SOLUTION MANUAL |
Finite Mathematics & Its Applications
| | | |
13th Edition by Larry J. Goldstein,
| | | | |
Chapters 1 - 12, Complete
| | | |
, Contents
Chapter 1: Linear Equations and Straight Lines
| | | | | 1–1
Chapter 2: Matrices
| 2–1
Chapter 3: Linear Programming, A Geometric Approach
| | | | | 3–1
Chapter 4: The Simplex Method
| | | 4–1
Chapter 5: Sets and Counting
| | | 5–1
Chapter 6: Probability
| 6–1
Chapter 7: Probability and Statistics
| | | 7–1
Chapter 8: Markov Processes
| | 8–1
Chapter 9: The Theory of Games
| | | | 9–1
Chapter 10: The Mathematics of Finance
| | | | 10–1
Chapter 11: Logic
| 11–1
Chapter 12: Difference Equations and Mathematical Models
| | | | | 12–1
, Chapter 1 |
Exercises |1.1 5
6. | Left |1, |down |
2
1. Right |2, |up |3 y
y
(2, |3)
x
x
( )
–1, | – |52|
7. | Left |20, |up |40
2. Left |1, |up |4 y
y
(–20, |40)
(–1, |4)
x
x
8. | Right |25, |up |30
3. | Down |2 y
y
(25, |30)
x
x
(0, |–2)
9. Point |Q |is |2 |units |to |the |left |and |2 |units |up |or
4. Right |2
y (—2,|2).
10. Point |P |is |3 |units |to |the |right |and |2 |units |down |or
(3,—2).
x
(2, |0) 1|
11. —2(1) |+ | (3) |=|—2 |+1|= |—1so | yes | the | point | is
3
on |the |line.
5. Left |2, |up |1 1|
y 12. —2(2) |+ | (6) |= |—1 |is | false, | so | no | the | point | is | not
3
on |the |line
(–2, |1)
x
Copyright |© |2023 |Pearson |Education, |Inc. 1-1
, Chapter |1: |Linear |Equations |and |Straight |Lines ISM: |Finite |Math
1| 24. | 0 |= |5
13 —2x |+ | y | = |—1 | Substitute | the | x | and | y no |solution
3
. x-intercept: |none
coordinates |of |the |point |into |the |equation:
|When |x |= |0, |y |=
f 1 | ıh| f h
' ,|3 →|—2 ' 1 ı +|1|(3)|=|—1|→|—1+1|=|—1 | is |5|y-intercept: |(0,
y' ı '
|5)
ı
| 2 | | |J y|2J 3
a |false |statement. |So |no |the |point |is |not 25. |When |y |= |0, |x |=
|on |the|line. |7 |x-intercept: |(7,
|0)|0 |= |7
f 1h f1 h
14 —2 ' ı + ' ı (—1) |=|—1 | is |true |so |yes |the |point |is no |solution
.
'y3 ıJ | | |'y3 ıJ y-intercept: |none
on |the |line. 26. | 0 |= |–8x
15. | m |= |5, |b |= |8 x |= |0
x-intercept: |(0, |0)
16. | m |= |–2 |and |b |= |–6 y |= |–8(0)
y |= |0
17. | y |= |0x |+ |3; |m |= |0, |b y-intercept: |(0, |0)
|= |3
2| 2| 1|
y |= | x|+|0; | m |= | , | b |= |0 27 0 |= | x |–|1
18 3
3 3 .
. x |= |3
19. | 14x|+|7|y |=|21 x-intercept: |(3, |0)
1|
7|y |=|—14x |+|21 y | = | (0) |–|1
3
y | =|—2x |+|3
y |= |–1
y-intercept: |(0, |–1)
20 x|— |y | =|3 y
. —y | =|—x |+|3
y | = |x|—|3
(3, |0)
21. | | | 3x |=|5 x
5 (0, |–1)
x |= |
3
1 2
28. When |x |= |0, |y |= |0.
22 – x |+ y | =|10
. 2 3 When |x |= |1, |y |= |2.
2| 1| y
y | = | x |+10
3 2
3|
y | = | x |+15 (1, |2)
4 x
(0, |0)
23. 0 |=|—4x |+|8
4x | = |8
x |= |2
x-intercept: |(2, |0)
y |= |–4(0) |+ |8
y |= |8
1-2 Copyright |© |2023 |Pearson |Education, |Inc.
