HW Chapter 8 Exponents - algebra1kraus / Home Page€¦ · · 2018-04-064 5 3 r s t r s t 67 5 48...
Transcript of HW Chapter 8 Exponents - algebra1kraus / Home Page€¦ · · 2018-04-064 5 3 r s t r s t 67 5 48...
Simplify each of the following:
1 2 7( )( )x x x 2
2 3 66 ( )( )a a a
3 4(6 )(2 )x x 4
4 2(3 )( 2 )cd c
Simplify each of the following assuming
that no denominator is equal to zero.
Leave NO negative exponents.
5 5
3
x
x 6
7
6
9
3
r
r
7 6
6
3
y
y 8
7 4
5 9
x y
x y
Simplify each of the following:
9 3
2x 10 4( 3x)
11 2( 6p) 12
323pq
Simplify each expression.
13 2 7
5
6 4
3
x x
x
14 3
4 23x y
15 2
5 4x
16
23
4
2x
3x
Simplify each of the following assuming
that no denominator is equal to zero.
Leave NO negative exponents.
17 3 2 2
4 5 3
r s t
r s t
18 6 7
5
48
6
a y
ab
19 3 2
4 5
7
21
w u
w u
20 11 7
5 9
8
2
a b
a b
21 3 28
32
x y
xy
HW Chapter 8 Exponents
22 The length of a rectangle is 23x y units.
The width of the rectangle is 3 24x y units.
What is the area of the rectangle?
23 Given the following dimensions of a
rectangle, find the area.
4 3x y
43xy
24 The area of a rectangle is 5 412x y units.
If the length is 2 34x y units, find the
width of the rectangle.
25 The length of a side of a square is
32a b units. Find the area of the square.
Simplify each of the following:
26 2 2 3( 3k m )( 2k m) 27
2 4( 5a b)(3a )
28 4 31( 15ax )( ax )
3 29
2 3 2(cd )(c d )
30 Simplify the following:
4 92 2
Simplify each of the following:
31 2(5t) 32 3
2 25x y
33 5
gh 34 2
3cd
35 Write the equation that represents the
following graph.
36 What do we call the graph in #35?
37 Determine if the following is correct.
If not, explain why and rework it
correctly.
3 5( 12 )( 12 )
15(-12)
38 Explain the steps that should be used
to simplify the following expression
and simplify it.
2
2 32a b
39 Simplify:
3
25x
40 Simplify:
2 2(2a b)( 4ab )
41 Which expression is equivalent
to 6
11 ?
A 2 3
11 11
B 4
211
C 1 6
11 11
D 2 4
11 11
42 Evelyn is going to buy a new computer
for $1100, including tax. She will pay
for the computer by making monthly
payments of $60. If Evelyn has made
p payments, which equation best
describes b, the remaining balance?
A 60 1100 b p
B 1100 60 b p
C 1100 60 b p
D 60 1100 b p
43 The area of a parallelogram is 6 635p q
square units. If the base of the
parallelogram measures 25pq units,
what is the height of the parallelogram?
( 0p and 0q )
44 Which expression is equivalent to
3 5
5 2
15
3
x y
x y?
F 3
2
5y
x
G 5x
y
H 2
3
5
3
y
x
J 3
2
5y
x
45 If 3y x ,what is equivalent to 12x ?
A 36y
B 15y
C 9y
D 4y
Simplify each expression:
46 4 3
4
w u
w u
47 10 5
11 5
2
10
a b
a b
48 8
2 7
24
8
kd
k d
49 12 8
14 6
48
16
r s
r s
50 What is the simplified form of 2 7
3 2 2
e f g
e f g?
F 5ef g H 5 9 3e f g
G 5f
eg J
9
5 3
f
e g
51 Explain the steps that should be used
to simplify the following expression.
3 5
6
8 2
4
x x
x
Determine if the following are correct.
If not, rework it correctly.
52 2 3 2214x
7x y y
5 24x y
53
231
cd4
2 51
8c d
54 The area of a rectangle is 11 530m n
square units. If the length of the
rectangle is 4 26m n units, how many
units wide is the rectangle? ( 0m and
0n )
A 7 35m n units
B 7 924m n units
C 15 736m n units
D 15 7180m n units
Find the missing exponent for the
following.
55 9 ? 12b b b
56 2 ? 95 5 25a a a
57 4
? 202 16c c
58 ?
4 3 113 5 45d d d
59 ?
3 24e e
60 Which equation best describes the
relationship between the corresponding
values of x and y shown in the table?
F 10y x
G 2 6y x
H 3 6y x
J 2 8y x
61 The side length of a square is 3 44x yz
units. What is the area of the square?
