igh
sp
ent
d d
olla
rs f
or r
efre
shm
ents
, d
ecor
ati
ons,
an
d
ad
ver
tisi
ng f
or a
dan
ce.
In a
dd
itio
n,
they
hir
ed a
ban
d f
or $
550.
a.
Wri
te a
n e
xp
ress
ion
th
at
rep
rese
nts
th
e co
st o
f th
e ban
d a
s a
550 −
d +
550
fract
ion
of
the
tota
l am
oun
t sp
ent
for
the
sch
ool
dan
ce.
b.
If d
is
$1650,
wh
at
per
cen
t of
th
e bu
dget
did
th
e ban
d a
ccou
nt
for?
25%
20. PH
YSIC
AL S
CIE
NC
E M
r. K
am
ink
si p
lan
s to
dis
lod
ge
a
tree
stu
mp
in
his
yard
by u
sin
g a
6-f
oot
bar
as
a l
ever
. H
e p
lace
s th
e bar
so t
hat
0.5
foo
t ex
ten
ds
from
th
e fu
lcru
m t
o th
e en
d o
f th
e bar
un
der
th
e tr
ee s
tum
p.
In
the
dia
gra
m,
b r
epre
sen
ts t
he
tota
l le
ngth
of
the
bar
an
d t
rep
rese
nts
th
e p
orti
on o
f th
e bar
bey
ond
th
e fu
lcru
m.
a.
Wri
te a
n e
qu
ati
on t
hat
can
be
use
d t
o ca
lcu
late
th
e
mec
han
ical
ad
van
tage.
b.
Wh
at
is t
he
mec
han
ical
ad
van
tage?
11
c.
If a
for
ce o
f 200 p
oun
ds
is a
pp
lied
to
the
end
of
the
lever
, w
hat
is t
he
forc
e p
lace
d o
n
the
tree
stu
mp
? 2200 l
b
b
fulc
rum
tree
stu
mp
t
11-3
MA
= b
- t −
t
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-3
Ch
ap
ter
11
21
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Sim
plify
ing
Rati
on
al
Exp
ressio
ns
1.PH
YSIC
AL S
CIE
NC
E P
ress
ure
is
equ
al
to
the
magn
itu
de
of a
for
ce d
ivid
ed b
y t
he
are
a o
ver
wh
ich
th
e fo
rce
act
s.
P=
F − A
Gabe
an
d S
hel
by e
ach
pu
sh o
pen
a d
oor
wit
h o
ne
han
d.
In o
rder
to
open
, th
e d
oor
requ
ires
20 p
oun
ds
of f
orce
. T
he
surf
ace
are
a o
f G
abe’
s h
an
d i
s 10 s
qu
are
in
ches
, an
d t
he
surf
ace
are
a o
f S
hel
by’s
han
d i
s 8 s
qu
are
in
ches
. W
hos
e h
an
d f
eels
th
e gre
ate
r p
ress
ure
?
Sh
elb
y’s
: 2
.5 l
b−
in 2 (vs
Gab
e’s
2 l
b− i
n 2 )
2. G
RA
PH
ING
Rec
all
th
at
the
slop
e of
a
lin
e is
a r
ati
o of
th
e ver
tica
l ch
an
ge
to
the
hor
izon
tal
chan
ge
in c
oord
inate
s fo
r tw
o giv
en p
oin
ts.
Wri
te a
rati
onal
exp
ress
ion
th
at
rep
rese
nts
th
e sl
ope
of
the
lin
e co
nta
inin
g t
he
poi
nts
at
(p,
r)
an
d (
7, -
3).
r +
3 −
p -
7
or
-3 -
r −
7 -
p
3. A
UTO
MO
BIL
ES
Th
e fo
rce
nee
ded
to
kee
p a
car
from
sk
idd
ing o
ut
of a
tu
rn o
n
a p
art
icu
lar
road
is
giv
en b
y t
he
form
ula
bel
ow.
Wh
at
forc
e is
req
uir
ed t
o k
eep
a
2000-p
oun
d c
ar
travel
ing a
t 50 m
iles
per
h
our
on a
cu
rve
wit
h r
ad
ius
of 7
50 f
eet
on t
he
road
? W
hat
valu
e of
r i
s ex
clu
ded
?
f=
0.0
672
w s 2 −
r
f =
for
ce i
n p
oun
ds
w
= w
eigh
t in
pou
nd
s
s
= s
pee
d i
n m
ph
r
= r
ad
ius
in f
eet
4
48 l
b,
r ≠
0
4.PA
CK
AG
ING
In
ord
er t
o sa
fely
sh
ip a
n
ew e
lect
ron
ic d
evic
e, t
he
dis
trib
uti
on
man
ager
at
Data
Pro
du
cts
Com
pan
y
det
erm
ines
th
at
the
pack
age
mu
st
con
tain
a c
erta
in a
mou
nt
of c
ush
ion
ing
on e
ach
sid
e of
th
e d
evic
e. T
he
dev
ice
is
shap
ed l
ike
a c
ube
wit
h s
ide
len
gth
x,
an
d s
ome
sid
es n
eed
mor
e cu
shio
nin
g
than
oth
ers
bec
au
se o
f th
e d
evic
e’s
des
ign
. T
he
vol
um
e of
a s
hip
pin
g
con
tain
er i
s re
pre
sen
ted
by t
he
exp
ress
ion
(x
2 +
6x +
8)(
x +
6).
Fin
d t
he
pol
yn
omia
l th
at
rep
rese
nts
th
e are
a o
f th
e to
p o
f th
e box
if
the
hei
gh
t of
th
e box
is
x +
2.
5. SC
HO
OL C
HO
ICE
Du
rin
g a
rec
ent
sch
ool
yea
r, t
he
rati
o of
pu
bli
c sc
hoo
l st
ud
ents
to
pri
vate
sch
ool
stu
den
ts i
n
the
Un
ited
Sta
tes
was
ap
pro
xim
ate
ly
7.6
to
1.
Th
e st
ud
ents
att
end
ing p
ubli
c sc
hoo
l ou
tnu
mber
ed t
hos
e att
end
ing
pri
vate
sch
ools
by 4
2,2
40,0
00.
a.
Wri
te a
rati
onal
exp
ress
ion
to
exp
ress
th
e ra
tio
of p
ubli
c sc
hoo
l st
ud
ents
to
x
pri
vate
sch
ool
stu
den
ts.
x +
42,2
40,0
00
−
x
b.
How
man
y s
tud
ents
att
end
ed p
rivate
sc
hoo
l?
6,4
00,0
00
11-3
x+ 2
x 2 +
10
x +
24
Answers (Lesson 11-3)
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 11 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
11
22
Gle
ncoe A
lgeb
ra 1
Sh
an
no
n’s
Ju
gg
lin
g T
heo
rem
Math
em
ati
cian
s lo
ok
at
vari
ou
s m
ath
em
ati
cal
ways
to r
ep
rese
nt
juggli
ng.
On
e w
ay t
hey
have f
ou
nd
to r
ep
rese
nt
juggli
ng i
s S
han
non
’s J
uggli
ng T
heore
m.
Sh
an
non
’s J
uggli
ng
Th
eore
m u
ses
the r
ati
on
al
equ
ati
on
f +
d −
v +
d =
b −
h
wh
ere
f i
s th
e f
ligh
t ti
me,
or
how
lon
g a
ball
is
in t
he a
ir,
d i
s th
e d
well
tim
e,
or
how
lon
g a
ball
is
in a
han
d,
v i
s th
e v
aca
nt
tim
e,
or
how
lon
g a
han
d i
s em
pty
, b i
s th
e n
um
ber
of
ball
s,
an
d h
is
the n
um
ber
of
han
ds
(eit
her
1 o
r 2 f
or
a r
eal-
life
sit
uati
on
, p
oss
ibly
more
for
a
com
pu
ter
sim
ula
tion
).
So,
giv
en
th
e v
alu
es
for
f, d
, v,
an
d h
, it
is
poss
ible
to d
ete
rmin
e t
he n
um
ber
of
ball
s bein
g
juggle
d.
If t
he f
ligh
t ti
me i
s 9 s
eco
nd
s, t
he d
well
tim
e i
s 3 s
eco
nd
s, t
he v
aca
nt
tim
e i
s 1
seco
nd
, an
d t
he n
um
ber
of
han
ds
is 2
, h
ow
man
y b
all
s are
bein
g j
uggle
d?
f +
d −
v +
d = b
−
h
Origin
al equation
9 +
3 −
1 +
3 = b
−
2
Repla
ce w
ith t
he v
alu
es g
iven.
12 −
4
= b
−
2
Sim
plif
y.
2
4 =
4b
Cro
ss m
ultip
ly.
6 =
b
Div
ide.
So,
the n
um
ber
of
ball
s bein
g j
uggle
d i
s 6.
Giv
en
th
e f
oll
ow
ing
in
form
ati
on
, d
ete
rm
ine t
he n
um
ber o
f b
all
s b
ein
g j
ug
gle
d.
1. fl
igh
t ti
me =
6 s
eco
nd
s, v
aca
nt
tim
e =
1 s
eco
nd
, d
well
tim
e =
1 s
eco
nd
, n
um
ber
of
han
ds =
27
2. fl
igh
t ti
me =
13 s
eco
nd
s, v
aca
nt
tim
e =
1 s
eco
nd
, d
well
tim
e =
5 s
eco
nd
s, n
um
ber
of
han
ds =
13
3. fl
igh
t ti
me =
4 s
eco
nd
s, v
aca
nt
tim
e =
1 s
eco
nd
, d
well
tim
e =
1 s
eco
nd
, n
um
ber
of
han
ds =
25
4. fl
igh
t ti
me =
16 s
eco
nd
s, v
aca
nt
tim
e =
1 s
eco
nd
, d
well
tim
e =
2 s
eco
nd
s, n
um
ber
of
han
ds =
212
5. fl
igh
t ti
me =
18 s
eco
nd
s, v
aca
nt
tim
e =
3 s
eco
nd
s,
dw
ell
tim
e =
2 s
eco
nd
s, n
um
ber
of
han
ds =
14
En
rich
men
t 11-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-4
Ch
ap
ter
11
23
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Mu
ltip
lyin
g a
nd
Div
idin
g R
ati
on
al
Exp
ressio
ns
Mu
ltip
ly R
ati
on
al
Exp
ress
ion
s T
o m
ult
iply
rati
on
al
exp
ress
ion
s, y
ou
mu
ltip
ly t
he
nu
mera
tors
an
d m
ult
iply
th
e d
en
om
inato
rs.
Th
en
sim
pli
fy.
F
ind
2 c 2 f
−
5a
b 2 ·
a 2 b
−
3cf .
2 c 2 f −
5a
b 2 ·
a 2 b −
3cf
= 2
a 2 b c 2 f −
15
a b 2 cf
Multip
ly.
= 1(a
bcf
)(2
ac) −
1(a
bcf
)(15
b)
Sim
plif
y.
= 2
ac −
15
b
Sim
plif
y.
F
ind
x 2 -
16
−
2x
+ 8
·
x +
4
−
x 2 +
8x
+ 1
6 .
x 2 -
16 −
2x +
8 ·
x +
4 −
x 2 +
8x +
16 = (x
- 4
)(x +
4)
−
2(x
+ 4
) ·
x +
4 −
(x +
4)(
x +
4)
Facto
r.
=
(x -
4)(
x +
4)
1
−
2(x
+ 4
) 1
·
x +
4 1
−
(x +
4)(
x +
4)
1
Sim
plif
y.
=
x -
4 −
2x +
8
M
ultip
ly.
Exerc
ises
Fin
d e
ach
pro
du
ct.
1. 6
ab −
a 2 b 2 ·
a 2 −
b 2
6a
−
b 3
2. m
p 2 −
3
·
4 −
mp
4p
−
3
3. x
+ 2 −
x -
4 ·
x -
4 −
x -
1
x +
2
−
x -
1
4.
m -
5 −
8
·
16 −
m -
5 2
5. 2
n -
8 −
n +
2 ·
2n
+ 4 −
n -
4
4
6.
x 2 -
64 −
2x +
16 ·
x +
8 −
x 2 +
16
x +
64
x -
8
−
2x +
16
7.
8x +
8 −
x 2 -
2x +
1 ·
x -
1 −
2x +
2
4
−
x -
1
8. a
2 -
25 −
a +
2 ·
a 2 -
4 −
a -
5
(a
+ 5
)(a -
2)
9.
x 2 +
6x +
8 −
2 x 2 +
9x +
4 ·
2 x 2 -
x -
1 −
x 2 -
3x +
2
x +
2
−
x -
2
10.
m 2 -
1 −
2 m
2 -
m -
1 ·
2m
+ 1 −
m 2 -
2m
+ 1
m +
1
−
(m -
1 ) 2
11.
n 2 -
1 −
n 2 -
7n
+ 1
0 ·
n
2 -
25 −
n2 +
6n
+ 5
n
- 1
−
n -
2
12. 3
p -
3r −
10
pr
·
20 p
2 r 2 −
p 2 -
r 2
6
pr
−
p +
r
13. a
2 +
7a
+ 1
2
−
a 2 +
2a
- 8
· a
2 +
3a
- 1
0
−
a 2 +
2a
- 8
14. v
2 -
4v -
21
−
3 v 2 +
6v
·
v 2 +
8v −
v 2 +
11
v +
24
v
- 7 −
3v +
6
(a
+ 3
)(a +
5)
−
(a -
2)(
a +
4)
11-4
Exam
ple
1
Exam
ple
2
Answers (Lesson 11-3 and Lesson 11-4)
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 11 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
11
24
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Mu
ltip
lyin
g a
nd
Div
idin
g R
ati
on
al
Exp
ressio
ns
Div
ide R
ati
on
al
Exp
ress
ion
s T
o d
ivid
e r
ati
on
al
exp
ress
ion
s, m
ult
iply
by t
he
reci
pro
cal
of
the d
ivis
or.
Th
en
sim
pli
fy.
F
ind
12 c 2 f
−
5 a
2 b
2
÷
c 2 f 2
−
10a
b .
