Deck 6: Systems of Linear Equations and Inequalities

Question 1

Find the value of the objective function z = 2x - 2y at each of the vertices and and then state the maximum and minimum values of the function.

A) maximum 10, minimum -16
B) maximum -16, minimum 10
C) maximum 10, minimum 16
D) maximum 16, minimum -16

Answer 1

maximum 10, minimum -16

Question 2

Find the value of the objective function z = 2x + 6y at each of the vertices and and then state the maximum and minimum values of the function.

A) maximum 54, minimum 48
B) maximum -48, minimum 54
C) maximum 54, minimum -48
D) maximum -48, minimum -54

Answer 2

maximum 54, minimum -48

Question 3

Find the value of the objective function z = 4x - 2y at each of the vertices and and then state the maximum and minimum values of the function.

A) maximum -32, minimum 32
B) maximum 20, minimum 32
C) maximum -32, minimum 20
D) maximum 20, minimum -32

Answer 3

maximum 20, minimum -32

Question 4

Find the value of the objective function z = 8x + 4y at each of the vertices and and then state the maximum and minimum values of the function.

A) maximum -28, minimum -68
B) maximum -28, minimum 68
C) maximum 68, minimum -28
D) maximum -28, minimum 28

Question 5

Maximize z = 4x + 3y subject to:

A) maximum 0
B) maximum 16
C) maximum 28
D) maximum 12

Question 6

Maximize z = 2x + 5y subject to:

A) maximum 6
B) maximum -6
C) maximum -15
D) maximum 15

Question 7

Find the value of the objective function z = 6x - 5y at each of the vertices and and then state the maximum and minimum values of the function.

Question 8

Maximize z = 6x - 3y subject to:

Question 9

Maximize z = -5x - 6y

Question 10

Minimize z = 8x + 2y

Question 11

Maximize z = 9x + 5y

A) 74
B) 20
C) 62
D) 32

Question 12

Minimize z = -8x - 5y

A) 32
B) 0
C) 33
D) 1

Question 13

Graph the linear inequality.

Question 14

Graph the linear inequality.

A)

B)

C)

D)

Question 15

Match the graph to the linear inequality.

A)
B)
C)
D)

Question 16

Graph the system of inequalities.

Question 17

Graph the system of inequalities.

A)

B)

C)

D)

Question 18

Match the graph to the system of inequalities.

A)

B)

C)

D)

Question 19

Graph the system of inequalities.

Question 20

Graph the system of inequalities.

A)

B)

C)

D)

Question 21

Match the graph to the system of inequalities.

A)

B)

C)

D)

Question 22

Graph the system of inequalities.

Question 23

Graph the system of inequalities.

A)

B)

C)

D)

Question 24

Match the graph to the system of inequalities.

A)

B)

C)

D)

Question 25

Employ the following supply and demand equations.

Write a system of linear inequalities corresponding to the consumer surplus.

Question 26

Employ the following supply and demand equations.

Write a system of linear inequalities corresponding to the consumer surplus.

A) P ? 261 - 0.04x; P ? 198; x ? 0
B) P ? 55 + 0.09x; P ? 198; x ? 0
C) P ? 261 - 0.04x; P ? 198; x ? 0
D) P ? 261 - 0.04x; P ? 198; x ? 0

Question 27

Employ the following supply and demand equations.

Write a system of linear inequalities corresponding to the producer surplus.

Question 28

Employ the following supply and demand equations.

Write a system of linear inequalities corresponding to the producer surplus.

A) P ? 122 - 0.05x; P ? 83; x ? 0
B) P ? 122 - 0.05x; P ? 83
C) P ? 52 + 0.04x; P ? 83; x ? 0
D) P ? 52 + 0.04x; P ? 83; x ? 0

Question 29

Graph the system of inequalities.

