Beginning Algebra Lial Hornsby McGinnis 11e

Beginning Algebra
Lial Hornsby McGinnis
9 781292 041018
11e
ISBN 978-1-29204-101-8
Beginning Algebra
Lial Hornsby McGinnis
Eleventh Edition
Pearson Education Limited
Edinburgh Gate
Harlow
Essex CM20 2JE
England and Associated Companies throughout the world
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ISBN 10: 1-292-04101-3
ISBN 10: 1-269-37450-8
ISBN 13: 978-1-292-04101-8
ISBN 13: 978-1-269-37450-7
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
Printed in the United States of America
Linear Equations and Inequalities in One Variable
Section 8
1. 7 , 6 1or 6, 72; Ú, … 1or … , Ú2 3. 10, q2 5. x 7 - 4
7. x … 4 9. 1 - q, 44
0
11. 1 - q, - 32
13. 14, q2
4
0
79. R = 5x - 100 81. P = 15x - 1002 - 1125 + 4x2 = x - 225;
0
87. 38, 104
4
– 1
2
0
–11
–2 0
25. It must be reversed when one is multiplying or dividing by a negative
27. 1 - q, 62
0
29. 3 - 10, q2
–10
0 2
31. 1 - q, - 32
–3
33. 1 - q, 04
6
– 11
0
6
3
–2
0
103. C - 24
5 , 0D
–2
0
1
3
–26
6
–30 –20 –10
–3
10
0
0
6
– 24
5
–5
0
105. (a) - 7 (b) 23 107. (a) - 14 (b) 22
109. (a) - 14
5
0
35. 120, q2
0
37. 3 - 3, q2
5
20
–3
39. 1 - q, - 34
1. 566 2. 5- 126 3. 576 4. E 23 F
16. 5206 17. 0 18. 5- 16 19. - 72
–5
12. 546
13. {all real numbers} 14. 5 - 196 15. {all real numbers}
Republicans: 48 21. Hawaii: 6425
45. 1 - q, 12
5. 5116 6. 5176
7. 556 8. 5 - 46 9. 556 10. 5 - 126 11. E 64
5 F
0
–1 0
43. 3 - 5, q2
(b) - 25
Review Exercises
0
–3
41. 1 - 1, q2
0
mi2;
20. Democrats: 70;
Rhode Island: 1212 mi2
22. Seven Falls: 300 ft; Twin Falls: 120 ft 23. 80° 24. 11, 13
25. h = 11 26. a = 28 27. r = 4.75 28. V = 904.32
47. 1 - q, 04
0
49. A - 12, q B
– 1
1
29. h =
0
a
b
30. h =
2a
b + B
31. 135°; 45° 32. 100°; 100°
33. 2 cm 34. diameter: approximately 19.9 ft; radius: approximately
9.95 ft; area: approximately 311 ft 2 35. 42.2°; 92.8° 36.
2
37.
0 1
51. 34, q2
97. 11, 32
101. 3 - 3, 64
6
4
–1 0
99. 3 - 26, 64
number.
10
0
2
95. A - 11
6 , - 3B
5
23. 1 - q, - 112
5
–3
93. 3 - 1, 64
0 1
10
0
91. 1 - 3, 42
–1 0
21. 35, q2
8
89. 10, 104
0
19. 31, q2
5
14
38.
3
4
39.
E 72 F
40. E -
8
3F
3
2
41. $3.06 42. 375 km
43. 10 bronze medals 44. 25.5 oz; $0.137 45. 6 46. 175%
53. 1 - q, 322
0
4
0
47. 2500 48. 3.75 L 49. $5000 at 5%; $5000 at 6%
8
32
5
12
5 q
55. C 12
, B
57. 1 - 21, q2
176
67. x … 20 69. 83 or greater 71. all numbers greater than 16
73. It is never less than - 13°F. 75. 32 or greater 77. 15 min
–3
17. C - 12, q B
60. 14, q2
1 2 3 4 5 6 7
62. The graph is the set of all real numbers. 63. x Ú 18 65. x 7 5
x 7 225 83. - 1 6 x 6 2 85. - 1 6 x … 2
15. 1 - q, 04
59. 546
61. 1 - q, 42
53. 3 - 4, q2
54. 1 - q, 72
0 1
–21
50. 8.2 mph 51. 13 hr 52. 2 12 hr
–7 0
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
55. 3 - 5, 62
–4
0
0
7
–5
56. B 57. 3 - 3, q2
0
6
–3
0
Linear Equations and Inequalities in One Variable
58. 1- q, 22
79. 8 qt
0
59. 33, q2
0
60. 346, q2
61. 1- q, - 52
–5
5D
0
P - 2L
(b) 18
2
10. 75°, 75° 11. 566 12. 5 - 296 13. 32 oz; $0.250
Kauai: 551 mi2 8. 50° 9. (a) W =
–4
0
3
2
63. C - 2, 32 D
64.