62 Which expression describes the area in
square units of a rectangle that has a
width of 3 24x y and a length of 2 33x y ?
F 6 612x y
G 5 512x y
H 6 67x y
J 5 57x y
x y
2 12
0 6
1 3
4 6
63 What is an equation for the line passing
through the point T and having a slope of
2 ?
A 2 2y x T
B 2y x
C 2 2y x
D 2y x
Simplify each of the following assuming
that no denominator is equal to zero.
Leave NO negative exponents.
64 4 9
5 8
9
15
x y
x y 65 3 7x x
66 2 43 5x x 67 2
47 2x
68 Which of the following expression is
equivalent to 312
4
x y
xy?
A 28x
B 23x
C 23x y
D 33x y
69 What is the simplified form of
3
9
3d
?
F 3
9
27d
G 3243d
H 3
1
243d
J 33d
70 Simplify the following: 3
24 5x
71 The area of a triangle is 3 510x y square
units, and the base of the triangle is
35xy units long. What is the triangle’s
height?
F 2 22x y units
G 4 825x y units
H 2 24x y units
J 4 84x y units
Find the missing exponent for the
following:
72 5 ? 11x x x
73 ?
2 83 81x x
74 ? 8 146 7 42x x x
75 ?
3 4 192 6 192x x x
76 What is the volume of a cube with an
edge length of 22
5x units?
A 68 cubic units
125x
B 44 cubic units
25x
C 62 cubic units
5x
D 424 cubic units
25x
77 Which expression describes the area in
square units of a rectangle that has a
width of 34x y and a length
of 2 36x y ?
F 5 410x y
G 6 324x y
H 6 310x y
J 5 424x y
Simplify each expression:
78 0
2
16
4
=
79 4 7
6
4 5
10
x x
x =
80
02 2
2 3
12
2
d ef
de f
=
81 4 63 3 =
82
32 41
3x y
=
83 2 6
1
8x y =
84 Which expression simplifies to 42x ?
A 42x
B
4
32
2x
C 4
1
2x
D 4
8
4x
85 Solve the inequality and graph.
5 10 15 45x x
86 Use the function to find the next 5
terms.
10
.03
NEXT NOW
NOW
87 Write an equation for the table first
using NEXT/NOW notation and then
as an exponential function.
x -1 0 1 2
y 50 10 2 0.4
88 Write an equation for the table first
using NEXT/NOW notation and then
as an exponential function.
x -1 0 1 2
y 25 125 625 3125
89 Use the function to find the next 5
terms.
1
3
9
NEXT NOW
NOW
Simplify the expressions
90 2 6t t
91 2(5 )xy
92 2
6p
93
4
2
s
t
94 3
5 25r r
95
2
0 6 38y x y
96 Write an equation for the list of
values using NEXT/NOW notation
and then use it to find the 8th term.
36 12 4 1.3
97 Solve the system
9 4 26
18 7 22
x y
x y
Identify each function as linear,
exponential growth, or exponential decay
98 1
43
xy 99 1
23
y x
100 .5xy 101 1
43
x
y
102 2 3y x 103 6y x
104 100(.47)xy 105 .47(100)xy
106 The Greens bought a condominium for
$83,000. Assuming that its value will
appreciate 6% per year, how much will
the condo be worth in five years when
they are ready to move again?
For each of the following identify the
growth factor and the growth rate.
107 3(1.68)xy
108 1
32
xy
109 (1 )xy a b
110One computer industry expert reported
that there were about 200,000,000
computers worldwide in 2001 and that
the number was increasing at an
annual rate of about 10%. What is the
number of computers that will be in
use in 2009?
111 Use the function to find the next 5
terms.
4
.5
NEXT NOW
NOW
112 Ten years ago, Mr. and Mrs. Boyce
bought a house for $96,000. The value
of their house appreciated at a steady
rate of 3%. What is the value of their
house now?
113 Identify the function as growth or
decay and write the equation to
model it.
(0, 2) (1, 5)
Use the equation .6(1.1)xy
114 Does it represent exponential
growth or decay?
115 Find the value when x = -4
116 Find the value when x = 2
117 Identify the function as growth or
decay and write the equation to
model it.
118 Identify the function as growth or
decay and write the equation to
model it.
119 A piece of machinery valued at
$2,500 depreciates at a steady rate
of 10% yearly. The owner plans to
replace the equipment after 15
years. What will the depreciated
value be at this time?
120 Shayna has a total of 50 music CDs in
two categories. The number of her
rock CDs is 8 more than twice the
number of her country CDs. Which
system of equations can be used to
find how many rock CDs, r, and
country CDs, c, Shayna has?