12 c 2 f
−
5 a
2 f 2
÷
c 2 f 2
−
10a
b =
12 c 2 f
−
5 a
2 b 2 ×
10a
b
−
c 2 f 2
=
1 2 1 c 2 f
1
−
1 5 a a
2 b 2 b
×
2 10 1 a
b 1
−
1 c 2 f 2
f
=
24
−
abf
F
ind
x
2 +
6x
- 2
7
−
x 2 +
11x
+ 1
8
÷
x -
3
−
x 2 +
x -
2 .
x 2 +
6x -
27
−
x 2 +
11
x +
18 ÷
x -
3
−
x 2 +
x -
2
= x
2 +
6x -
27
−
x 2 +
11x +
18
× x
2 +
x -
2
−
x -
3
=
(x
+ 9
)(x -
3)
−
(x +
9)(
x +
2)
×
(x +
2)(
x -
1)
−
x -
3
=
1
(x +
9)(
x -
3)
1
−
1 (x
+ 9
)(x +
2)
1 ×
1 (
x +
2)(
x -
1)
−
x -
3 1
=
x -
1
Exerc
ises
Fin
d e
ach
qu
oti
en
t.
1. 1
2a
b
−
a 2 b 2
÷ b
−
a
12
−
b 2
2. n
−
4 ÷
n
−
p
p
−
4
3. 3
xy 2
−
8
÷ 6
xy y
−
16
4. m
- 5
−
8
÷ m
- 5
−
16
2
5. 2
n -
4
−
2n
÷
n 2 -
4
−
n
1
−
n +
2
6. y
2 -
36
−
y 2 -
49 ÷
y +
6
−
y +
7
y -
6
−
y -
7
7. x
2 -
5x +
6
−
5
÷
x -
3
−
15
3(x
- 2
) 8. a
2 b 3 c
−
3 r 2 t
÷ 6
a 2 bc
−
8r t
2 u
4 b
2 tu
−
9r
9. x
2 +
6x +
8
−
x 2 +
4x +
4
÷ x
+ 4
−
x +
2 1
10. m
2 -
49
−
m
÷
m
2 -
13m
+ 4
2
−
3 m
2
3
m(m
+ 7
) −
m
- 6
11. n
2 -
5n
+ 6
−
n 2 +
3n
÷
3 -
n
−
4n
+ 1
2
-4(n
- 2
) −
n
12. p
2 -
2p
r +
r 2
−
p
+ r
÷
p 2 -
r 2
−
p +
r
p -
r
−
p +
r
13. a
2 +
7a
+ 1
2
−
a
2 +
3a
- 1
0
÷ a
2 -
9
−
a 2 -
25
(a +
4)(
a -
5)
−
(a -
2)(
a -
3)
14.
a 2 -
9
−
2 a
2 +
13
a -
7
÷
a +
3
−
4 a
2 -
1
(a -
3)(
2a
+ 1
)
−
a +
7
11-4
Exam
ple
1
Exam
ple
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-4
Ch
ap
ter
11
25
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Mu
ltip
lyin
g a
nd
Div
idin
g R
ati
on
al
Exp
ressio
ns
Fin
d e
ach
pro
du
ct.
1.
14
−
c 2
· c
5
−
2c
7c
2
2.
3 m
2
−
2t
·
t 2
−
12
m 2 t
−
8
3. 2
a 2 b
−
b 2 c
· b
−
a
2a
−
c
4. 2
x 2 y
−
3 x 2 y ·
3xy
−
4y
x
−
2
5. 3
(4m
- 6
) −
18r
·
9 r 2
−
2(4
m -
6)
3r
−
4
6. 4
(n +
2)
−
n(n
- 2
) ·
n -
2
−
n +
2
4
−
n
7. (y
- 3
)(y +
3)
−
4
·
8
−
y +
3 2y
-6
8. (x
- 2
)(x +
2)
−
x(8
x +
3)
·
2(8
x +
3)
−
x -
2
2
(x +
2)
−
x
9. (a
- 7
)(a
+ 7
)
−
a(a
+ 5
)
· a
+ 5
−
a +
7
a -
7
−
a
10.
4(b
+ 4
) −
(b -
4)(
b -
3)
· b
- 3
−
b +
4
4
−
b -
4
Fin
d e
ach
qu
oti
en
t.
11. c3
−
d
3 ÷
d3
−
c3
c
6
−
d
6
12. x
3
−
y
2 ÷
x3
−
y
1
−
y
13. 6
a3
−
4f
2 ÷
2
a2
−
12f
2 9
a
14. 4
m3
−
rp
2
÷ 2
m
−
rp
2m
2
−
p
15. 3
b +
3
−
b +
2
÷ (
b +
1)
3
−
b +
2
16. x
- 5
−
x +
3 ÷
(x -
5)
1
−
x +
3
17. x
2 -
x -
12
−
6
÷
x +
3
−
x -
4
(x -
4)2
−
6
18. a
2 -
5a
- 6
−
3
÷
a -
6
−
a +
1 (a
+ 1
)2
−
3
19. m
2 +
2m
+ 1
−
10
m -
10
÷
m +
1
−
20
2
(m +
1)
−
m -
1
20. y
2 +
10
y +
25
−
3y -
9
÷
y +
5
−
y -
3
y +
5
−
3
21.
b +
4
−
b2 -
8b
+ 1
6
÷
2b +
8
−
b -
8
b
- 8
−
2(b
- 4
)2
22. 6
x +
6
−
x -
1
÷ x
2 +
3x +
2
−
2x -
2
12
−
x +
2
11-4
Answers (Lesson 11-4)
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 11 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
11
26
Gle
ncoe A
lgeb
ra 1
Practi
ce
Mu
ltip
lyin
g a
nd
Div
idin
g R
ati
on
al
Exp
ressio
ns
Fin
d e
ach
pro
du
ct.
1. 1
8 x 2
−
10 y 2 ·
15 y 3
−
24x
9xy
−
8
2.
24 rt
2
−
8 r 4
t 3 ·
12 r 3
t 2
−
36 r 2
t 1
−
r 2
3. (x
+ 2
)(x +
2)
−
8
·
72
−
(x
+ 2
)(x -
2)
9
(x +
2)
−
x -
2
4.
m
+ 7
−
(m
- 6
)(m
+ 2
) ·
(m -
6)(
m +
4)
−
(m
+ 7
)
m +
4
−
m +
2
5.
a -
4
−
a 2 -
a -
12 ·
a +
3
−
a -
6
1
−
a -
6
6.
4x +
8
−
x 2
·
x
−
x 2 -
5x -
14
4
−
x(x
- 7
)
7. n
2 +
10n
+ 1
6
−
5
n -
10
·
n
- 2
−
n 2 +
9n
+ 8
n +
2
−
5(n
+ 1
) 8.
3
y -
9
−
y 2 -
9y +
20
· y
2 -
8y +
16
−
y -
3
3
(y -
4)
−
y -
5
9. b
2 +
5b
+ 4
−
b 2 -
36
·
b 2 +
5b
- 6
−
b 2 +
2b
- 8
(b
+ 1
)(b
- 1
)
−
(b
- 6
)(b
- 2
) 10.
t 2
+ 6
t +
9
−
t 2
- 1
0t
+ 2
5
·
t 2 -
t -
20
−
t 2 +
7t
+ 1
2 t
+ 3
−
t -
5
11. 2
8a
2
−
7b
2
÷ 2
1a
3
−
35b
20
−
3ab
12.
mn
2p
3
−
x
4y
2
÷ m
np
2
−
x
3y
np
−
xy
13.
2a
−
a -
1 ÷
(a
+ 1
)
2a
−
(a
+ 1
)(a -
1)
14.
z2 -
16
−
3z
÷ (
z -
4)
z +
4
−
3z
15.
4y +
20
−
y -
3
÷
y +
5
−
2y -
6 8
16.
4x +
12
−
6x -
24 ÷
2x +
6
−
x +
3
x +
3
−
3(x
- 4
)
17.
b
2 +
2b -
8
−
b2 -
11b +
18 ÷
2
b -
8
−
2b -
18
b +
4
−
b -
4
18.
3x -
3
−
x2 -
6x +
9
÷
6x -
6
−
x2 -
5x +
6
x -
2
−
2(x
- 3
)
19.
a2 +
8a
+ 1
2
−
a
2 -
7a +
10 ÷
a2 -
4a -
12
−
a
2 +
3a -
10
2
0.
y2 +
6y -
7
−
y2 +
8y -
9
÷ y
2 +
9y +
14
−
y
2 +
7y -
18
(a
+ 6
)(a
+ 5
)
−
(a
- 6
)(a -
5)
y -
2
−
y +
2
21. B
IOLO
GY
Th
e h
eart
of
an
aver
age
per
son
pu
mp
s abou
t 9000 l
iter
s of
blo
od p
er d
ay.
How
man
y q
uart
s of
blo
od d
oes
the
hea
rt p
um
p p
er h
our?
(H
int:
On
e qu
art
is
equ
al
to
0.9
46 l
iter
.) R
oun
d t
o th
e n
eare
st w
hol
e n
um
ber
. 396 q
t/h
22. T
RA
FFIC
O
n S
atu
rday,
it t
ook
Ms.
Tor
res
24 m
inu
tes
to d
rive
20 m
iles
fro
m h
er h
ome
to h
er o
ffic
e. D
uri
ng F
rid
ay’s
ru
sh h
our,
it
took
75 m
inu
tes
to d
rive
the
sam
e d
ista
nce
.
a.
Wh
at
was
Ms.
Tor
res’
s aver
age
spee
d i
n m
iles
per
hou
r on
Satu
rday?
50 m
ph
b.
Wh
at
was
her
aver
age
spee
d i
n m
iles
per
hou
r on
Fri
day?
16 m
ph
11-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-4
Ch
ap
ter
11
27
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Mu
ltip
lyin
g a
nd
Div
idin
g R
ati
on
al
Exp
ressio
ns
1.JO
BS
Ros
a e
arn
ed $
26.2
5 f
or b
abysi
ttin
g
for
31 − 2 h
ours
. A
t th
is r
ate
, h
ow m
uch
wil
l sh
e ea
rn b
abysi
ttin
g f
or 5
hou
rs?
2. H
OM
EW
OR
K A
leja
nd
ro a
nd
An
der
wer
e w
ork
ing o
n t
he
foll
owin
g h
omew
ork
p
roble
m.
Fin
d n
- 1
0
−
n +
3
· 2
n +
6
−
n +
3 .
A
leja
nd
ro’s
Sol
uti
on
n -
10
−
n +
3
· 2
n +
6
−
n +
3
= 2
(n -
10)(
n -
3 ) 1
−−
(n +
3)(
n +
3 ) 1
= 2
n -
20
−
n +
3
A
nd
er’s
Sol
uti
on
n -
10
−
n +
3
· 2
n +
6
−
n +
3
= 2
(n -
10)(
n -
3 ) 1
−−
n
+ 3
1
= 2
n -
20
Is e
ith
er o
f th
em c
orre
ct?
Exp
lain
.
Ale
jan
dro
is c
orr
ect
becau
se h
e
mu
ltip
lied
den
om
inato
rs.
An
der
treate
d t
he d
en
om
inato
r like i
t w
as
an
ad
dit
ion
pro
ble
m.
3. G
EO
METR
Y S
up
pos
e th
e ra
tion
al
exp
ress
ion
5k
2m
3
−
2a
b r
epre
sen
ts t
he
are
a
of a
sec
tion
in
a t
iled
flo
or a
nd
2km
−
a
re
pre
sen
ts t
he
sect
ion
’s l
ength
. W
rite
a r
ati
onal
exp
ress
ion
to
rep
rese
nt
the
sect
ion
’s w
idth
.
4. TR
AV
EL H
elen
e tr
avel
s 800 m
iles
fro
m
Am
ari
llo
to B
row
nsv
ille
at
an
aver
age
spee
d o
f 40 m
iles
per
hou
r. S
he
mak
es
the
retu
rn t
rip
dri
vin
g a
n a
ver
age
of
60 m
iles
per
hou
r. W
hat
is t
he
aver
age
rate
for
th
e en
tire
tri
p?
(Hin
t: R
ecall
th
at
t =
d ÷
r.)
48 m
ph
5. M
AN
UFA
CTU
RIN
G I
nd
ia w
ork
s in
a
met
al
shop
an
d n
eed
s to
dri
ll e
qu
all
y
space
d h
oles
alo
ng a
str
ip o
f m
etal.
Th
e ce
nte
rs o
f th
e h
oles
on
th
e en
ds
of t
he
stri
p m
ust
be
exact
ly 1
in
ch f
rom
each
en
d.
Th
e re
main
ing h
oles
wil
l be
equ
all
y
space
d.
a.
If t
her
e are
x e
qu
all
y s
pace
d h
oles
, w
rite
an
exp
ress
ion
for
th
e n
um
ber
of
equ
al
space
s are
th
ere
bet
wee
n h
oles
.
x -
1
b.
Wri
te a
n e
xp
ress
ion
for
th
e d
ista
nce
bet
wee
n t
he
end
scr
ews
if t
he
len
gth
is
ℓ.
c.
Wri
te a
rati
onal
equ
ati
on t
hat
rep
rese
nts
th
e d
ista
nce
bet
wee
n t
he
hol
es o
n a
pie
ce o
f m
etal
that
is "
in
ches
lon
g a
nd
mu
st h
ave
x e
qu
all
y
space
d h
oles
.
d.
How
man
y h
oles
wil
l be
dri
lled
in
a
met
al
stri
p t
hat
is 6
fee
t lo
ng w
ith
a
dis
tan
ce o
f 7 i
nch
es b
etw
een
th
e ce
nte
rs o
f ea
ch s
crew
? 1
1
dd
dd
d
1
inch
1
inch
"
11-4 $37.5
0
5km
2
−
4b
! -
2
d =
! -
2
−
x -
1
Answers (Lesson 11-4)
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 11 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
11
28
Gle
ncoe A
lgeb
ra 1
Geo
metr
ic S
eri
es
A g
eom
etri
c se
ries
is
a s
um
of
the t
erm
s in
a g
eom
etri
c se
qu
ence
. E
ach
term
of
a g
eom
etr
ic
sequ
en
ce i
s fo
rmed
by m
ult
iply
ing t
he p
revio
us
term
by a
con
stan
t te
rm c
all
ed
th
e c
om
mon
rati
o.