Question 30

Find the solution to the system of inequalities.
2x + 4y < 7
4y ≥ 15 - 2x

Question 31

Find the solution to the system of inequalities.
5x + 2y < 5
2y < 13 - 5x

Question 32

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 33

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 34

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 35

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 36

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 37

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 38

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 39

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 40

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 41

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 42

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 43

Select the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A)
B)
C)
D)

Question 44

Write the partial fraction decomposition for the given rational expression.

A)
B)
C)
D)

Question 45

Write the partial fraction decomposition for the given rational expression.

A)
B)
C)
D)

Question 46

Write the partial fraction decomposition for the given rational expression.

A)
B)
C)
D)

Question 47

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

Question 48

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

Question 49

Write the partial fraction decomposition for the given rational expression.

Question 50

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

Question 51

Write the partial fraction decomposition for the given rational expression.

Question 52

Write the partial fraction decomposition for the given rational expression.

Question 53

Solve the system of linear equations for a, b, and c.
6a - 4b + 7c = 652
A + 7b - 2c = -33
6a - 5b + 8c = 73

A) (-4, -5, 3)
B) ( 3, -5, 4)
C) (4, -5, 3)
D) (-5, 3, 4)

Question 54

Solve the system of linear equations for k, m, and n.
4k + 3m - 3n = 10
5k - 5m - 2n = 30
3k - 2m - 8n = 49

A) (1, -3, -5)
B) (1, 3, -5)
C) (-5, -3, 1)
D) (-5, 3, 1)

Question 55

Solve the system of linear equations for s, t, and u.
6s - 7t + 4u = 19
7s + 6t + 4u = -21
7s - 8t + 2u = 19

A) (1, -3, -1)
B) (-1, 1, -3)
C) (-3, -1, 1)
D) (-1, -3, 1)

Question 56

Solve the linear system of equations for k, m, and n.
-6k - 3m + 4n = -21
-4k + 5m - 2n = -21
-3k - 8m - 8n = -47

A) (1, 5, 3)
B) (3, 1, 5)
C) (5, 1, 3)
D) (5, 3, 1)

Question 57

Ocean Beach Financial Planning offers three types of investments: low-risk, medium-risk, and high-risk. A customer decides to invest $6600 and is given three options for investing in the three funds. Determine the interest rate percentage for the low-risk, l, medium-risk, m, and high-risk, h, investments based on the interest earned for each option in the first year.
$300l + $750m + $5550h = $429.00
$500l + $1150m + $4950h = $409.00
$350l + $1200m + $5050h = $417.00

A) (2%, 6%, 8%)
B) (0%, 4%, 6%)
C) (1%, 5%, 7%)
D) (7%, 5%, 1%)

Question 58

Solve the system of linear equations for v, w, and x.
-4v - 5w + 8x = 14
8v - 8w - 2x = 122
7v + 4w + 6x = 64

Question 59

An object is thrown upward, and the following table depicts the height of the ball t seconds after the projectile is released.

Find the initial height (h0), initial velocity (v0), and acceleration (a) due to gravity.

Question 60

Solve the system of equations.

Question 61

Solve the system of linear equations for a, b, and c.

A) (-3, -3, 5)
B) (5, -3, 3)
C) (3, -3, 5)
D) (-3, 5, 3)

Question 62

Solve the system of linear equations for x, y, and z.

A) (-3, -1, 2)
B) (-3, 1, 2)
C) (2, -1, -3)
D) (2, 1, -3)

Question 63

Solve the system of linear equations for x, y, and z.