A r = 2c
r − 50 = c
B r − c = 50
c = 2r + 8
C r + c = 50
r = 2c + 8
D r + c = 50
c = 2r − 8
121 Identify the function as growth or
decay and write the equation to
model it.
(0, 1) (1, 6)
(0, 1)
(1, .75)
(0, 4)
(1, 1)
122 Write an equation for the table first
using NEXT/NOW notation and then
as an exponential function.
x -1 0 1 2
y 1/8 1/4 1/2 1
Use the equation 2(.75)xy
123 Does it represent exponential
growth or decay?
124 Find the value when x = -4
125 Find the value when x = 2
126 Zeller Industries bought a piece of
weaving equipment for $50,000. It
is expected to depreciate at a steady
rate of 10% per year. What will the
value be after 6 years?
For each of the following identify the
decay factor and the decay rate.
127 3(.68)xy
128 1
.32
xy
129 (1 )xy a b
130 Use the function to find the next 5
terms.
4
16
NEXT NOW
NOW
131 Kyle has saved $500 of the money he
earned working at Carousel Music. If
he spends 10% of the money each
week, how much money will he have
left after 6 weeks?
Simplify the expressions
132
3
1
5z
133
2 5
3 7
(6 )x y
x y
134 4
4x
135 2
2 54 3p p
136
22
16
4
xz
z
Compare each of the following with the
graph of the function
1
8
x
y
137
12
8
x
y 138
1
8
x
y
139
1 1
4 8
x
y 140
13
8
x
y
Tell whether the points would lie on
the graph of an exponential growth or
exponential decay. Write a rule for the
function.
141 0,6 and 1,4.8
142 0,8 and 1,4.8
143 0,6 and 1,12.8
144 Write the equation of the line that
passes through the points (-3,6) and
(5,46).
145 In 2003 a family bought a boat for
$4000. The boat depreciates at a
rate of 7% annually. In 2006 a
person offers to buy the boat for
$3000. Should the family sell the
boat?
Compare each of the following with the
graph of the function 3xy
146 4 3xy 147 2.5 3xy
148 1
34
xy 149 3xy
150 If a population triples each year,
what is the growth factor? Growth
rate?
151 There are 25 students in Ms. Leo’s
math class. The ratio of boys to girls is
2:3. Which equation can be used to
determine g, the number of girls in
Ms. Leo’s class?
A 2 g
=5 25
B 3 g
=5 25
C 2 g
=3 25
D 3 25
=5 g
152 Solve the system
5 2 16
3 4 20
x y
x y
REVIEW
1 Simplify: 2 3y y y
2 Simplify:
3 6
5 9
18
3
a b
a b
3 Simplify:
6 2
5
12
18
x y
x y
4 Simplify: 0
3
14
5
5 Simplify: 8 2 35 3a b a b
6 The area of a rectangle is 3 942x y units
and the width of the rectangle is 2 67x y
units. Write an expression that
describes the length of the rectangle?
7 Simplify: 5
ab
8 Simplify: 3
2 512 s t
9 Simplify:
04
5
13
18
r
r
10 Simplify:
3 4
6 2 5
5
35
a b c
a b c
11 Find the missing exponent for the
following.
A 3 ? 3 13p p p p
B 3 ? 2 84 3 5 60x x x x
C ?
3 96 216x k
D ?
2 112 9 288g g g
12 Simplify: 2 4 3221
3x y x y
13 Simplify:
3
2
8
4h
14 Simplify: 3 2
4 5
2 3
18
a b b
a b
15 Find the area of a square if the length
of a side measures 2 38g h units.
16 Simplify: 3
3 4 2 25a b c ab c
17 A race car driver bought a car for
$85,000. The car will depreciate at a
steady rate of 11% yearly. The owner
plans to drive the car for 5 years.
What will the depreciated value be at
this time? (round to the nearest dollar)
18 Use the function to find the next 5
terms.
.4
25
NEXT NOW
NOW
19 Write an equation for the table first
using NEXT/NOW notation and then
as an exponential function.
x -1 0 1 2
y 18 9 4.5 2.25
20 Identify the function as growth or
decay and write the equation to
model it.
(0, 6)
(1, 2)
21 Use the equation 16(.25)xy
Does it represent exponential
growth or decay?
Find the value when x = 4
Find the value when x = -2
22 Identify the growth factor and the
growth rate.
A 3(1.68)xy B 1
32
xy
23 Eight years ago, Dan & Suzanne
bought land to build a house on near
Possum Kingdom for $230,000. The
value of their land appreciated at a
steady rate of 3%. What is the value
of their land today? (round to the nearest dollar)
24 Compare each of the following with
the graph of the function 2xy
A 1
24
xy B 2.5 2xy
C 4 2xy D 2xy