1 +
1
−
2 +
1
−
4 +
1
−
8 ←
geom
etr
ic s
equ
en
ce w
here
th
e c
om
mon
rati
o i
s 1
−
2
Th
e s
um
of
a g
eom
etr
ic s
eri
es
can
be r
ep
rese
nte
d b
y t
he r
ati
on
al
exp
ress
ion
x0
(r
)n -
1
−
r -
1
, w
here
x0 i
s th
e f
irst
term
of
the s
eri
es,
r i
s th
e c
om
mon
rati
o,
an
d n
is
the
nu
mber o
f te
rms.
In t
he e
xam
ple
above,
1 +
1
−
2 +
1
−
4 +
1
−
8 =
1 ․
( 1
−
2 ) 4
- 1
−
1
−
2 -
1
or
15
−
8 .
You
can
ch
eck
th
is b
y e
nte
rin
g 1
+ 1
−
2 +
1
−
4 +
1
−
8 a
calc
ula
tor.
T
he r
esu
lt i
s th
e s
am
e.
Rew
rit
e e
ach
su
m a
s a
ra
tio
na
l ex
pressio
n a
nd
sim
pli
fy.
1. 9 +
3 +
1 +
1
−
3 +
1
−
9
121
−
9
2. 500 +
250 +
125 +
62 1
−
2
1875
−
2
3. 6 +
1 +
1
−
6 +
1
−
36
259
−
36
4. 100 +
20
+ 4
+ 4
−
5
624
−
5
5. 1000 +
100 +
10 +
1 +
1
−
10 +
1
−
100 +
1
−
100
1,1
11,1
11
−
1000
6. 55 +
5 +
5
−
11 +
5
−
121
7320
−
121
En
rich
men
t 11-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-4
Ch
ap
ter
11
29
Gle
ncoe A
lgeb
ra 1
Sp
read
sheet
Act
ivit
y
Revo
luti
on
s p
er
Min
ute
On
e o
f th
e c
hara
cteri
stic
s th
at
mak
es
a s
pre
ad
sheet
pow
erf
ul
is t
he a
bil
ity t
o r
eca
lcu
late
valu
es
in f
orm
ula
s au
tom
ati
call
y.
You
can
use
th
is a
bil
ity t
o i
nvest
igate
real-
worl
d
situ
ati
on
s.
Exerc
ises
Use t
he s
prea
dsh
eet
of
rev
olu
tio
ns p
er m
inu
te.
1. H
ow
is
the n
um
ber
of
revolu
tion
s aff
ect
ed
if
the s
peed
of
a w
heel
of
a g
iven
dia
mete
r is
dou
ble
d?
RP
M i
s c
ut
in h
alf
.
2. N
am
e t
wo w
ays
that
you
can
dou
ble
th
e R
PM
of
a b
icycl
e w
heel. D
ou
ble
th
e s
peed
o
r h
alv
e t
he d
iam
ete
r o
f th
e w
heel, k
eep
ing
th
e s
am
e s
peed
.
U
se a
sp
rea
dsh
eet
to i
nv
esti
ga
te t
he e
ffect
of
do
ub
lin
g
the d
iam
ete
r o
f a
tir
e o
n t
he n
um
ber o
f rev
olu
tio
ns t
he t
ire m
ak
es a
t
a g
iven
sp
eed
.
Use
dim
en
sion
al
an
aly
sis
to f
ind
th
e f
orm
ula
for
the r
evolu
tion
s p
er
min
ute
of
a t
ire w
ith
dia
mete
r of
x i
nch
es
traveli
ng a
t y m
iles
per
hou
r.
1 r
evolu
tion
−
π
· x
×
y
−
1
×
1
−
60 m
inu
tes
×
63,3
60
−
1
=
1056y r
evolu
tion
s
−−
π ·
x
min
ute
s
Ste
p 1
U
se C
olu
mn
A o
f th
e
spre
ad
sheet
for
dia
mete
r
of
the t
ire i
n i
nch
es.
Use
Colu
mn
B f
or
the s
peed
in
mil
es
per
hou
r.
Ste
p 2
C
olu
mn
C c
on
tain
s th
e
form
ula
for
the n
um
ber
of
rota
tion
s p
er
min
ute
.
Noti
ce t
hat
in E
xce
l, π
is
en
tere
d a
s P
I( )
.
Ste
p 3
C
hoose
valu
es
for
the d
iam
ete
r
an
d s
peed
an
d s
tud
y t
he r
esu
lts
show
n i
n t
he s
pre
ad
sheet.
To
com
pare
th
e r
evolu
tion
s p
er
min
ute
for
dou
ble
d d
iam
ete
rs,
keep
th
e s
peed
con
stan
t
an
d c
han
ge t
he d
iam
ete
rs.
It a
pp
ears
th
at
wh
en
th
e
dia
mete
r is
dou
ble
d,
the
nu
mber
of
revolu
tion
s p
er
min
ute
is
halv
ed
.
A
1 3 4 5 62
BC
Dia
mete
r (i
n.)
Sp
eed
(m
ph
)R
PM
=(1
056*B
2)/
(A2*P
I())
=(1
056*B
3)/
(A3*P
I())
=(1
056*B
4)/
(A4*P
I())
=(1
056*B
5)/
(A5*P
I())
Sh
eet
1S
heet
2S
heet
3
A
1 3 4 5 62
BC
Dia
mete
r (i
n.)
Sp
eed
(m
ph
)R
PM
18487.4
4
9243.7
2
4621.8
6
2310.9
3
1 2 4 8
55
55
55
55
Sh
eet
1S
heet
2S
heet
3
11-4
Exam
ple
1
Answers (Lesson 11-4)
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 11 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
11
30
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Div
idin
g P
oly
no
mia
ls
Div
ide P
oly
no
mia
ls b
y M
on
om
ials
T
o d
ivid
e a
poly
nom
ial
by a
mon
om
ial,
div
ide
each
term
of
the p
oly
nom
ial
by t
he m
on
om
ial.
F
ind
(4r
2 -
12r) ÷
(2r).
(4r2
- 1
2r)
÷ 2
r = 4
r2 -
12
r −
2r
=
4r2
−
2r -
12r −
2r
Div
ide e
ach t
erm
.
= 2r4r2 −
12r - 1
2r 6
−
2r 1
S
implif
y.
=
2r -
6
Sim
plif
y.
F
ind
(3x
2 -
8x +
4) ÷
(4x).
(3x
2 -
8x +
4) ÷
4x =
3x
2 -
8x +
4
−
4x
=
3x
2
−
4x -
8x −
4x +
4 −
4x
=
3x4 3
x2
−
4x -
8x −
4x +
4 −
4x
=
3
x −
4 -
2 +
1 −
x
Exerc
ises
Fin
d e
ach
qu
oti
en
t.
1. (x
3 +
2x
2 -
x) ÷
x x
2 +
2x -
1
2. (2
x3 +
12x
2 -
8x) ÷
(2x)
x2 +
6x -
4
3. (x
2 +
3x -
4) ÷
x x
2 +
3 -
4 −
x
4. (4
m2 +
6m
- 8
) ÷
(2
m2)
2 +
3 −
m -
4 −
m2
5. (3
x3 +
15
x2 -
21x) ÷
(3x)
x2 +
5x -
7
6. (8
m2p
2 +
4m
p -
8p
) ÷
p 8m
2p
+ 4
m -
8
7. (8
y4
+ 1
6y
2 -
4) ÷
(4
y2) 2
y2 +
4 -
1 −
y2
8. (1
6x
4y
2+
24xy +
5) ÷
(xy) 16
x3y +
24 +
5 −
xy
9. 1
5x
2 -
25
x +
30
−
5
3
x2 -
5x +
6
10. 1
0a
2b
+ 1
2a
b -
8b
−−
2a
5ab
+ 6
b -
4b −
a
11. 6
x3 +
9x
2 +
9
−
3x
2
x2 +
3x +
3 −
x
12. m
2 -
12
m +
42
−
3m
2
1
−
3 -
4 −
m +
14 −
m2
13. m
2p
2 -
5m
p +
6
−
m2p
2
1 -
5 −
mp +
6 −
m2p
2
14.
p2 -
4p
r +
6r2
−
pr
p
−
r -
4 +
6r −
p
15. 6
a2b
2 -
8a
b +
12
−−
2a
2
3
b2 -
4b −
a +
6 −
a2
16. 2
x2y
3 -
4x
2y
2 -
8xy
−−
2a
2b
2
xy
2 -
2xy -
4
17. 9
x2y
2z -
2xyz +
12x
−−
xy
18.
2a
3b
3 +
8a
2b
2 -
10a
b +
12
−−
2a
2b
2
9
xyz -
2z +
12 −
y
ab
+ 4
-
5 −
ab +
6 −
a2b
2
11-5
Exam
ple
1Exam
ple
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-5
Ch
ap
ter
11
31
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Div
idin
g P
oly
no
mia
ls
Div
ide P
oly
no
mia
ls b
y B
ino
mia
ls
To d
ivid
e a
poly
nom
ial
by a
bin
om
ial,
fact
or
the
div
iden
d i
f p
oss
ible
an
d d
ivid
e b
oth
div
iden
d a
nd
div
isor
by t
he G
CF
. If
th
e p
oly
nom
ial
can
not
be f
act
ore
d,
use
lon
g d
ivis
ion
.
F
ind
(x
2 +
7x +
10) ÷
(x +
3).
Ste
p 1
D
ivid
e t
he f
irst
term
of
the d
ivid
en
d,
x2 b
y t
he f
irst
term
of
the d
ivis
or,
x.
x
x +
3 # $$$$
$$$$$$$$$$
$$$$$$$$$$
$$$$$$$$$$
$$$$$$$$$$
$$$$$$$$$
x2 +
7x +
10
(-
) x
2 +
3x
Multip
ly x
and x
+ 3
.
4x
Subtr
act.
Ste
p 2
B
rin
g d
ow
n t
he n
ext
term
, 10.
Div
ide t
he f
irst
term
of
4x +
10 b
y x
.
x +
4
x +
3 # $$$$
$$$$$$$$$$
$$$$$$$$$$
$$$$$$$$$$
$$$$$$$$$$
$$$$$$$$$
x2 +
7x +
10
x
2 +
3x
4x +
10
(-
) 4
x +
12
M
ultip
ly 4
and x
+ 3
.
-
2
Subtr
act.
Th
e q
uoti
en
t is
x +
4 w
ith
rem
ain
der -
2.
Th
e q
uoti
en
t ca
n b
e w
ritt
en
as
x +
4 +
-
2 −
x +
3 .
Exerc
ises
Fin
d e
ach
qu
oti
en
t.
1. (b
2 -
5b +
6) ÷
(b -
2)
b -
3
2. (x
2 -
x -
6) ÷
(x -
3)
x +
2
3. (x
2 +
3x -
4) ÷
(x -
1)
x +
4
4. (m
2 +
2m
- 8
) ÷
(m
+ 4
) m
- 2
5. (x
2 +
5x +
6) ÷
(x +
2)
x +
3
6. (m
2 +
4m
+ 4
) ÷
(m
+ 2
) m
+ 2
7. (2
y2 +
5y +
2) ÷
( y
+ 2
) 2y +
1
8. (8
y2 -
15y -
2) ÷
( y
- 2
) 8y +
1
9. 8
x2 -
6x -
9
−
4x +
3
2
x -
3
10. m
2 -
5m
- 6
−
m -
6
m
+ 1
11. x
3 +
1 −
x -
2
x2 +
2x +
4 +
9 −
x -
2
12. 6
m3 +
11
m2 +
4m
+ 3
5
−−
2m
+ 5
3
m2 -
2m
+ 7
13.
6a
2 +
7a
+ 5
−
2a
+ 5
3
a -
4 +
25 −
2a +
5
14. 8
p3 +
27 −
2p
+ 3
4
p2 -
6p
+ 9
11-5
Exam
ple
Answers (Lesson 11-5)
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 11 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
11
32
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Div
idin
g P
oly
no
mia
ls
Fin
d e
ach
qu
oti
en
t.
1. (2
0x
2 +
12x) ÷
4x 5
x +
3
2. (1
8n
2 +
6n
) ÷
3n
6
n +
2
3. (b
2 -
12b
+ 5
) ÷
2b
b
−
2 -
6 +
5 −
2b
4. (8
r2 +
5r -
20) ÷
4r
2r +
5 −
4 -
5 −
r
5. 1
2p
3r2
+ 1
8p
2r -
6p
r −−
6p
2r
2
pr +
3 -
1 −
p
6. 1
5k
2u
- 1
0ku
+ 2
5u
2
−−
5ku
3
k -
2 +
5u −
k
7. (x
2 -
5x -
6) ÷
(x -
6)
x +
1
8. (a
2 -
10a
+ 1
6) ÷
(a
- 2
) a
- 8
9. (n
2 -
n -
20) ÷
(n
+ 4
) n
- 5
10. ( y
2 +
4y -
21) ÷
( y
- 3
) y +
7
11. (h
2 -
6h
+ 9
) ÷
(h
- 2
) h
- 4
+
1 −
h -
2
12. (b
2 +
5b
- 2
) ÷
(b
+ 6
) b
- 1
+
4 −
b +
6
13. ( y
2 +
6y +
1) ÷
( y
+ 2
) y +
4 -
7 −
y +
2
14. (m
2 -
2m
- 5
) ÷
(m
- 3
) m
+ 1
-
2 −
m -
3
15. 2
c2 -
5c -
3
−
2c +
1
c -
3
16.
2r2
+ 6
r -
20
−
2r -
4
r +
5
17. x
3 -
3x
2 -
6x -
20
−−
x -
5
x
2 +
2x +
4
18. p
3 -
4p
2 +
p +
6
−
p -
2
p
2 -
2p
- 3
19. n
3 -
6n
- 2 −
n +
1
n
2 -
n -
5 +
3 −
n +
1
20. y
3 -
y2 -
40 −
y -
4
y
2 +
3y +
12 +
8 −
y -
4
11-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-5
Ch
ap
ter
11
33
Gle
ncoe A
lgeb
ra 1
Practi
ce
Div
idin
g P
oly
no
mia
ls
Fin
d e
ach
qu
oti
en
t.