1. 5 - 66 2. 5216 3. 0 4. 5306 5. 5all real numbers6
40 46
6. wins: 100; losses: 62 7. Hawaii: 4021 mi2; Maui: 728 mi2;
62. 1- q, - 42
A 43,
Test
3
0 10
–2
0
1
14. 2300 mi 15. $8000 at 3%; $14,000 at 4.5% 16. 4 hr
17. 1- q, 44
2
18. 1- 2, 64
4
3
0 1
2
5
65. 88 or more 66. all numbers less than or equal to - 13
I
68. r =
pt
80. faster train: 80 mph; slower train: 50 mph 81. 44 m
82. 50 m or less
2
69. 1 - q, 22 70. 5- 96 71. 5706 72.
74. 5all real numbers6 75. $304
76. 4000 calories
Gate Bridge: 4200 ft; Brooklyn Bridge: 1596 ft
67. 576
E 134 F
0
–2
4
0
6
19. 83 or more 20. When an inequality is multiplied or divided by a
negative number, the direction of the inequality symbol must be reversed.
73. 0
77. Golden
78. 100 oz; $0.060
177
178
Linear Equations and
Inequalities in Two
Variables; Functions
1
Linear Equations
in Two Variables;
The Rectangular
Coordinate System
2
Graphing Linear
Equations in Two
Variables
3
The Slope of a Line
4
Writing and
Graphing Equations
of Lines
5
Graphing Linear
Inequalities in Two
Variables
6
Introduction to
Functions
Deklofenak/Shutterstock
Summary Exercises on
Linear Equations and
Graphs
In recent years, college students, like U.S. consumers as a whole, have increased their
dependency on credit cards. In 2008, 84% of undergraduates had at least one credit
card, up from 76% in 2004. The average (mean) outstanding balance for undergraduates grew from $946 in 2004 to a record-high $3173 in 2008, with 92% of these
students using credit cards to pay direct education expenses. (Source: Sallie Mae.)
In Example 7 of Section 2, we examine a linear equation in two variables that
models credit card debt in the United States.
From Chapter 3 of Beginning Algebra Eleventh Edition, Margaret L. Lial, John Hornsby and Terry McGinnis. Copyright © 2012 by Pearson
Education, Inc. All rights reserved.
179
Linear Equations and Inequalities in Two Variables; Functions
Linear Equations in Two Variables;
The Rectangular Coordinate System
1
2
3
4
5
6
Interpret graphs.
Write a solution as
an ordered pair.
Decide whether a
given ordered pair
is a solution of a
given equation.
Complete ordered
pairs for a given
equation.
Complete a table
of values.
Plot ordered pairs.
NOW TRY
EXERCISE 1
Refer to the line graph in
FIGURE 1 .
(a) Estimate the average price
of a gallon of gasoline in
2006.
(b) About how much did the
average price of a gallon
of gasoline increase from
2006 to 2008?
OBJECTIVE 1 Interpret graphs. A line graph is used to show changes or trends
in data over time. To form a line graph, we connect a series of points representing
data with line segments.
EXAMPLE 1
Interpreting a Line Graph
The line graph in FIGURE 1 shows average prices of a gallon of regular unleaded gasoline in the United States for the years 2001 through 2008.
Average U.S. Gasoline Prices
3.40
3.20
3.00
2.80
2.60
2.40
2.20
2.00
1.80
1.60
1.40
1.20
0
'01 '02 '03 '04 '05 '06 '07 '08
Year
Source: U.S. Department of Energy.
FIGURE 1
Gmosher/iStockphoto
OBJECTIVES
Price (in dollars per gallon)
1
(a) Between which years did the average price of a gallon of gasoline decrease?
The line between 2001 and 2002 falls, so the average price of a gallon of gasoline decreased from 2001 to 2002.
(b) What was the general trend in the average price of a gallon of gasoline from 2002
through 2008?
The line graph rises from 2002 to 2008, so the average price of a gallon of gasoline increased over those years.
NOW TRY ANSWERS
1. (a) about $2.60
(b) about $0.65
180
(c) Estimate the average price of a gallon of gasoline in 2002 and 2008. About how
much did the price increase between 2002 and 2008?
Move up from 2002 on the horizontal scale to the point plotted for 2002. Looking across at the vertical scale, this point is about three-fourths of the way between
the lines on the vertical scale for $1.20 and $1.40. Halfway between the lines for
$1.20 and $1.40 would be $1.30. So, it cost about $1.35 for a gallon of gasoline in
2002.
Similarly, move up from 2008 on the horizontal scale to the point plotted for
2008. Then move across to the vertical scale. The price for a gallon of gasoline in
2008 was about $3.25.
Between 2002 and 2008, the average price of a gallon of gasoline increased by
about
$3.25 - $1.35 = $1.90.
NOW TRY