A) (-3, 2, -2)
B) (-3, -2, -2)
C) (-2, 2, -3)
D) (-2, -2, -3)

Question 64

Solve the system of linear equations by substitution.
5x + 2y = -19
8x - 4y = -52

A) (5, -3)
B) (-5, 3)
C) (-5, -3)
D) (5, 3)

Question 65

Solve the system of linear equations by substitution.
2x - 8y = 12
6x - 7y = -15

A) (6, -3)
B) (-3, -6)
C) (-6, -3)
D) (6, 3)

Question 66

Solve the system of linear equations by substitution.
2z - 7w = 18
2z - 7w = 5

A) (2, 7)
B) (18, 5)
C) infinite number of solutions
D) no solution

Question 67

Solve the system of linear equations by substitution.
-9p - 3q = -45
-18p - 6q = -90

A) (3, 6)
B) (-1, 1)
C) infinite number of solutions
D) no solution

Question 68

Solve the system of linear equations by elimination.
5d + 7f = 16
-5d - 3f = -24

A) (6, -2)
B) (-2, 6)
C) (-6, -2)
D) (-2, -6)

Question 69

Solve the system of linear equations by elimination.
3x - 14y = 52
6x - 28y = -104

A) (-8, 2)
B) (8, -2)
C) infinite number of solutions
D) no solution

Question 70

Solve the system of linear equations by elimination.
-9x - 2y = 72
-18x + 6y = 54

A) (6, 9)
B) (9, 6)
C) (-9, -6)
D) (-6, -9)

Question 71

Solve the system of linear equations by elimination.
9t + 10q = -112
27t + 13q = -268

A) (8, -4)
B) (-8, -4)
C) (-4, -8)
D) (-4, 8)
E) None of the above.

Question 72

Solve the system of linear equations by graphing the following equations.
2x + 4y = -2
9x + 8y = 21

A) (5, -3)
B) (-3, 5)
C) (-5, -3)
D) (5, 3)

Question 73

Solve the system of linear equations by graphing the following equations.
-10x + 5y = 110
-7x + 4y = 81

A) (8, -7)
B) (-7, 8)
C) (7, 8)
D) (8, 7)

Question 74

Solve the system of linear equations by graphing the following equations.
-2x - 6y = 14
-5x + 7y = -31

A) (-3, 2)
B) (2, -3)
C) (-2, -5)
D) (14, -31)

Question 75

Solve the system of linear equations by graphing the following equations.
4x - 3y = 7
2x - 6y = 26

A) (-2, -5)
B) (-5, -2)
C) (5, -2)
D) (-2, 5)

Question 76

Starbucks Coffee sells its House Blend for $9.52 per pound and its Sumatra coffee for $11.18 per pound. How many pounds of each type of coffee did a Starbucks outlet sell in one day if the total number of pounds sold was 60 and the day's receipts totaled $637.60? Let h represent the number of pounds of House Blend and s the number of pounds of Sumatra sold. Round your answer to the nearest pound.

A) h = 40 pounds, s = 20 pounds
B) h = 20 pounds, s = 40 pounds
C) h = 55 pounds, s = 5 pounds
D) h = 5 pounds, s = 55 pounds

Question 77

A health food company mixes dried fruit with walnuts to make a trail mix blend. How many pounds of each ingredient must be mixed if dried fruit sells for $6.63 per pound, walnuts sell for $4.38 per pound, and the company produces 65 pounds per batch valued at $419.70? Let d represent the number of pounds of dried fruit and w the number of pounds of walnuts.

A) d = 15 pounds, w = 50 pounds
B) d = 50 pounds, w = 15 pounds
C) d = 5 pounds, w = 60 pounds
D) d = 60 pounds, w = 5 pounds

Question 78

A catering company mixes cooked shredded beef with roasted Anaheim chilies to use as the filling in their house specialty burrito. How many pounds of both shredded beef that sells for$6.63 per pound and chilies that sell for $1.62 per pound must be mixed to produce 95 pounds of the mixture, witch sells for $454.50? Let b represent the number of pounds of beef and c represent the number of pounds of chilies.

A) b = 35 pounds, c = 60 pounds
B) b = 60 pounds, c = 35 pounds
C) b = 70 pounds, c = 25 pounds
D) b = 25 pounds, c = 70 pounds

Question 79

Solve the system of linear equations by substitution.
7t - 2u = 39
2t + 6u = -48

Question 80

Solve the system of linear equations by elimination.
-4j + 3k = 3
-3j - 3k = -45