1. (6
q2 -
18q
- 9
) ÷
9q
2. (y
2 +
6y +
2) ÷
3y
3. 1
2a
2b -
3a
b2 +
42a
b
−−
6a
2b
2
q −
3 -
2 -
1 −
q
y −
3 +
2 +
2 −
3y
2 -
b −
2a +
7 −
a
4. 2
m3p
2 +
56
mp
- 4
m2p
3
−−
8m
3p
5. (x
2 -
3x -
40) ÷
(x +
5)
6. (3
m2 -
20m
+ 1
2) ÷
(m
- 6
)
p
−
4 +
7 −
m2 -
p
2
−
2m
x -
8
3m
- 2
7. (a
2 +
5a
+ 2
0) ÷
(a
- 3
)
8. (x
2 -
3x -
2) ÷
(x +
7)
9. (t
2 +
9t +
28) ÷
(t +
3)
a +
8 +
44 −
a -
3
x -
10 +
68 −
x +
7
t +
6 +
10 −
t +
3
10. (n
2 -
9n
+ 2
5) ÷
(n
- 4
)
11.
6r2
- 5
r -
56
−
3r +
8
12.
20w
2 +
39w
+ 1
8
−−
5w
+ 6
n
- 5
+
5 −
n -
4
2r -
7
4w
+ 3
13. (x
3 +
2x
2 -
16) ÷
(x -
2)
14. (t
3 -
11t -
6) ÷
(t +
3)
x
2 +
4x +
8
t2
- 3
t -
2
15. x
3 +
6x
2 +
3x +
1
−−
x -
2
16. 6
d3 +
d2 -
2d
+ 1
7
−−
2d
+ 3
x
2 +
8x +
19 +
39 −
x -
2
3d
2 -
4d
+ 5
+
2 −
2d
+ 3
17. 2
k3 +
7k
2 -
7
−
2k -
3
18. 9
y3 -
y -
1 −
3y +
2
k
2 +
2k
- 3
+
2 −
2k +
3
3y
2 -
2y +
1 -
3 −
3y +
2
19. LA
ND
SC
APIN
G Joce
lyn
is
desi
gn
ing a
bed
for
cact
us
speci
men
s at
a b
ota
nic
al
gard
en
. T
he t
ota
l are
a c
an
be m
od
ele
d b
y t
he e
xp
ress
ion
2x
2 +
7x +
3,
wh
ere
x i
s in
feet.
a.
Su
pp
ose
in
on
e d
esi
gn
th
e l
en
gth
of
the c
act
us
bed
is
4x,
an
d i
n a
noth
er,
th
e l
en
gth
is
2x +
1.
Wh
at
are
th
e w
idth
s of
the t
wo d
esi
gn
s?
b.
If x
= 3
feet,
wh
at
wil
l be t
he d
imen
sion
s of
the c
act
us
bed
in
each
of
the d
esi
gn
s?12 f
t b
y 3
.5 f
t; 7
ft
by 6
ft
20. FU
RN
ITU
RE
T
eri
is
up
hols
teri
ng t
he s
eats
of
fou
r ch
air
s an
d a
ben
ch.
Sh
e n
eed
s 1
−
4
squ
are
yard
of
fabri
c fo
r each
ch
air
, an
d 1
−
2 s
qu
are
yard
for
the b
en
ch.
If t
he f
abri
c at
the s
tore
is
45 i
nch
es
wid
e,
how
man
y y
ard
s of
fabri
c w
ill
Teri
need
to c
over
the c
hair
s
an
d t
he b
en
ch i
f th
ere
is
no w
ast
e?
11-5
x −
2 +
7 −
4 +
3 −
4x ;
x +
3
1 1
−
5 y
d
Answers (Lesson 11-5)
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 11 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
11
34
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Div
idin
g P
oly
no
mia
ls
1.TEC
HN
OLO
GY
T
he s
urf
ace
are
a (
in
squ
are
mil
lim
ete
rs)
of
a r
ect
an
gu
lar
com
pu
ter
mic
roch
ip i
s re
pre
sen
ted
by t
he
exp
ress
ion
x2 -
12x +
35,
wh
ere
x i
s th
e
nu
mber
of
circ
uit
s. I
f th
e w
idth
of
the
chip
is
x -
5 m
illi
mete
rs,
wri
te a
p
oly
nom
ial
that
rep
rese
nts
th
e l
en
gth
.
2. H
OM
EW
OR
K Y
ou
r cl
ass
mate
Ava
wri
tes
her
an
swer
to a
hom
ew
ork
p
roble
m o
n t
he c
halk
board
. S
he h
as
si
mp
lifi
ed
6
x2 -
12
x −
6
as
x2 -
12
x.
Is t
his
co
rrect
? If
not,
wh
at
is t
he c
orr
ect
si
mp
lifi
cati
on
? T
his
is n
ot
co
rrect.
S
he f
org
ot
to f
acto
r 6 f
rom
th
e
–12x t
erm
. T
he c
orr
ect
an
sw
er
s
ho
uld
be 6
(x2 -
2x) −
6
=
x2 -
2x.
3. C
IVIL
EN
GIN
EER
ING
S
up
pose
5400 t
on
s of
con
crete
cost
s (5
00 +
d)
doll
ars
. W
rite
a f
orm
ula
th
at
giv
es
the c
ost
C o
f t
ton
s
of
con
crete
.
4.SH
IPPIN
G T
he O
vers
eas
Sh
ipp
ing
Com
pan
y l
oad
s ca
rgo i
nto
a c
on
tain
er
to
be s
hip
ped
aro
un
d t
he w
orl
d.
Th
e v
olu
me
of
their
sh
ipp
ing c
on
tain
ers
is
dete
rmin
ed
by t
he f
oll
ow
ing e
qu
ati
on
.
x3+
21
x2+
99x+
135
Th
e c
on
tain
er’
s h
eig
ht
is x
+ 3
. W
rite
an
exp
ress
ion
th
at
rep
rese
nts
th
e a
rea o
f th
e
base
of
the s
hip
pin
g c
on
tain
er.
x
2 +
18
x +
45
5.C
IVIL
EN
GIN
EER
ING
G
reen
shie
ld’s
F
orm
ula
can
be u
sed
to d
ete
rmin
e t
he
am
ou
nt
of
tim
e a
tra
ffic
lig
ht
at
an
in
ters
ect
ion
sh
ou
ld r
em
ain
gre
en
.
G=
2.1
n+
3.7
G
= g
reen
tim
e i
n s
eco
nd
s
n
= a
vera
ge n
um
ber
of
veh
icle
s tr
aveli
ng
in e
ach
lan
e p
er
ligh
t cy
cle
W
rite
a s
imp
lifi
ed
exp
ress
ion
to
rep
rese
nt
the a
vera
ge g
reen
lig
ht
tim
e
p
er
veh
icle
.
6. SO
LID
GEO
METR
Y T
he s
urf
ace
are
a o
f a r
igh
t cy
lin
der
is g
iven
by t
he f
orm
ula
S
= 2π
r2 +
2π
rh
.
a.
Wri
te a
sim
pli
fied
rati
on
al
exp
ress
ion
th
at
rep
rese
nts
th
e r
ati
o o
f th
e
surf
ace
are
a t
o t
he c
ircu
mfe
ren
ce o
f th
e c
yli
nd
er.
r +
h −
1
b.
Wri
te a
sim
pli
fied
rati
on
al
exp
ress
ion
th
at
rep
rese
nts
th
e r
ati
o o
f th
e
surf
ace
are
a t
o t
he a
rea o
f th
e b
ase
.
2 +
2h −
r
11-5 x –
7 m
m
5
00t +
dt −
5400
2.1
+ 3
.7 −
n
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-5
Ch
ap
ter
11
35
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Syn
theti
c D
ivis
ion
You
can
div
ide a
poly
nom
ial
such
as
3x
3 -
4x
2 -
3x -
2 b
y a
bin
om
ial
such
as
x -
3 b
y
a p
roce
ss c
all
ed
sy
nth
eti
c d
ivis
ion
. C
om
pare
th
e p
roce
ss w
ith
lon
g d
ivis
ion
in
th
e
foll
ow
ing e
xp
lan
ati
on
.
D
ivid
e (
3x 3 -
4x 2 -
3x -
2)
by
(x -
3)
usin
g s
yn
theti
c d
ivis
ion
.
1. S
how
th
e c
oeff
icie
nts
of
the t
erm
s in
d
esc
en
din
g o
rder.
2. T
he d
ivis
or
is x
- 3
. S
ince
3 i
s to
be
subtr
act
ed
, w
rite
3 i
n t
he c
orn
er
.
3. B
rin
g d
ow
n t
he f
irst
coeff
icie
nt,
3.
4. M
ult
iply
. 3 .
3 =
9
5. A
dd
. -
4 +
9 =
5
6. M
ult
iply
. 3 .
5 =
15
7. A
dd
. -
3 +
15 =
12
8. M
ult
iply
. 3 .
12 =
36
9. A
dd
. -
2 +
36
= 3
4
Ch
eck
U
se l
on
g d
ivis
ion
.
3x
2 +
5x +
12
x -
3 ! """""
""""""""""
""""""""""
""""""""""
""""""""""
""""""""""
""""""""""
""""""""""
"
3x
3 -
4x
2 -
3x -
2
3x
3 -
9x
2
5
x2 -
3
x
5
x2 -
15x
12x -
2
12
x -
36
34
Th
e r
esu
lt i
s 3
x2 +
5x +
12 +
34
−
x -
3 .
Div
ide b
y u
sin
g s
yn
theti
c d
ivis
ion
. C
heck
yo
ur r
esu
lt u
sin
g l
on
g d
ivis
ion
.
1. (x
3 +
6x
2 +
3x +
1)
÷ (
x -
2)
2. (x
3 -
3x
2 -
6x -
20)
÷ (
x -
5)
x
2 +
8x +
19 +
39 −
x -
2
x
2 +
2x +
4
3. (2
x3 -
5x +
1)
÷ (
x +
1)
4. (3
x3 -
7x
2 +
4)
÷ (
x -
2)
2
x2 -
2x -
3 +
4 −
x +
1
3x
2 +
x -
2
5. (x
3 +
2x
2 -
x +
4)
÷ (
x +
3)
6. (x
3 +
4x
2 -
3x -
11)
÷ (
x -
4)
x
2 -
x +
2 -
2 −
x +
3
x
2 +
8x +
29 +
105 −
x -
4
3
3
-4
-3
-2
9
15
36
3
5
12
34
3x
2 +
5x +
12,
rem
ain
der
34
11-5
Exam
ple
Answers (Lesson 11-5)
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 11 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
11
36
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Ad
din
g a
nd
Su
btr
acti
ng
Rati
on
al
Exp
ressio
ns
Ad
d a
nd
Su
btr
act
Rati
on
al
Exp
ress
ion
s w
ith
Lik
e D
en
om
inato
rs
To a
dd
ra
tion
al
exp
ress
ion
s w
ith
lik
e d
en
om
inato
rs,
ad
d t
he n
um
era
tors
an
d t
hen
wri
te t
he s
um
over
the c
om
mon
den
om
inato
r. T
o s
ubtr
act
fra
ctio
ns
wit
h l
ike d
en
om
inato
rs,
subtr
act
th
e
nu
mera
tors
. If
poss
ible
, si
mp
lify
th
e r
esu
ltin
g r
ati
on
al
exp
ress
ion
.
F
ind
5n
−
15
+ 7n
−
15 .
5n
−
15 +
7n
−
15 =
5n
+ 7
n
−
15
A
dd t
he n
um
era
tors
.
=
12n
−
5
S
implif
y.
=
12n
−
15 5
4n
D
ivid
e b
y 3
.
=
4n
−
5
Sim
plif
y.
F
ind
3x
+ 2
−
x -
2
-
4x
−
x -
2 .
3x +
2
−
x -
2
-
4x
−
x -
2 =
3x +
2 -
4x
−
x -
2
The c
om
mon
denom
inato
r is
x -
2.
=
2 -
x
−
x -
2
Subtr
act.
=
-1(x
- 2
) −
x -
2
2 -
x =
-1(x
- 2
)
=
-1(x
- 2
) −
x -
2
=
-1
−
1
Sim
plif
y.
=
-1
Exerc
ises
Fin
d e
ach
su
m o
r d
ifferen
ce.
1. 3
−
a +
4
−
a 7
−
a
2. x
2
−
8
+ x
−
8 x
2 +
x
−
8
3. 5
x
−
9
- x
−
9 4
x
−
9
4. 1
1x
−
15
y -
x
−
15y 2
x
−
3y
5. 2
a -
4
−
a -
4
+
-a
−
a -
4 1
6.
m +
1
−
2m
- 1
+ 3
m -
3
−
2m
- 1
2
7. y
+ 7
−
y +
6 -
1
−
y +
6 1
8. 3
y +
5
−
5
- 2
y
−
5
y +
5
−
5
9. x
+ 1
−
x -
2 +
x -
5
−
x -
2 2
10.
5a
−
3b
2 +
10
a
−
3b
2
5a
−
b2
11. x
2 +
x
−
x
- x
2 +
5x
−
x
-
4
12. 5
a +
2
−
a2
- 4
a +
2
−
a2
1
−
a
13. 3
x +
2
−
x +
2
+ x
+ 6
−
x +
2 4
14. a
- 4
−
a +
1 +
a +
6
−
a +
1 2
11-6
Exam
ple
1Exam
ple
2
1 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-6
Ch
ap
ter
11
37
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Ad
din
g a
nd
Su
btr
acti
ng
Rati
on
al
Exp
ressio
ns
Ad
d a
nd
Su
btr
act
Rati
on
al
Exp
ress
ion
s w
ith
Un
like D
en
om
inato
rs
Ad
din
g
or
subtr
act
ing r
ati
on
al
exp
ress
ion
s w
ith
un
lik
e d
en
om
inato
rs i
s si
mil
ar
to a
dd
ing a
nd
su
btr
act
ing f
ract
ion
s w
ith
un
lik
e d
en
om
inato
rs.
