CHAPTER 1 REVIEW SECTION 1.1 The Language of Algebra 1... Full file at https://TestbankDirect.eu/... So the radius is 4 in... Full file at https://TestbankDirect.eu/... The angles are
Trang 1CHAPTER 1 REVIEW
SECTION 1.1
The Language of Algebra
1 a C = 2t + 15
b
w
l= 25
c P = u – 3
2
3 w – 43
4 1( 10)
3 x−
SECTION 1.2
The Real Number System
5 a 7
b 0, 7
6 a –5, 0, 7
b –5, 0, 2.4, 7, 2, 3.6,15
7 a − 3, , π 0.13242368
b all
8 a 5, 3, 2, 3.6
3
b 2.4, 7, π,
4
15 , 0.13242368…
9 a 7
b none
10 a 0
b –5, 7
11
12
13 a false
14 a false
b true
15 a –16 > –17
b – (–1.8) <
2
1
2
16 a false
b true
17 −18 =18
18 − −6.26 =−6.26
SECTION 1.3
Operations with Real Numbers
19 –13 + (–14) = –27
20 –70.5 + 80.6 = 10.1
21 1 1 1 2 1
− − = − i −
2 1
4 4 3 4
= − −
= −
22 –6 – (–8) = –6 + 8
= 2
23 (–4.2)( –3.0) = 12.6
10 16 160
1
32
= −
25 0.2 11
2
2 =
−
−
p T = 30p
6.0 30(6.0) = 180 6.5 30(6.5) = 195 7.0 30(7.0) = 210 7.5 30(7.5) = 225 8.0 30(8.0) = 240
3 4
7 2.75 3
2.3 Full file at https://TestbankDirect.eu/
Trang 226 9 21 9 1
− ÷ = − ⋅
3
56
= −
27 15 – 25 – 23 = –10 – 23
28 –3.5 + (–7.1) + 4.9 = –10.6 + 4.9
29 –3(–5)( –8) = 15(–8)
30 –1(–1)( –1)( –1) = 1(–1)( –1)
= –1(–1) = 1
31 (–3)5 = –243
32 2 ( )2
2
2 2
−
⎛− ⎞ =
4 81
=
33 ( )3
0.4 =0.064
34 –52 = – (5)(5) = –25
35 4= 2
36 − 100=−10
25 = 25 3 5
=
38 0.64 =0.8
39 − + −6 2( 5)2= − +6 2(25)
6 50 44
= − +
=
40 20 ( )( )3 2 ( )1 5 6 1( )
4
−
5 6 1
= − +
=
41 4 (5 9)− − 2= − −4 ( 4)2
4 16 12
= −
= −
42 4 6[ 1 5(25 3 )] 4 6[ 1 5(25 27)]+ − − − 3 = + − − −
4 6[ 1 5( 2)]
4 6[ 1 10]
4 6[9]
4 54 58
= + − − −
= + − +
= +
= +
=
43 2 1.3 ( 2.7)− + − = − 2 4
2(4) 8
=
=
44 ( )
36 4 1
=
( )2
1 32
36 5 33
36 25 33 11 3
+
=
−
=
−
=
=
45 ( )3 6 ( ) ( )( )( )
2
−
−
3,000 1( )
3,000
=
46 − − ⋅( 2 4)2÷ ⋅ = − −8 2 ( 8)2÷ ⋅ 8 2
64 8 2
8 2 16
= − ÷ ⋅
= − ⋅
= −
47 ( ) ( 2 2) ( ) ( ) ( )( ) ( ) ( 2 2)
( )( )
2 4 8 16
2 28 56
=
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Trang 348
2
2 4 ( 3) ( 3) 4(2)( 2)
a
3 9 16 4
3 25 4
3 5 4 2 4 1 2
− +
=
−
=
−
=
−
=
= −
SECTION 1.4
Simplifying Algebraic Expressions Using
Properties of Real Numbers
49 3(x + 7) = 3x + 21
50 t · 5 = 5t
51 –x + x = 0
52 (27 + 1) + 99 = 27 + (1 + 99)
53 8 1
8
1
=
⋅
54 0 + m = m
55 1 · 9.87 = 9.87
56 5(–9)(0)(2,345) = 0
57 (–3 · 5)2 = –3(5 · 2)
58 (t + z) · t = (z + t) · t
102
102 =
125 −=
−
60 a 0
6
0 =
0
88
61 8(9x + 6) = 72x + 48