Finite Mathematics & Its Applications
| | | |
13th Edition by Larry J. Goldstein,
| | | | |
Chapters 1 - 12, Complete
| | | |
, Contents
Chapter 1: Linear Equations and Straight Lines
| | | | | 1–1
Chapter 2: Matrices
| 2–1
Chapter 3: Linear Programming, A Geometric Approach
| | | | | 3–1
Chapter 4: The Simplex Method
| | | 4–1
Chapter 5: Sets and Counting
| | | 5–1
Chapter 6: Probability
| 6–1
Chapter 7: Probability and Statistics
| | | 7–1
Chapter 8: Markov Processes
| | 8–1
Chapter 9: The Theory of Games
| | | | 9–1
Chapter 10: The Mathematics of Finance
| | | | 10–1
Chapter 11: Logic
| 11–1
Chapter 12: Difference Equations and Mathematical Models
| | | | | 12–1
, Chapter 1 |
Exercises |1.1 5
6. | Left |1, |down |
2
1. Right |2, |up |3 y
y
(2, |3)
x
x
( )
–1, | – |52|
7. | Left |20, |up |40
2. Left |1, |up |4 y
y
(–20, |40)
(–1, |4)
x
x
8. | Right |25, |up |30
3. | Down |2 y
y
(25, |30)
x
x
(0, |–2)
9. Point |Q |is |2 |units |to |the |left |and |2 |units |up |or
4. Right |2
y (—2,|2).
10. Point |P |is |3 |units |to |the |right |and |2 |units |down |or
(3,—2).
x
(2, |0) 1|
11. —2(1) |+ | (3) |=|—2 |+1|= |—1so | yes | the | point | is
3
on |the |line.
5. Left |2, |up |1 1|
y 12. —2(2) |+ | (6) |= |—1 |is | false, | so | no | the | point | is | not
3
on |the |line
(–2, |1)
x
Copyright |© |2023 |Pearson |Education, |Inc. 1-1
, Chapter |1: |Linear |Equations |and |Straight |Lines ISM: |Finite |Math
1| 24. | 0 |= |5
13 —2x |+ | y | = |—1 | Substitute | the | x | and | y no |solution
3
. x-intercept: |none
coordinates |of |the |point |into |the |equation:
|When |x |= |0, |y |=
f 1 | ıh| f h
' ,|3 →|—2 ' 1 ı +|1|(3)|=|—1|→|—1+1|=|—1 | is |5|y-intercept: |(0,
y' ı '
|5)
ı
| 2 | | |J y|2J 3
a |false |statement. |So |no |the |point |is |not 25. |When |y |= |0, |x |=
|on |the|line. |7 |x-intercept: |(7,
|0)|0 |= |7
f 1h f1 h
14 —2 ' ı + ' ı (—1) |=|—1 | is |true |so |yes |the |point |is no |solution
.
'y3 ıJ | | |'y3 ıJ y-intercept: |none
on |the |line. 26. | 0 |= |–8x
15. | m |= |5, |b |= |8 x |= |0
x-intercept: |(0, |0)
16. | m |= |–2 |and |b |= |–6 y |= |–8(0)
y |= |0
17. | y |= |0x |+ |3; |m |= |0, |b y-intercept: |(0, |0)
|= |3
2| 2| 1|
y |= | x|+|0; | m |= | , | b |= |0 27 0 |= | x |–|1
18 3
3 3 .
. x |= |3
19. | 14x|+|7|y |=|21 x-intercept: |(3, |0)
1|
7|y |=|—14x |+|21 y | = | (0) |–|1
3
y | =|—2x |+|3
y |= |–1
y-intercept: |(0, |–1)
20 x|— |y | =|3 y
. —y | =|—x |+|3
y | = |x|—|3
(3, |0)
21. | | | 3x |=|5 x
5 (0, |–1)
x |= |
3
1 2
28. When |x |= |0, |y |= |0.
22 – x |+ y | =|10
. 2 3 When |x |= |1, |y |= |2.
2| 1| y
y | = | x |+10
3 2
3|
y | = | x |+15 (1, |2)
4 x
(0, |0)
23. 0 |=|—4x |+|8
4x | = |8
x |= |2
x-intercept: |(2, |0)
y |= |–4(0) |+ |8
y |= |8
1-2 Copyright |© |2023 |Pearson |Education, |Inc.