Ad
din
g a
nd
Su
btr
acti
ng
Rati
on
al
Exp
ressio
ns
Ste
p 1
F
ind t
he L
CD
of
the e
xpre
ssio
ns.
Ste
p 2
C
hange e
ach e
xpre
ssio
n into
an e
quiv
ale
nt
expre
ssio
n w
ith t
he L
CD
as
the d
enom
inato
r.
Ste
p 3
A
dd o
r subtr
act
just
as w
ith e
xpre
ssio
ns w
ith lik
e d
enom
inato
rs.
Ste
p 4
S
implif
y if
necessary
.
F
ind
n +
3
−
n
+ 8n
- 4
−
4n
.
Fact
or
each
den
om
inato
r.
n
= n
4n
= 4
. n
L
CD
= 4
n
Sin
ce t
he d
en
om
inato
r of
8n
- 4
−
4n
is
alr
ead
y
4n
, on
ly n
+ 3
−
n
need
s to
be r
en
am
ed
.
n +
3
−
n
+ 8
n -
4
−
4n
= 4
(n +
3)
−
4n
+ 8
n -
4
−
4n
=
4n
+ 1
2
−
4n
+ 8
n -
4
−
4n
=
12n
+ 8
−
4n
=
3n
+ 2
−
n
F
ind
3x
−
x2 -
4x -
1
−
x -
4 .
3
x
−
x2 -
4x -
1
−
x -
4 =
3x
−
x(x
- 4
) -
1
−
x -
4
=
3
x
−
x(x
- 4
) -
1
−
x -
4 ·
x
−
x
=
3
x
−
x(x
- 4
) -
x
−
x(x
- 4
)
=
2
x
−
x(x
- 4
)
=
2
−
x -
4
Exerc
ises
Fin
d e
ach
su
m o
r d
ifferen
ce.
1. 1
−
a +
7
−
3a 1
0
−
3a
2.
1
−
6x +
3
−
8 4
+ 9
x
−
24
x
3. 5
−
9
x -
1
−
x2 5
x -
9
−
9x
2
4.
6
−
x2 -
3
−
x3 6
x -
3
−
x3
5.
8
−
4a
2 +
6
−
3a 2
+ 2
a
−
a2
6.
4
−
h +
1 +
2
−
h +
2
6h
+ 1
0
−
(h
+ 1
)(h
+ 2
)
7.
y
−
y -
3 -
3
−
y +
3
y
2 +
9
−
(y
- 3
)(y +
3)
8.
y
−
y -
7 -
y +
3
−
y2 -
4y -
21 y
- 1
−
y -
7
9.
a
−
a +
4 +
4
−
a -
4
a
2 +
16
−
(a
+ 4
)(a -
4)
10.
6
−
3(m
+ 1
) +
2
−
3(m
- 1
)
8m
- 4
−
3(m
+ 1
)(m
- 1
)
11.
4
−
x -
2y -
2
−
x +
2y
2x +
12y
−
(x +
2y)(
x -
2y)
12.
a
- 6
b
−
2a
2 -
5a
b +
2b
2 -
7
−
a -
2b
-
13a
+ b
−
(2a
- b
)(a
- 2
b)
13.
y +
2
−
y2 +
5y +
6 +
2 -
y
−
y2 +
y -
6 0
14.
q
−
q2 -
16 +
q
+ 1
−
q2 +
5q
+ 4
2q
- 4
−
(q
- 4
)(q
+ 4
)
11-6
Exam
ple
1Exam
ple
2
Facto
r th
e
denom
inato
r.
The L
CD
is
x(x
- 4
).
1 ·
x =
x
Subtr
act
num
era
tors
.
Sim
plif
y.
Answers (Lesson 11-6)
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 11 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
11
38
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Ad
din
g a
nd
Su
btr
acti
ng
Rati
on
al
Exp
ressio
ns
Fin
d e
ach
su
m o
r d
iffe
ren
ce.
1. 2
y
−
5
+ y
−
5
3y
−
5
2. 4
r −
9
+ 5
r −
9
r
3. t
+ 3
−
7
- t −
7 3
−
7
4. c
+ 8 −
4
- c +
6 −
4
1
−
2
5. x
+ 2 −
3
+ x
+ 5 −
3
2
x +
7
−
3
6. g
+ 2 −
4
+ g
- 8 −
4
g
- 3
−
2
7.
x −
x -
1 -
1 −
x -
1
1
8.
3
r −
r +
3 -
r −
r +
3
2
r −
r
+ 3
Fin
d t
he L
CM
of
ea
ch
pa
ir o
f p
oly
no
mia
ls.
9.
4x
2y,
12xy
2 1
2x
2y
2
10.
n +
2,
n -
3 (
n +
2)(
n -
3)
11. 2
r -
1,
r +
4 (
2r
- 1
)(r
+ 4
) 12.
t +
4,
4t +
16 4
(t +
4)
Fin
d e
ach
su
m o
r d
iffe
ren
ce.
13. 5
−
4r -
2 −
r2
5r
- 8
−
4r2
14.
5x −
3y
2 -
2x −
9y
15
x -
2xy
−
9y
2
15.
x −
x +
2 -
4 −
x -
1
x2 -
5x -
8
−
(x +
2)(
x -
1)
16.
d -
1 −
d -
2 -
3 −
d +
5
d
2 +
d +
1
−
(d -
2)(
d +
5)
17.
b −
b -
1 +
2 −
b -
4
b
2 -
2b
- 2
−
(b -
1)(
b -
4)
18.
k −
k -
5 +
k -
1 −
k +
5
2k
2 -
k +
5
−
(k -
5)(
k +
5)
19. 3
x +
15 −
x2 -
25 +
x −
x +
5
x2 -
2x +
15
−
(x +
5)(
x -
5)
20.
x -
3 −
x2 -
4x +
4 +
x +
2 −
x -
2
x2 +
x -
7
−
(x -
2)2
11-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-6
Ch
ap
ter
11
39
Gle
ncoe A
lgeb
ra 1
Practi
ce
Ad
din
g a
nd
Su
btr
acti
ng
Rati
on
al
Exp
ressio
ns
Fin
d e
ach
su
m o
r d
iffe
ren
ce.
1. n
−
8 +
3n −
8
2. 7
u −
16 +
5u −
16
3. w
+ 9 −
9
+ w
+ 4 −
9
n
−
2
3u
−
4
2w
+ 1
3
−
9
4. x
- 6 −
2
- x
- 7 −
2
5. n
+ 1
4 −
5
- n
- 1
4 −
5
6
.
6 −
c -
1 -
-
2 −
c -
1
1
−
2
28
−
5
8
−
c -
1
7. x
- 5 −
x +
2 +
-
2 −
x +
2
8. r +
5 −
r -
5 +
2r -
1 −
r -
5
9. 4
p +
14 −
p +
4
+ 2
p +
10 −
p +
4
x -
7
−
x +
2
3r
+ 4
−
r -
5
6
Fin
d t
he L
CM
of
ea
ch
pa
ir o
f p
oly
no
mia
ls.
10. 3
a3b
2,
18a
b3
11. w
- 4
, w
+ 2
12. 5
d -
20,
d -
4
1
8a
3b
3
(w
- 4
)(w
+ 2
) 5
(d -
4)
13. 6
p +
1,
p -
1
14. x
2 +
5x +
4,
(x +
1)2
15. m
2 +
3m
- 1
0,
m2 -
4
(
6p
+ 1
)(p
- 1
) (
x +
4)(
x +
1)2
(
m +
5)(
m -
2)(
m +
2)
Fin
d e
ach
su
m o
r d
iffe
ren
ce.
16. 6
p −
5x
2 -
2p −
3x
18
p -
10
xp
−
15
x2
17. m
+ 4 −
m -
3 -
2 −
m -
6
m
2 -
4m
- 1
8
−
(m -
3)(
m -
6)
18.
y +
3 −
y2 -
16 +
3y -
2 −
y2 +
8y +
16
4y
2 -
7y +
20
−
(y +
4)2
(y -
4)
19.
p +
1 −
p2 +
3p
- 4
+
p −
p +
4
p
2 +
1
−
(p
+ 4
)(p
- 1
)
20.
t +
3 −
t2 -
3t -
10 -
4t -
8 −
t2 -
10
t +
25
21.
4y −
y2 -
y -
6 -
3y +
3 −
y2 -
4
-3t2
- 2
t +
1
−
(t +
2)(
t -
5)2
y
2 -
2y +
9
−
−
(y
- 3
)(y +
2)(
y -
2)
22. SER
VIC
E M
em
bers
of
the n
inth
gra
de c
lass
at
Pin
e R
idge H
igh
Sch
ool
are
org
an
izin
g
into
serv
ice g
rou
ps.
Wh
at
is t
he m
inim
um
nu
mber
of
stu
den
ts w
ho m
ust
part
icip
ate
for
all
stu
den
ts t
o b
e d
ivid
ed
in
to g
rou
ps
of
4,
6,
or
9 s
tud
en
ts w
ith
no o
ne l
eft
ou
t? 36
23. G
EO
METR
Y F
ind
an
exp
ress
ion
for
the p
eri
mete
r of
rect
an
gle
AB
CD
. U
se t
he f
orm
ula
P =
2" +
2w
.
4(4
a +
3b
) −
2a +
b
11-6
5a+
4b
2a+
bB
A
CD
3a+
2b
2a+
b
Answers (Lesson 11-6)
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 11 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
11
40
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Rati
on
al
Exp
ressio
ns w
ith
Un
like D
en
om
inato
rs
1.TEX
AS
Of
the
254 c
oun
ties
in
Tex
as,
4 a
re l
arg
er t
han
6000 s
qu
are
mil
es.
An
oth
er 2
1 c
oun
ties
are
sm
all
er t
han
300 s
qu
are
mil
es.
Wh
at
fract
ion
of
the
cou
nti
es a
re 3
00 t
o 6000 s
qu
are
mil
es
in s
ize?
2. S
WIM
MIN
G P
ower
Poo
ls i
nst
all
s sw
imm
ing p
ools
. T
o d
eter
min
e th
e ap
pro
pri
ate
siz
e of
poo
l fo
r a y
ard
, th
ey
mea
sure
th
e le
ngth
of
the
yard
in
met
ers
an
d c
all
th
at
valu
e x.
Th
e le
ngth
an
d
wid
th o
f th
e p
ool
are
calc
ula
ted
wit
h t
he
dia
gra
m b
elow
. W
rite
an
exp
ress
ion
in
si
mp
lest
for
m f
or t
he
per
imet
er o
f a
rect
an
gu
lar
poo
l fo
r th
e giv
en v
ari
able
d
imen
sion
s.
m x 4
m2x 5
3. EG
YPTIA
N F
RA
CTIO
NS
An
cien
t E
gyp
tian
s u
sed
on
ly u
nit
fra
ctio
ns,
wh
ich
are
fra
ctio
ns
in t
he
form
1
−
n .
Th
eir
math
emati
cal
not
ati
on o
nly
all
owed
for
a
nu
mer
ato
r of
1.
Wh
en t
hey
nee
ded
to
exp
ress
a f
ract
ion
wit
h a
nu
mer
ato
r ot
her
th
an
1,
they
wro
te i
t as
a s
um
of
un
it f
ract
ion
s. A
n e
xam
ple
is
show
n
bel
ow.
5
−
6 =
1
−
3 +
1
−
2
Sim
pli
fy t
he
foll
owin
g e
xp
ress
ion
so
it i
s a s
um
of
un
it f
ract
ion
s.
5x +
6
−
10x
2 +
12
x +
2
x
−
8x
2
1
−
2x +
1
−
4x
4.IN
SU
RA
NC
E F
or a
hos
pit
al
stay,
Pau
l’s
hea
lth
in
sura
nce
pla
n r
equ
ires
him
to
pay 2 − 5
th
e co
st o
f th
e fi
rst
day i
n t
he
hos
pit
al
an
d 1 − 5
th
e co
st o
f th
e se
con
d a
nd
thir
d d
ays.
If
Pau
l’s
hos
pit
al
stay i
s 3
days
an
d c
ost
him
$420,
wh
at
was
the
full
dail
y c
ost?
5. PA
CK
AG
E D
ELIV
ER
Y F
red
rick
sbu
rg
Parc
el E
xp
ress
del
iver
ed a
tot
al
of
498 p
ack
ages
on
Mon
day,
Tu
esd
ay,
an
d
Wed
nes
day.
On
Tu
esd
ay,
they
del
iver
ed
7 l
ess
than
2 t
imes
th
e n
um
ber
of
pack
ages
del
iver
ed o
n M
ond
ay.
On
W
edn
esd
ay,
they
del
iver
ed t
he
aver
age
nu
mber
del
iver
ed o
n M
ond
ay a
nd
T
ues
day.
a.
Wri
te a
rati
onal
equ
ati
on t
hat
rep
rese
nts
th
e su
m o
f th
e n
um
ber
s of
pack
ages
del
iver
ed o
n M
ond
ay,
Tu
esd
ay,
an
d W
edn
esd
ay.
b.
How
man
y p
ack
ages
wer
e d
eliv
ered
on M
ond
ay?
113
11-6
13
x
−
10
229
−
254
an
sw
er:
x +
2x -
7 +
3x -
7
−
2
or
498
Sam
ple
$525
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-6
Ch
ap
ter
11
41
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Su
m a
nd
Dif
fere
nce o
f A
ny T
wo
Lik
e P
ow
ers
Th
e su
m o
f an
y t
wo
lik
e p
ower
s ca
n b
e w
ritt
en a
n +
bn,
wh
ere
n i
s a p
osit
ive
inte
ger
. T
he
dif
fere
nce
of
lik
e p
ower
s is
an -
bn.
Un
der
wh
at
con
dit
ion
s are
th
ese
exp
ress
ion
s ex
act
ly
div
isib
le b
y (
a +
b)
or (
a -
b)?
Th
e an
swer
dep
end
s on
wh
eth
er n
is
an
od
d o
r ev
en n
um
ber
.