62 –(6y – 2) = –6y + 2
63 (3x – 2y)1.2 = 3.6x – 2.4y
4
3 3 6 1 4 8 4
3 c2 − c+ = c2 − c+
65 8(6k) = 48k
66 (–7.5x)( –10y) = 75xy
67 –9(–3p)( –7) = –189p
68 15a + 7 + 30a + 9 = 45a + 16
69 3g2 + g2 – 3g2 – g2 = 0
70 –m+4(m–12n) – (–8n) = –m + 4m – 48n + 8n
= 3m – 40n
5x−4x= ⋅5 4x− ⋅4 5x
13 20
x
=
72 21.45l – 45.99l = –24.54l
73 4⎡⎣−2(a3−a2) (−2 3a2−6a3)⎤⎦
4 10 4
74 3(2 9) 5( 1) 6 27 5 5
4 h+ −4 h− =4h+ 4 −4h+ 4
1 8 4
h h
SECTION 1.5
Solving Linear Equations Using Properties of Equality
75 6 – x ≟ 2x + 24
6 – (–6) ≟ 2(–6) + 24
6 + 6 ≟ –12 + 24
12 = 12 Yes, –6 is a solution
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Trang 476 ( 3) 12
3
5 x− =−
( 3) 12 3
−
−
− 6
( )9 12 3
−
−
-15 ≠ -12
No, –6 is not a solution
77
45 5
5 225
x x x
= −
⎛ ⎞ = −
⎜ ⎟
⎝ ⎠
= −
78
3.67 4.23 3.67 3.67 4.23 3.67
7.9
t t
t
=
79
0.0035 0.25 0.0035 0.25 0.25 0.25 0.014
g g g
=
=
=
80
4 4
x x x x
= +
− = + −
− =
= −
81
12 5
x x x x
x
− = −
− = −
− = −
=
82
9 3
27 3 3
27 3
7 20 7 7 3
20 7 3
20 7
2
20 7
2
5 20 6 7 3
−
=
−
=
−
−
=
−
+
= +
−
−
=
−
−
− +
=
−
−
−
+
=
−
−
− +
= +
−
−
x x x x x
x x
x x
x x
x x
x x
83
( ) ( )
4 1 1 25 1
6
y y y y y y y
= −
84
5 3 2 13 13 17 18
5 3 13 15 17 18
5 39 45 17 18
39 50 17 18
21 50 17
21 50 50 17 50
11 7
x x
x x
x
= Full file at https://TestbankDirect.eu/
Trang 585
34 200 200 24 200
34 176
34 176
88 17
x x
x x
x
=
=
=
86
12 13
156 13 13
156 13
168 12 168 168 13
12 168 13
4 12 4 4 168 9
12 4 168 9
1 3 12 14 4
3 12
1 3
14 4 3
=
=
=
+
−
= +
−
−
=
−
+
−
−
= +
−
−
−
=
−
⎟
⎠
⎞
⎜
⎝
⎛− −
=
⎟
⎠
⎞
⎜
⎝
−
−
=
−
y y y y
y
y y
y y
y y
y y
y y
87
06 0 1
06 0 1
06 0
=
−
−
=
−
−
−
=
−
k k k
88
5 10 4
10
8
p p p
= −
= −
= −
89
0 6
0 6 6
0 6
3 3 3 3 6
3 3 6
3 3
7
3 3 7
3 5 2 8
3 ) 5 ( ) 1 4 ( 2
6
3 6 6
5 3
1 4 6
6
3 6
5 3
1 4
=
=
=
+
−
= +
−
−
=
−
−
−
=
−
−
−
=
−
−
=
−
− +
−
= +
− +
⎟
⎠
⎞
⎜
⎝
⎛ −
=
⎟
⎠
⎞
⎜
⎝
−
= +
− +
t t t t t
t t t t
t t
t t t
t t
t
t t
t
t t t
90
3
5 1
5 4 5 1
5 1
5 4 5 1
6 3 9 0 6 3 5 1 6 3
9 0 5 1 6 3
9 0 5 1 5 37 9 33
9 0 ) 3 75 ( 5 0 9 33
=
=
=
+
= + +
−
= +
−
= +
−
=
−
−
x x x x x x x
91
x x x
x
x x
x x
2 2 10 2 12 2
2 10 12 2
2 10 ) 6 ( 2
− +
=
−
−
+
=
−
+
=
−
–12≠10
no solution, ∅; contradiction
92
1 1
3 1 3 3 1 3
1 3 1 3
1 3 1 2 5
) 1 3 ( 1 2 5
−
=
−
+
−
−
= +
−
−
−
−
=
−
−
−
−
=
− +
−
+
−
=
− +
−
x x
x x
x x
x x
x
x x
x
all real numbers, ℝ; identity
SECTION 1.6
Solving Formula; Geometry
93 10.5 12.5 3.5 4.5 31 ft+ + + = Full file at https://TestbankDirect.eu/
Trang 694 C d= π
17 3.14159( )
53.41 cm
≈
≈
2
A=πr
( )
2
2
2
2
2 17 2 8.5 72.25 3.14159 72.25 226.98 cm
d
π
π π π
⎛ ⎞
= ⎜ ⎟⎝ ⎠
⎛ ⎞
= ⎜ ⎟⎝ ⎠
=
=
≈
≈
3
V = πr
( )
3
3
4 7.5 3 4 421.875 3
4 3.14159 421.875 3
1,767.15 m
π
π
=
=
≈
≈
96 a A= s2
2
2
10
100 in
=
=
3
V = πr h
Find the diameter: 10 – 1 – 1 = 8 in
So the radius is 4 in
( ) ( ) ( )( )
2
3
1
4 15 3
1
16 15 3
1 240 3 80 251.3 in
π
π π
=
=
=
=
≈
97 1 2
for 3
V = πr h h
2 2 2
2
2
1
3 3
3
3
3
V r h
V h r V h r
π π π
π
π
⋅ = ⋅
=
=
=
=
98
0 for 2
0
0
0
0 2 2
0
2 2 0
2 2 0
2 2
2 2 2
2
2
K
Mv
K Iw
K Iw
M v
K Iw M
v
+
⋅ = ⋅
−
=
−
=
−
=
99 = +a (n−1) for d d
( 1) ( 1) ( 1) ( 1)
1
1
a d n
a d n
=
− =
−
−
=
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Trang 7100 9x−5y=35 for y
9 7 5 9 7 5
= − +
SECTION 1.7
Using Equations to Solve Problems
101
O’Hare x million
Atlanta (x + 20.7) million
Total 159.3 million
( 20.7) 159.3
2 20.7 159.3
10 2 20.7 10 159.3
20 207 1,593
20 207 207 1,593 207
20 1,386
20 1,386
69.3 20.7 90.0
x x x x x x
x x x x
=
=
=
O’Hare served 69.3 million passengers and Atlanta served 90.0 million
102 245 – 5c
103
Item stored
number sold
cost of storage for 1
total cost of storage
computers x + 150 $2.50 2.50(x+150)
printer cost + computer cost=total storage cost
1.50 2.50 150 2,775
10 1.5 2.5 150 10 2,775
15 25 3,750 27,750
40 3,750 27,750
40 3,750 3,750 27,750 3,750
40 24,000
40 24,000
600
x x
x x x
=
=
=
There are 600 printers in the warehouse
104
1st piece x
2nd piece x + 3
3rd piece (x + 3) + 3 = x + 6
4th piece (x + 6) + 3 = x + 9
Total length 186
51 9
48 6
45 3 42 4
168 4 4
168 4
18 186 18 18 4
186 18 4
186 ) 9 ( ) 6 ( ) 3 (
= +
= +
= +
=
=
=
−
=
− +
= +
= + + + + + +
x x x x x x x
x
x x
x x
The lengths of the cable are 42 ft, 45 ft,
48 ft, and 51 ft
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Trang 8105 The angles are supplementary (sum is
180°)
1st angle x
2nd angle
15 2
1 −x
Sum 180 1
15 180 2
3
15 180 2
3
15 15 180 15 2
3 195 2
195
130 1
15 50 2
x x
x x x x
+⎜ − ⎟=
=
=
=
The angle measures are 50° and 130°
106 Let width = x
Then the length = x + 13
134 2 26 2
134 4 26
134 26 4 26 26
108 4
108 4
27 27
13 40
x x x x x x x
=
=
=
=
The dimensions are 27 in by 40 in
SECTION 1.8
More About Problem Solving
107 99 is 80% of what?