Use l
on
g d
ivis
ion
to
fin
d t
he f
oll
ow
ing
qu
oti
en
ts.
(Hint:
Writ
e
a3 +
b3 a
s a
3 +
0a
2 +
0a
+ b
3.)
Is t
he n
um
era
tor e
xa
ctl
y
div
isib
le b
y t
he d
en
om
ina
tor? W
rit
e yes o
r no.
1. a
3 +
b3
−
a
+ b
2.
a3 +
b3
−
a
- b
3.
a3 -
b3
−
a
+ b
4.
a3 -
b3
−
a
- b
yes
no
n
o
yes
5.
a4 +
b4
−
a
+ b
6.
a4 +
b4
−
a
- b
7.
a4 -
b4
−
a
+ b
8.
a4 -
b4
−
a
- b
n
o
no
yes
yes
9. a
5 +
b5
−
a
+ b
10.
a5 +
b5
−
a
- b
11.
a5 -
b5
−
a +
b
12.
a5 -
b5
−
a -
b
yes
no
n
o
yes
13. U
se t
he
wor
ds
od
d a
nd
even
to
com
ple
te t
hes
e tw
o st
ate
men
ts.
a
. a
n +
bn i
s d
ivis
ible
by a
+ b
if
n i
s ,
an
d b
y n
eith
er
a +
b n
or a
- b
if
n i
s .
b
. a
n -
bn i
s d
ivis
ible
by a
- b
if
n i
s ,
an
d b
y b
oth
a +
b a
nd
a -
b i
f n
is
.
14. D
escr
ibe
the
sign
s of
th
e te
rms
of t
he
qu
otie
nts
wh
en t
he
div
isor
is
a -
b.
T
he t
erm
s a
re a
ll p
osit
ive.
15. D
escr
ibe
the
sign
s of
th
e te
rms
of t
he
qu
otie
nt
wh
en t
he
div
isor
is
a +
b.
T
he t
erm
s a
re a
ltern
ate
ly p
osit
ive a
nd
neg
ati
ve.
11-6
od
deven
od
deven
Answers (Lesson 11-6)
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 11 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
11
42
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Mix
ed
Exp
ressio
ns a
nd
Co
mp
lex F
racti
on
s
Sim
plify
Mix
ed
Exp
ress
ion
s A
lgebra
ic e
xp
ress
ion
s su
ch a
s a
+ b
−
c an
d 5
+ x
+ y −
x +
3 a
re
call
ed
mix
ed
ex
pressio
ns.
Ch
an
gin
g m
ixed
exp
ress
ion
s to
rati
on
al
exp
ress
ion
s is
sim
ilar
to c
han
gin
g m
ixed
nu
mbers
to i
mp
rop
er
fract
ion
s.
S
imp
lify
5 +
2 −
n .
5 +
2 −
n =
5 ·
n −
n
+ 2
−
n
LC
D is n
.
=
5n
+ 2 −
n
A
dd t
he n
um
era
tors
.
Th
ere
fore
, 5 +
2 −
n =
5n
+ 2 −
n
.
S
imp
lify
2 +
3 −
n +
3 .
2 +
3 −
n +
3 =
2(n
+ 3
) −
n +
3
+
3 −
n +
3
=
2n
+ 6 −
n +
3 +
3 −
n +
3
=
2n
+ 6
+ 3 −
n +
3
=
2n
+ 9 −
n +
3
Th
ere
fore
, 2 +
3 −
n +
3 =
2n
+ 9 −
n +
3 .
Exerc
ises
Writ
e e
ach
mix
ed
ex
pressio
n a
s a
ra
tio
na
l ex
pressio
n.
1. 4 +
6 −
a 4
a +
6 −
a
2. 1
−
9x -
3 1
- 2
7x −
9x
3. 3
x -
1 −
x2 3
x3 -
1 −
x2
4. 4
−
x2 -
2 4
- 2
x2
−
x2
5. 10 +
60 −
x +
5
1
0x +
110 −
x +
5
6.
h −
h +
4 +
2 3
h +
8 −
h +
4
7.
y −
y -
2 +
y2
y
3 -
2y
2 +
y −
y -
2
8. 4 -
4 −
2x +
1
8x −
2x +
1
9. 1 +
1 −
x
x
+ 1 −
x
10.
4 −
m -
2 -
2m
4
- 2
m2 +
4m
−
m -
2
11. x
2 +
x +
2 −
x -
3
x
3 -
3x
2 +
x +
2
−
x -
3
12. a
- 3
+ a
- 2 −
a +
3
a
2 +
a -
11 −
a +
3
13. 4
m +
3p −
2t
8
mt +
3p −
2t
14. 2q
2 +
q −
p +
q
q
+ 2
rq2 +
2q
3
−
r +
q
15.
2 −
y2 -
1 -
4y
2 2
- 4
y4 +
4y
2
−
y2 -
1
16. t2
+ p
+ t −
p -
t
p
t2 -
t3 +
p +
t
−
p -
t
11-7
Exam
ple
1Exam
ple
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-7
Ch
ap
ter
11
43
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Mix
ed
Exp
ressio
ns a
nd
Co
mp
lex F
racti
on
s
Sim
plify
Co
mp
lex F
ract
ion
s If
a f
ract
ion
has
on
e o
r m
ore
fra
ctio
ns
in t
he n
um
era
tor
or
den
om
inato
r, i
t is
call
ed
a c
om
ple
x f
ra
cti
on
.
Sim
plify
ing
a
Co
mp
lex F
racti
on
Any c
om
ple
x f
raction a
−
b −
c −
b
where
b ≠
0,
c ≠
0,
and d
≠ 0
, can b
e e
xpre
ssed a
s a
d −
bc .
S
imp
lify
2 +
4 −
a −
a +
2 −
3
.
2 +
4 −
a −
a +
2 −
3
= 2
a −
a +
4 −
a −
a +
2 −
3
Fin
d t
he L
CD
for
the n
um
era
tor
and r
ew
rite
as lik
e f
ractions.
=
2a
+ 4 −
a
−
a +
2 −
3
Sim
plif
y t
he n
um
era
tor.
=
2a
+ 4 −
a
·
3 −
a +
2
Rew
rite
as t
he p
roduct
of
the n
um
era
tor
and t
he r
ecip
rocal of
the d
enom
inato
r.
=
2(a
+ 2
) −
a
·
3 −
a +
2
Facto
r.
=
6 −
a
Div
ide a
nd s
implif
y.
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
1. 2
2 −
5 −
3 3
−
4
1
6 −
25
2.
3 −
x −
4 −
y
3
y −
4x
3.
x −
y3 −
x3
−
y2
1
−
x2y
4. 1
- 1
−
x −
1 +
1 −
x
x
- 1 −
x +
1
5. 1
- 1
−
x −
1 -
1 −
x2
x −
x +
1
6.
1 −
x -
3 −
2 −
x2 -
9
x
+ 3 −
2
7.
x2 -
25 −
y
−
x3 -
5x
2
x
+ 5 −
x2y
8.
x -
12 −
x -
1 −
x -
8 −
x -
2
(x
+ 3
)(x -
2)
−
(x +
1)(
x +
2)
9.
3 −
y +
2 -
2 −
y -
2
−
1 −
y +
2 -
2 −
y -
2
y
- 1
0 −
-y -
6
11-7
Exam
ple
Answers (Lesson 11-7)
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 11 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
11
44
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Mix
ed
Exp
ressio
ns a
nd
Co
mp
lex F
racti
on
s
Writ
e e
ach
mix
ed
ex
pressio
n a
s a
ra
tio
na
l ex
pressio
n.
1. 6 +
4 −
h
6h
+ 4 −
h
2. 7 +
6 −
p
7p
+ 6 −
p
3. 4
b +
b −
c 4
bc +
b −
c
4. 8
q -
2q −
r 8
qr -
2q −
r
5. 2 +
4 −
d -
5
2d
- 6 −
d -
5
6. 5 -
6 −
f +
2
5f +
4 −
f +
2
7. b
2 +
12 −
b +
3
b3 +
3b
2 +
12
−
b +
3
8. m
-
6 −
m -
7
m2 -
7m
- 6
−
m -
7
9. 2
a +
a -
2 −
a
2
a2 +
a -
2 −
a
10. 4r -
r +
9 −
2r
8
r2 -
r -
9 −
2r
Sim
pli
fy e
ach
ex
pressio
n.
11.
21 −
2
−
43 −
4
10−
19
12.
3 2
−
3 −
5 2
−
5
55 −
81
13.
r −
n2 −
r2
−
n
1 −
rn
14.
a2
−
b3 −
a −
b
a −
b2
15. x
2y −
c −
xy
3
−
c2
xc −
y2
16.
r -
2 −
r +
3 −
r -
2 −
3
3 −
r +
3
17.
w +
4 −
w
−
w2 -
16 −
w
1 −
w -
4
18. x
2 -
1 −
x
−
x -
1 −
x2
x(x
+ 1
) 19.
b2 -
4 −
b2 +
7b
+ 1
0
−
b -
2
1 −
b +
5
20. k
2 +
5k
+ 6 −
k2 -
9
−
k +
2
1 −
k -
3
21. g
+
12 −
g +
8 −
g +
6
g
+ 2 −
g +
8
22. p
+
9 −
p -
6 −
p -
3
p
- 3 −
p -
6
11-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-7
Ch
ap
ter
11
45
Gle
ncoe A
lgeb
ra 1
Practi
ce
Mix
ed
Exp
ressio
ns a
nd
Co
mp
lex F
racti
on
s
Writ
e e
ach
mix
ed
ex
pressio
n a
s a
ra
tio
na
l ex
pressio
n.
1. 14 -
9 −
u
2. 7
d +
4d −
c
3. 3
n +
6 -
n −
n
14u
- 9 −
u
7d
c +
4d −
c
3n
2 -
n +
6 −
n
4. 5
b -
b +
3 −
2b
5. 3 +
t +
5 −
t2 -
1
6. 2
a +
a -
1 −
a +
1
10b
2 -
b -
3
−
2b
3t2
+ t
+ 2 −
t2 -
1
2a
2 +
3a
- 1
−
a +
1
7. 2
p +
p +
1 −
p -
3
8. 4
n2 +
n
- 1 −
n2 -
1
9. (t
+ 1
) +
4 −
t +
5
2p
2 -
5p
+ 1
−
p -
3
4n
3 +
4n
2 +
1
−
n +
1
t2 +
6t +
9 −
t +
5
Sim
pli
fy e
ach
ex
pressio
n.
10.
3 2
−
5 −
2 5
−
6
6 −
5
11.
m2
−
6p −
3m −
p2
m
p −
18
12.
x2 -
y2
−
x2
−
x +
y −
3x
3
(x -
y) −
x
13. a
- 4 −
a2
−
a2 -
16 −
a
1 −
a(a
+ 4
) 14.
q2 -
7q +
12
−
q2 -
16
−
q -
3
1 −
q +
4
15.
k
2 +
6k −
k2 +
4k -
5
−
k
- 8 −
k2 -
9k +
8
k
(k +
6) −
k +
5
16.
b2 +
b -
12 −
b2 +
3b -
4 −
b -
3 −
b2 -
b
b
17.
g -
10 −
g +
9
−
g -
5 −
g +
4
(g +
10)(
g +
4)
−
(g +
9)(
g +
5)
18.
y +
6 −
y -
7 −
y -
7 −
y +
6
(y
- 6
)(y +
6)
−
(y -
7)(
y +
7)
19
. TR
AV
EL
R
ay a
nd
Jan
are
on
a 1
2 1
−
2 -h
ou
r d
rive f
rom
Sp
rin
gfi
eld
, M
isso
uri
, to
Ch
icago,
Illi
nois
. T
hey s
top
for
a b
reak
every
3 1
−
4 h
ou
rs.
a.
Wri
te a
n e
xp
ress
ion
to m
od
el
this
sit
uati
on
. 1
2 1
−
2 −
3 1
−
4
b.
How
man
y s
top
s w
ill
Ray a
nd
Jan
mak
e b
efo
re a
rriv
ing i
n C
hic
ago?
3
20. C
AR
PEN
TR
Y T
ai
need
s se
vera
l 2 1
−
4 -in
ch w
ood
en
rod
s to
rein
forc
e t
he f
ram
e o
n a
fu
ton
.
Sh
e c
an
cu
t th
e r
od
s fr
om
a 2
4 1
−
2 -in
ch d
ow
el
pu
rch
ase
d f
rom
a h
ard
ware
sto
re.
How
man
y
wood
en
rod
s ca
n s
he c
ut
from
th
e d
ow
el?
10
11-7
Answers (Lesson 11-7)
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 11 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
11
46
Gle
ncoe A
lgeb
ra 1
1.C
YC
LIN
G N
ata
lie r
od
e i
n a
bic
ycl
e e
ven
t
for
chari
ty o
n S
atu
rday.
It t
ook
her
2 − 3 o
f
an
hou
r to
com
ple
te t
he 1
8-m
ile r
ace
.W
hat
was
her
avera
ge s
peed
in
mil
es
per
hou
r? 27 m
ph
2. Q
UIL
TIN
G M
rs.
Tan
tora
sew
s an
d s
ell
s
Am
ish
baby q
uil
ts.
Sh
e b
ou
gh
t 42 3
−
4 y
ard
s
of
back
ing f
abri
c, a
nd
2 1
−
4 y
ard
s are
need
ed
for
each
qu
ilt
she s
ew
s. H
ow
m
an
y q
uil
ts c
an
sh
e m
ak
e w
ith
th
e
back
ing f
abri
c sh
e b
ou
gh
t?
3. T
RA
VE
L T
he F
ran
z f
am
ily t
ravele
d f
rom
G
alv
est
on
to W
aco
for
a f
am
ily r
eu
nio
n.