99 0.80
99 0.80
99 0.80 0.80 0.80 123.75
124
x x x x x
=
=
=
≈
It has been recorded about 124 days
108 Let x = percent of markdown
new fee 375 original fee 550 markdown x · 550
new fee = original fee – markdown
375 550 550
375 550 550 550 550
175 550
175 550
0.318
0.32
x x x x
x x
=
≈ The markdown is 32% of the original registration fee
109 Let x = percent of decrease
# sold in 2007 290,282
# sold in 2008 235,924
% decrease x · 290,282
# sold 06 = # sold 05 – % Decrease
235,924 290,282 290,282 235,924 290,282 290,282 290,282 290,282
54,358 290,282 54,358 290,282 290,282 290,282 0.187
18.7%
x x x
x x
x
=
= The percent decrease is 18.7%
110 Let x = percent of increase
# sold in 2007 193,900
# sold in 2008 198,309
% increase x · 193,900
# sold 08 = # sold 07 + % Increase
198,309 193,900 193,900 198,309 193,900 193,900 193,900 193,900
4,409 193,900 4,409 193,900 193,900 193,900 0.023
2.3%
x x x
x x x
=
=
=
= The percent increase is 2.3%
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Trang 9111
Account Principal · Rate · Time = Interest
10% x 0.10 1 0.10x
9% 25,000 – x 0.09 1 0.09(25,000-x)
Combined
Interest 2,430
10% Int + 9% Int = Combined Int
000 , 7 000 , 25
000 , 18
01 0
180 01 0
01 0
180 01 0
250 , 2 2,430 250
, 2 250 , 2 01 0
2,430 250
, 2 01 0
2,430 09
0 250 , 2 10 0
2,430 )
000 , 25 ( 09 0 10 0
=
−
=
=
=
−
=
− +
= +
=
− +
=
− +
x x x x x
x
x x
x x
She invested $18,000 at 10% and $7,000 at 9%
112
Rate · Time = Distance
celebrity 1 t t photographer 1.5 t – 1 1.5(t–1)
Since the photographer will catch the celebrity, the distances for both will be the same (equal)
Celebrity Distance = Photographer Distance
1.5( 1) 1.5 1.5 1.5 1.5 1.5 1.5 0.5 1.5
0.5 1.5 0.5 0.5 3
1 2
t t
t t
=
− =
The photographer will catch the celebrity
in 2 minutes
113
Amount · Strength = Pure concentrate 4% pesticide x 0.04 0.04x
12% pesticide 20 0.12 0.12(20) 10% solution x + 20 0.10 0.10(x + 20)
0.04 0.12(20) 0.10( 20) 0.04 2.4 0.10 2
100 0.04 2.4 100 0.10 2
6 240 200
6 240 240 200 240
20 3 2 6 3
x x
x x
x x
− = −
− = −
=
= 2
6
3 gallons of the 4% solution are needed
114
Type of Coffee Pounds · Price = Value
Robust 90 – x 8.40 8.40(90 – x)
mild value + robust value = mixture value
7.50 8.40 90 7.90 90 7.5 756 8.4 711
10 7.5 756 8.4 10 711
75 7,560 84 7,110
9 7,560 7,110
9 7,560 7,560 7,110 7,560
50
40
x x
x x x x
− = −
=
=
=
He needs 50 pounds of mild coffee and 40 pounds of robust coffee
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