Dri
vin
g t
heir
van
, th
ey a
vera
ged
30
mil
es
per
hou
r on
th
e w
ay t
o W
aco
an
d
45 m
iles
per
hou
r on
th
e r
etu
rn t
rip
h
om
e t
o G
alv
est
on
. W
hat
is t
heir
avera
ge
rate
for
the e
nti
re t
rip
? (H
int:
Rem
em
ber
that
avera
ge r
ate
equ
als
tota
l d
ista
nce
d
ivid
ed
by t
ota
l ti
me a
nd
th
at
tim
e c
an
be r
ep
rese
nte
d a
s a r
ati
o o
f d
ista
nce
x t
o r
ate
.) 36 m
ph
4. PH
YSIC
AL S
CIE
NC
E T
he v
olu
me o
f a
gas
vari
es
dir
ect
ly a
s th
e K
elv
in
tem
pera
ture
T a
nd
in
vers
ely
as
the
pre
ssu
re P
, w
here
k i
s th
e c
on
stan
t of
vari
ati
on
.
V
= k
( T
−
P )
If
k =
13
−
157 , f
ind
th
e v
olu
me i
n l
iters
of
heli
um
gas
at
273 d
egre
es
Kelv
in a
nd
13
−
3
atm
osp
here
s of
pre
ssu
re.
Rou
nd
you
r an
swer
to t
he n
eare
st h
un
dre
dth
.
5.2
2 L
5.SA
FETY
T
he O
ccu
pati
on
al
Safe
ty a
nd
H
ealt
h A
dm
inis
trati
on
pro
vid
es
safe
ty
stan
dard
s in
th
e w
ork
pla
ce t
o k
eep
w
ork
ers
fre
e f
rom
dan
gero
us
work
ing
con
dit
ion
s. O
SH
A r
eco
mm
en
ds
that
for
gen
era
l co
nst
ruct
ion
th
ere
be 5
foot-
can
dle
s of
illu
min
ati
on
in
wh
ich
to w
ork
. A
fore
man
usi
ng a
lig
ht
mete
r fi
nd
s th
at
the i
llu
min
ati
on
of
a c
on
stru
ctio
n l
igh
t on
a s
urf
ace
8 f
eet
from
th
e s
ou
rce i
s 11 f
oot-
can
dle
s. T
he i
llu
min
ati
on
p
rod
uce
d b
y a
lig
ht
sou
rce v
ari
es
invers
ely
as
the s
qu
are
of
the d
ista
nce
fr
om
th
e s
ou
rce.
I is
ill
um
inati
on
(in
foot-
can
dle
s).
I
=
k
−
d2
d i
s th
e d
ista
nce
fro
m t
he s
ou
rce
(in
feet)
.
k i
s a c
on
stan
t.
a.
Fin
d t
he i
llu
min
ati
on
of
the s
am
e
ligh
t at
a d
ista
nce
of
15 3
−
4 f
eet.
Rou
nd
you
r an
swer
to t
he n
eare
st h
un
dre
dth
.
2.8
4 f
oo
t-can
dle
s
b.
Is t
here
en
ou
gh
ill
um
inati
on
at
this
d
ista
nce
to m
eet
OS
HA
requ
irem
en
ts
for
ligh
tin
g?
n
o
c.
In o
rder
to c
om
ply
wit
h O
SH
A,
wh
at
is t
he m
axim
um
all
ow
able
work
ing
dis
tan
ce f
rom
th
is l
igh
t so
urc
e?
Rou
nd
you
r d
eci
mal
an
swer
to n
eare
st t
en
th.
11.9
ft
Wo
rd
Pro
ble
m P
racti
ce
Mix
ed
Exp
ressio
ns a
nd
Co
mp
lex F
racti
on
s
11-7
19
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-8
Ch
ap
ter
11
47
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Co
nti
nu
ed
Fra
cti
on
s
Con
tin
ued
fra
ctio
ns
are
a s
peci
al
typ
e o
f co
mp
lex f
ract
ion
. E
ach
fra
ctio
n i
n a
con
tin
ued
fr
act
ion
has
a n
um
era
tor
of
1.
1 +
1
−
2 +
1
−
3 +
1
−
4
Ev
alu
ate
th
e c
on
tin
ued
fra
cti
on
ab
ov
e.
Sta
rt
at
the b
ott
om
an
d
wo
rk
yo
ur w
ay
up
.
Ste
p 1
3 +
1
−
4 =
12
−
4
+ 1
−
4 =
13
−
4
Ste
p 2
1
−
13 =
4
−
13
Ste
p 3
2 +
4
−
13 =
26
−
13 +
4
−
13 =
30
−
13
Ste
p 4
1
−
3
0
−
13 =
13
−
30
Ste
p 5
1 +
13
−
30 =
1 1
3
−
30
Ch
an
ge 1
3
−
7
into
a
co
nti
nu
ed
fra
cti
on
.
Ste
p 1
13
−
7
= 7
−
7 +
6
−
7 =
1 +
6
−
7
Ste
p 2
6
−
7 =
1
−
7
Ste
p 3
7
−
6 =
1 +
1
−
6
Sto
p,
because t
he n
um
era
tor
is 1
.
Thus,
13
−
7
can b
e w
ritten a
s 1
+
1
−
1 +
1
−
6
11-7
Exam
ple
1Exam
ple
2
Ev
alu
ate
ea
ch
co
nti
nu
ed
fra
cti
on
.
1. 0 +
1
−
2 +
1
−
4 +
1
−
6 +
1
−
8
2. 0 +
1
−
1 +
1
−
2
+ 1
−
6
3. 3 +
1
−
1 +
1
−
1 +
1
−
1
+ 1
−
2
4. 1 +
1
−
3 +
1
−
5
+ 1
−
7
Ch
an
ge e
ach
fra
cti
on
in
to a
co
nti
nu
ed
fra
cti
on
.
5.
71
−
26
2 +
1
−
1 +
1
−
2 +
1
−
1 +
1
−
2 +
1
−
2
6.
9
−
56 0 +
1
−
6 +
1
−
4 +
1
−
2
7.
4626
−
2065
2 +
1
−
4 +
1
−
6 +
1
−
8 +
1
−
10
204
−
457
13
−
19
3
5
−
8
1 3
6
−
115
Answers (Lesson 11-7)
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 11 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
11
48
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Rati
on
al
Fu
ncti
on
s a
nd
Eq
uati
on
s
So
lve R
ati
on
al
Eq
uati
on
s R
ati
on
al
eq
ua
tio
ns a
re e
qu
ati
on
s th
at
con
tain
rati
on
al
exp
ress
ion
s. T
o s
olv
e e
qu
ati
on
s co
nta
inin
g r
ati
on
al
exp
ress
ion
s, m
ult
iply
each
sid
e o
f th
e
equ
ati
on
by t
he l
east
com
mon
den
om
inato
r.
Rati
on
al
equ
ati
on
s ca
n b
e u
sed
to s
olv
e w
ork
pro
ble
ms a
nd r
ate
pro
ble
ms.
Exerc
ises
So
lve e
ach
eq
ua
tio
n.
Sta
te a
ny
ex
tra
neo
us s
olu
tio
ns.
1. x
- 5 −
5
+ x
−
4 =
8 20
2. 3
−
x =
6 −
x +
1 1
3. x
- 1 −
5
= 2
x -
2 −
15
1
4.
8 −
n -
1 =
10 −
n +
1 9
5. t
-
4 −
t +
3 =
t +
3 -
4 1
−
3
6. m
+ 4 −
m
+ m
−
3 =
m −
3
-4;
7. q
+ 4 −
q -
1 +
q −
q +
1 =
2
- 3
−
2
8. 5
- 2
x −
2
- 4
x +
3 −
6
= 7
x +
2 −
6
1
0
−
17
9. m
+ 1 −
m -
1 -
m −
1 -
m =
1
-2
10. x
2 -
9 −
x -
3 +
x2 =
9
-3 o
r 2
11.
2 −
x 2 -
36 -
1 −
x -
6 =
0
-4;
6 i
s
12.
4z −
z 2 +
4z +
3 =
6 −
z +
3 +
4 −
z +
1
-3 i
s
extr
an
eo
us
extr
an
eo
us
13.
4 −
4 -
p -
p
2
−
p -
4 =
4
-6,
2
14. x
2 -
16 −
x -
4 +
x 2 =
16
-4,
3;
4 i
s
extr
an
eo
us
S
olv
e x
- 3
−
3
+ x
−
2 =
4.
x
- 3 −
3
+ x
−
2 =
4
6 ( x
- 3 −
3
+ x
−
2 ) =
6(4
) T
he L
CD
is 6
.
2(x
- 3
) +
3x =
24
D
istr
ibutive P
ropert
y
2
x -
6 +
3x =
24
D
istr
ibutive P
ropert
y
5
x =
30
Sim
plif
y.
x =
6
Div
ide e
ach s
ide b
y 5
.
Th
e s
olu
tion
is
6.
S
olv
e
15
−
x 2 -
1
=
5
−
2(x
- 1
) . S
tate
an
y e
xtr
an
eo
us s
olu
tio
ns.
15 −
x 2 -
1 =
5 −
2(x
- 1
) O
rigin
al equation
30(x
- 1
) =
5(x
2 -
1)
Cro
ss m
ultip
ly.
30x -
30 =
5x
2 -
5
Dis
trib
utive P
ropert
y
0 =
5x
2 -
30
x +
30
- 5
A
dd -
30x +
30 t
o
each s
ide.
0 =
5x
2 -
30
x +
25
S
implif
y.
0 =
5(x
2 -
6x +
5)
Facto
r.
0 =
5(x
- 1
)(x -
5)
Facto
r.
x =
1 or
x =
5
Zero
Pro
duct
Pro
pert
y
Th
e n
um
ber
1 i
s an
extr
an
eou
s so
luti
on
, si
nce
1
is a
n e
xcl
ud
ed
valu
e f
or
x.
So,
5 i
s th
e s
olu
tion
of
the e
qu
ati
on
.
11-8
Exam
ple
1Exam
ple
2
extr
an
eo
us
0 i
s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-8
Ch
ap
ter
11
49
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Fu
ncti
on
s a
nd
Rati
on
al
Eq
uati
on
s
Use
Rati
on
al
Eq
uati
on
s to
So
lve P
rob
lem
s R
ati
on
al
equ
ati
on
can
be u
sed
to
solv
e w
ork
pro
ble
ms a
nd
ra
te p
ro
ble
ms.
11-8
W
OR
K P
RO
BLE
M M
arla
ca
n p
ain
t P
ercy
’s k
itch
en
in
3 h
ou
rs.
Percy
ca
n p
ain
t it
in
2 h
ou
rs.
Wo
rk
ing
to
geth
er,
ho
w l
on
g w
ill
it t
ak
e M
arla
an
d P
ercy
to
p
ain
t th
e k
itch
en
?
In t
hou
rs,
Marl
a c
om
ple
tes
t ·
1 −
3 o
f th
e j
ob a
nd
Perc
y c
om
ple
tes
t ·
1 −
2 o
f th
e j
ob.
So a
n
equ
ati
on
for
com
ple
tin
g t
he w
hole
job i
s t −
3 +
t −
2 =
1.
t −
3 +
t −
2 =
1
2t +
3t =
6
Multip
ly e
ach t
erm
by 6
.
5
t =
6
Add lik
e t
erm
s.
t =
6 −
5
Solv
e.
So i
t w
ill
tak
e M
arl
a a
nd
Perc
y 1
1 −
5 h
ou
rs t
o p
ain
t th
e r
oom
if
they w
ork
togeth
er.
Exam
ple
Exerc
ises
1. G
REETIN
G C
AR
DS
It
tak
es
Ken
esh
a 4
5 m
inu
tes
to p
rep
are
20 g
reeti
ng c
ard
s. I
t ta
kes
Pau
la 3
0 m
inu
tes
to p
rep
are
th
e s
am
e n
um
ber
of
card
s. W
ork
ing t
ogeth
er
at
this
rate
, h
ow
lon
g w
ill
it t
ak
e t
hem
to p
rep
are
th
e c
ard
s?
2. B
OA
TIN
G A
moto
rboat
wen
t u
pst
ream
at
15 m
iles
per
hou
r an
d r
etu
rned
dow
nst
ream
at
20 m
iles
per
hou
r. H
ow
far
did
th
e b
oat
travel
on
e w
ay i
f th
e r
ou
nd
tri
p t
ook
3.5
hou
rs?
30 m
i
3. FLO
OR
ING
M
aya a
nd
Regin
ald
are
in
stall
ing h
ard
wood
flo
ori
ng.
Maya c
an
in
stall
fl
oori
ng i
n a
room
in
4 h
ou
rs.
Regin
ald
can
in
stall
flo
ori
ng i
n a
room
in
3 h
ou
rs.
How
lo
ng w
ou
ld i
t ta
ke t
hem
if
they w
ork
ed
togeth
er?
4. B
ICY
CLIN
G S
tefa
n i
s bic
yli
ng o
n a
bik
e t
rail
at
an
avera
ge o
f 10 m
iles
per
hou
r. E
rik
st
art
s bic
ycl
ing o
n t
he s
am
e t
rail
30 m
inu
tes
late
r. I
f E
rik
avera
ges
16 m
iles
per
hou
r,
how
lon
g w
ill
it t
ak
e h
im t
o p
ass
Ste
fan
? 50 m
in
12
−
7
h o
r ab
ou
t 1.7
1 h
ou
rs
18 m
in
Answers (Lesson 11-8)
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 11 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
11
50
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Rati
on
al
Fu
ncti
on
s a
nd
Eq
uati
on
s
So
lve e
ach
eq
ua
tio
n.
Sta
te a
ny
ex
tra
neo
us s
olu
tio
ns.
1.
5
−
c =
2
−
c +
3 -
5
2.
3
−
q =
5
−
q+
4 6
3.
7
−
m +
1 =
12
−
m +
2
2
−
5
4.
3
−
x +
2 =
5
−
x +
8 7
5.
y
−
y -
2 =
y +
1
−
y -
5
1 −
2
6. b
- 2
−
b
= b
+ 4
−
b +
2 -
1
7. 3
m
−
2 -
1
−
4 =
10m
−
8
1
8. 7
g
−
9
+ 1
−
3 =
5g
−
6
6
9. 2
a +
5
−
6
- 2
a
−
3
= -
1
−
2 4
10. n
- 3
−
10
+ n
- 5
−
5
= 1
−
2 6
11. c
+ 2
−
c +
c +
3
−
c =
7 1
12. 3
b -
4
−
b
- b
- 7
−
b
= 1
-
3
13. m
- 4
−
m
- m
– 1
1
−
m +
4
=
1
−
m 2
14.
f +
2
−
f -
f +
1
−
f +
5 =
1
−
f -
1
15. r
+ 3
−
r -
1 -
r
−
r -
3 =
0 9
16.
u +
1
−
u -
2 -
u
−
u +
1 =
0 - 1
−
4
17.
- 2
−
x +
1 +
2
−
x =
1 -
2,
1
18.
5
−
m –
4 -
m
−
2m
– 8
= 1
6
19. A
CTIV
ISM
M
au
ry a
nd
Tyra
are
mak
ing p
hon
e c
all
s to
sta
te r
ep
rese
nta
tives’
off
ices
to
lobby f
or
an
iss
ue.
Mau
ry c
an
call
all
120 s
tate
rep
rese
nta
tives
in 1
0 h
ou
rs.
Tyra
can
call
all
120 s
tate
rep
rese
nta
tives
in 8
hou
rs.
How
lon
g w
ou
ld i
t ta
ke t
hem
to c
all
all
120 s
tate
rep
rese
nta
tives
togeth
er?
4 4
−
9 h
r
11-8
Lesson 11-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Practi
ce
Rati
on
al
Fu
ncti
on
s a
nd
Eq
uati
on
s
So
lve e
ach
eq
ua
tio
n.
Sta
te a
ny
ex
tra
neo
us s
olu
tio
ns.
1.
5
−
n +
2 =
7
−
n +
6
2.
x
−
x -
5 =
x +
4
−
x -
6
3. k
+ 5
−
k
= k
- 1
−
k +
9
8
4
-
3
4.
2h
−
h -
1 =
2h
+ 1
−
h +
2
5. 4
y
−
3
+ 1
−
2 =
5y
−
6
6. y
- 2
−
4
- y
+ 2
−
5
= -
1
- 1
−
5
-1
-2
7. 2
q -
1
−
6
- q
−
3 =
q +
4
−
18
8.
5
−
p -
1 -
3
−
p +
2 =
0
9.
3t
−
3t
- 3
-
1
−
9t
+ 3
= 1
-
7
- 1
3 −
2
- 1
−
2
10.
4x
−
2x +
1 -
2
x
−
2x +
3 =
1
11. d
- 3
−
d
- d
- 4
−
d -
2 =
1
−
d
12. 3
y -
2
−
y -
2
+
y 2
−
2 -
y =
-3
3 −
2
4
4;
extr
an
eo
us:
2
13.
2
−
m +
2 -
m +
2
−
m -
2 =
7
−
3
14. n
+ 2
−
n
+ n
+ 5
−
n +
3 =
- 1
−
n
15.
1
−
z +
1 -
6 -
z
−
6z
= 0
-
1,
2 −
5
- 9
−
5 , -
1
-3,
2
16.
2p
−
p -
2 +
p
+ 2
−
p 2 -
4 =
1
17. x
+ 7
−
x 2 -
9 -
x
−
x +
3 =
1
18.
2n
−
n -
4 -
n
+ 6
−
n 2 -
16 =
1
-
3;
extr
an
eo
us: -
2
-2,
4
-5, -
2
19. P
UB
LIS
HIN
G T
race
y a
nd
Ala
n p
ubli
sh a
10-p
age i
nd
ep
en
den
t n
ew
spap
er
on
ce a
mon
th.
At
pro
du
ctio
n,
Ala
n u
suall
y s
pen
ds
6 h
ou
rs o
n t
he l
ayou
t of
the p
ap
er.
Wh
en
Tra
cey
help
s, l
ayou
t ta
kes
3 h
ou
rs a
nd
20 m
inu
tes.
a.
Wri
te a
n e
qu
ati
on
th
at
cou
ld b
e u
sed
to d
ete
rmin
e h
ow
lon
g i
t w
ou
ld t
ak
e T
race
y t
o
do t
he l
ayou
t by h
ers
elf
.
b.
How
lon
g w
ou
ld i
t ta
ke T
race
y t
o d
o t
he j
ob a
lon
e?
7 h
30 m
in
20. T
RA
VE
L E
mil
io m
ad
e a
rran
gem
en
ts t
o h
ave L
yn
da p
ick
him
up
fro
m a
n a
uto
rep
air
shop
aft
er
he d
rop
ped
his
car
off
. H
e c
all
ed
Lyn
da t
o t
ell
her
he w
ou
ld s
tart
walk
ing a
nd
to l
ook
for
him
on
th
e w
ay.
Em
ilio
an
d L
yn
da l
ive 1
0 m
iles
from
th
e a
uto
sh
op
. It
tak
es
Em
ilio
2 1
−
4 h
ou
rs t
o w
alk
th
e d
ista
nce
an
d L
yn
da 1
5 m
inu
tes
to d
rive t
he d
ista
nce
.
a.
If E
mil
io a
nd
Lyn
da l
eave a
t th
e s
am
e t
ime,
wh
en
sh
ou
ld L
yn
da e
xp
ect
to s
pot
Em
ilio
on
th
e r
oad
?
b.
How
far
wil
l E
mil
io h
ave w
alk
ed
wh
en
Lyn
da p
ick
s h
im u
p?
1 m
i
11-8
Ch
ap
ter
11
51
Gle
ncoe A
lgeb
ra 1
Sam
ple
an
sw
er:
1 −
6 ( 1
0
−
3 )
+ 1
−
t ( 1
0
−
3 )
= 1
in 1
3 1
−
2 m
in
Answers (Lesson 11-8)
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 11 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
11
52
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Rati
on
al
Fu
ncti
on
s a
nd
Eq
uati
on
s
1. ELEC
TR
ICIT
Y T
he c
urr
en
t in
a s
imp
le
ele
ctri
c ci
rcu
it v
ari
es
invers
ely
as
the
resi
stan
ce.
If t
he c
urr
en
t is
20 a
mp
s w
hen
th
e r
esi
stan
ce i
s 5 o
hm
s, f
ind
th
e
curr
en
t w
hen
th
e r
esi
stan
ce i
s 8 o
hm
s.
12.5
am
ps
2. M
ASO
NR
Y S
am
an
d B
ela
i are
maso
ns
wh
o a
re w
ork
ing t
o b
uil
d a
sto
ne w
all
th
at
wil
l be 1
20 f
eet
lon
g.
Sam
work
s fr
om
on
e e
nd
an
d i
s able
to b
uil
d o
ne
ten
-foot
sect
ion
in
5 h
ou
rs.
Bela
i w
ork
s fr
om
th
e o
ther
en
d a
nd
is
able
to f
inis
h
a t
en
-foot
sect
ion
in
4 h
ou
rs.
How
lon
g
wil
l it
tak
e S
am
an
d B
ela
i to
fin
ish
bu
ild
ing t
he w
all
?
26 h
ou
rs a
nd
40 m
inu
tes
3. N
UM
BER
S T
he f
orm
ula
to f
ind
th
e s
um
of
the f
irst
n w
hole
nu
mbers
is
sum
= n
2 +
n −
2
. In
ord
er
to e
nco
ura
ge
stu
den
ts t
o s
how
up
earl
y t
o a
sch
ool
dan
ce,
the d
an
ce c
om
mit
tee d
eci
des
to
charg
e l
ess
for
those
wh
o c
om
e t
o t
he
dan
ce e
arl
y.
Th
eir
pla
n i
s to
ch
arg
e t
he
firs
t st
ud
en
t to
arr
ive 1
pen
ny.
Th
e
seco
nd
stu
den
t th
rou
gh
th
e d
oor
is
charg
ed
2 p
en
nie
s; t
he t
hir
d s
tud
en
t th
rou
gh
th
e d
oor
is c
harg
ed
3 p
en
nie
s,
an
d s
o o
n.
How
mu
ch m
on
ey,
in t
ota
l,
wou
ld p
aid
by t
he f
irst
150 s
tud
en
ts?
11,3
25 p
en
nie
s o
r $113.2
5
4. N
AU
TIC
AL A
ferr
y c
ap
tain
keep
s tr
ack
of
the p
rogre
ss o
f h
is s
hip
in
th
e s
hip
’s
log.
On
e d
ay,
he r
eco
rds
the f
oll
ow
ing
en
try.
Wit
h t
he
rece
nt
spri
ng s
now
mel
t, t
he
curr
ent
is r
un
nin
g s
tron
g t
od
ay.
Th
e
six-m
ile
trip
dow
nst
rea
m t
o W
hyte
’s
lan
din
g w
as
ver
y q
uic
k.
How
ever
, w
e
on
ly c
over
ed t
wo m
iles
in
th
e sa
me
am
ou
nt
of
tim
e w
hen
we
hea
ded
ba
ck u
pst
rea
m.
Wri
te a
rati
on
al
equ
ati
on
usi
ng b
for
the
speed
of
the b
oat
an
d c
for
the s
peed
of
the s
tream
an
d s
olv
e f
or
b i
n t
erm
s of
c.
6
−
b +
c =
2
−
b -
c ;
b =
2c
5. H
EA
LTH
CA
RE
T
he t
ota
l n
um
ber
of
Am
eri
can
s w
ait
ing f
or
kid
ney a
nd
heart
tr
an
spla
nts
is
ap
pro
xim
ate
ly 6
6,5
00.
Th
e
rati
o o
f th
ose
aw
ait
ing a
kid
ney
tran
spla
nt
to t
hose
aw
ait
ing a
heart
tr
an
spla
nt
is a
bou
t 20 t
o 1
.
a. H
ow
man
y p
eop
le a
re o
n e
ach
of
the
wait
ing l
ists
? R
ou
nd
you
r an
swers
to
the n
eare
st h
un
dre
d.
kid
ney:
63,3
00;
heart
: 3200
b. T
hese
tw
o g
rou
ps
mak
e u
p a
bou
t 3
−
4 o
f
the t
ran
spla
nt
can
did
ate
s fo
r all
org
an
s. A
bou
t h
ow
man
y o
rgan
tr
an
spla
nt
can
did
ate
s are
th
ere
alt
ogeth
er?
Rou
nd
you
r an
swer
to t
he
neare
st t
hou
san
d.
89,0
00
11-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 11-8
Ch
ap
ter
11
53
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Win
nin
g D
ista
nces
In 1
999,
Hic
ham
El
Gu
err
ou
j se
t a w
orl
d r
eco
rd f
or
the m
ile r
un
wit
h
a t
ime o
f 3:4
3.1
3 (
3 m
in 4
3.1
3 s
). I
n 1
954,
Roger
Ban
nis
ter
ran
th
e
firs
t m
ile u
nd
er
4 m
inu
tes
at
3:5
9.4
. H
ad
th
ey r
un
th
ose
tim
es
in t
he
sam
e r
ace
, h
ow
far
in f
ron
t of
Ban
nis
ter
wou
ld E
l G
uerr
ou
j h
ave b
een
at
the f
inis
h?
Use
d −
t =
r.
Sin
ce 3
min
43.1
3 s
= 2
23.1
3 s
, an
d 3
min
59.4
s =
239.4
s,
El
Gu
err
ou
j’s
rate
was
5280 f
t −
223.1
3 s
an
d B
an
nis
ter’
s ra
te w
as
5280 f
t −
239.4
s .
rt
d
El G
uerr
ouj
5280 −
223.1
3
223.1
35280 f
eet
Bannis
ter
5280 −
239.4
223.1
3 5
280 −
239.4
. 2
23.1
3 o
r 4921.2
feet
Th
ere
fore
, w
hen
El
Gu
err
ou
j h
it t
he t
ap
e,
he w
ou
ld b
e 5
280 -
4921.2
, or
358.8
feet,
ah
ead
of
Ban
nis
ter.
Let’
s se
e w
heth
er
we c
an
develo
p a
fo
rmu
la f
or
this
typ
e o
f p
roble
m.
L
et
D =
th
e d
ista
nce
race
d,
W
= t
he w
inn
er’
s ti
me,
an
d L
= t
he l
ose
r’s
tim
e.
Foll
ow
ing t
he s
am
e p
att
ern
, you
obta
in t
he r
esu
lts
show
n
in t
he t
able
at
the r
igh
t.
Th
e w
inn
ing d
ista
nce
wil
l be D
- D
W −
L .
1. S
how
th
at
the e
xp
ress
ion
for
the w
inn
ing d
ista
nce
is
equ
ivale
nt
to D
(L -
W) −
L
.
D
- D
W
−
L
= D
L
−
L
- D
W
−
L
= D
L -
DW
−
L
=
D(L
- W
) −
L
Use t
he f
orm
ula
win
nin
g d
ista
nce =
D(L
-
W)
−
L
to
fin
d t
he w
inn
ing
dis
tan
ce t
o t
he n
ea
rest
ten
th f
or e
ach
of
the f
oll
ow
ing
Oly
mp
ic r
aces.
2. w
om
en
’s 4
00 m
ete
r re
lay:
Can
ad
a 4
8.4
s (
1928);
East
Germ
an
y 4
1.6
s (
1980)
56.2
mete
rs
3. m
en
’s 2
00 m
ete
r fr
eest
yle
sw
imm
ing:
Yevgen
y S
ad
ovyi
1 m
in 4
6.7
0 s
(1992);
Mic
hael
Gro
ss 1
min
47.4
4 s
(1984)
1.4
mete
rs
4. m
en
’s 5
0,0
00 m
ete
r w
alk
: V
yach
esl
av I
van
en
ko 3
h 3
8 m
in 2
9 s
(1988);
Hart
wig
Gau
ter
3 h
49 m
in 2
4 s
(1980)
2379.4
mete
rs
5. w
om
en
’s 4
00 m
ete
r fr
eest
yle
rela
y:
Un
ited
Sta
tes
3 m
in 3
9.2
9 s
(1996);
East
Germ
an
y 3
min
42.7
1 s
(1980)
6.1
mete
rs
11-8
rt
d
Win
ner
D −
W
w D
−
W ·
W =
D
Loser
D −
L
w D
−
L ·
W =
DW −
L
Answers (Lesson 11-8)
ERROR: undefined
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