# Quiz 9: Systems of Equations and Inequalities

Mathematics

Q 1Q 1

Use the method of substitution to solve the system.
A)( - 4, -21 )
B)( - 4, -21 ), ( 9, 44 )
C)( - 4, -21 ), ( 8, 44 )
D)( 9, 44 )
E)no solution

Free

Multiple Choice

B

Q 2Q 2

Use the method of substitution to solve the system.
A)( 0, 2 )
B)( 4, 0 )
C)( 4, 0 ), ( 0, 2 )
D)( 4, 1 ), ( 0, 2 )
E)no solution

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C

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B

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Q 7Q 7

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.
A)maximum of 20 at
B)maximum of 24 at
C)maximum of 0 at
D)maximum of 22 at
E)maximum of 18 at

Free

Multiple Choice

Q 8Q 8

A manufacturer of cell phones makes a profit of $23 on a deluxe model and $31 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 240 phones. How many of each type should be produced daily in order to maximize the profit?
A)31 standard and 80 deluxe
B)80 standard and 160 deluxe
C)160 standard and 80 deluxe
D)200 standard and 40 deluxe
E)160 standard and 60 deluxe

Free

Multiple Choice

Q 9Q 9

A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.1, and a regular notebook, which sells for $0.85. The production cost is $1.00 for each deluxe notebook and $0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 7,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?
A)2,000 deluxe and 5,000 regular
B)3,000 deluxe and 4,000 regular
C)2,300 deluxe and 4,000 regular
D)2,500 deluxe and 4,000 regular
E)3,000 deluxe and 5,000 regular

Free

Multiple Choice

Q 10Q 10

A small firm manufactures bookshelves and desks for microcomputers. For each product it is necessary to use a table saw and a power router. To manufacture each bookshelf, the saw must be used for hour and the router for 1 hour. A desk requires the use of each machine for 2 hours. The profits are $20 per bookshelf and $50 per desk. If the saw can be used for 8 hours per day and the router for 12 hours per day, how many bookshelves and desks should be manufactured each day to maximize the profit?
A)4 bookshelves and 2 desks
B)2 bookshelves and 2 desks
C)2 bookshelves and 4 desks
D)0 bookshelves and 4 desks
E)2 bookshelves and 0 desks

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Q 16Q 16

Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

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Multiple Choice

Q 17Q 17

Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 18Q 18

Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 19Q 19

Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent.
E)The equations are dependent.

Free

Multiple Choice

Q 20Q 20

Three average monthly low temperatures for Detroit are listed in the table. Month
Temperature
Feb)
Aug)
Nov)
54)24° F
107)34° F
86)1° F
Let correspond to January, to February, . . . , and to December. Determine a quadratic function that interpolates the data - that is, determine the constants a, b, and c such that , and .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 21Q 21

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A. (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 22Q 22

Find the determinant of the matrix.
A)15,232.88
B)3,046.58
C)22,849.32
D)7,616.44
E)30,465.76

Free

Multiple Choice

Q 23Q 23

Use Cramer's rule, whenever possible, to solve the system.
A)
B)
C)
D)The equations are dependent.
E)The system is inconsistent.

Free

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Q 25Q 25

Use the method of substitution to solve the system.
A)( - 7, -18 )
B)( 9, 14 )
C)( - 7, -18 ), ( 9, 14 )
D)( - 7, -18 ), ( 8, 14 )
E)no solution

Free

Multiple Choice

Q 26Q 26

Use the method of substitution to solve the system.
A)( 4, 0 ), ( -32, 6 )
B)( -32, 6 )
C)( 4, 1 ), ( -32, 6 )
D)( 4, 0 )
E)no solution

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Q 31Q 31

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.
A)maximum of 44 at
B)maximum of 40 at
C)maximum of 42 at
D)maximum of 46 at
E)maximum of 0 at

Free

Multiple Choice

Q 32Q 32

A manufacturer of cell phones makes a profit of $26 on a deluxe model and $30 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 240 phones. How many of each type should be produced daily in order to maximize the profit?
A)160 standard and 60 deluxe
B)30 standard and 80 deluxe
C)80 standard and 160 deluxe
D)200 standard and 40 deluxe
E)160 standard and 80 deluxe

Free

Multiple Choice

Q 33Q 33

A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.25, and a regular notebook, which sells for $0.9. The production cost is $1.00 for each deluxe notebook and $0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 8,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?
A)2,500 deluxe and 5,000 regular
B)2,000 deluxe and 6,000 regular
C)2,300 deluxe and 5,000 regular
D)3,000 deluxe and 5,000 regular
E)3,000 deluxe and 6,000 regular

Free

Multiple Choice

Q 34Q 34

A small firm manufactures bookshelves and desks for microcomputers. For each product it is necessary to use a table saw and a power router. To manufacture each bookshelf, the saw must be used for hour and the router for 1 hour. A desk requires the use of each machine for 2 hours. The profits are $20 per bookshelf and $50 per desk. If the saw can be used for 8 hours per day and the router for 12 hours per day, how many bookshelves and desks should be manufactured each day to maximize the profit?
A)8 bookshelves and 8 desks
B)0 bookshelves and 1 desks
C)8 bookshelves and 0 desks
D)8 bookshelves and 1 desks
E)1 bookshelves and 8 desks

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Q 40Q 40Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

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Multiple Choice

Q 41Q 41Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 42Q 42Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 43Q 43

Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent.
E)The equations are dependent.

Free

Multiple Choice

Q 44Q 44

Three average monthly low temperatures for Detroit are listed in the table. Month
Temperature
Feb)
Aug)
Nov)
54)71° F
106)31° F
85)67° F
Let correspond to January, to February, . . . , and to December. Determine a quadratic function that interpolates the data - that is, determine the constants a, b, and c such that , and .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 45Q 45

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A. (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)
A)
B)
C)
D)
E)

Free

Multiple Choice

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Q 47Q 47

Use Cramer's rule, whenever possible, to solve the system.
A)
B)
C)
D)The equations are dependent.
E)The system is inconsistent.

Free

Multiple Choice

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Q 49Q 49

Use the method of substitution to solve the system.
A)( - 3, -16 )
B)( - 3, -16 ), ( 6, 11 )
C)( 6, 11 )
D)( - 3, -16 ), ( 5, 11 )
E)no solution

Free

Multiple Choice

Q 50Q 50

Use the method of substitution to solve the system.
A)( 7, 0 ), ( 3, 2 )
B)( 7, 0 )
C)( 3, 2 )
D)( 7, 1 ), ( 3, 2 )
E)no solution

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Q 55Q 55

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.
A)maximum of 12 at
B)maximum of 14 at
C)maximum of 16 at
D)maximum of 0 at
E)maximum of 18 at

Free

Multiple Choice

Q 56Q 56

A manufacturer of cell phones makes a profit of $24 on a deluxe model and $30 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 200 phones. How many of each type should be produced daily in order to maximize the profit?
A)120 standard and 80 deluxe
B)60 standard and 140 deluxe
C)30 standard and 80 deluxe
D)120 standard and 60 deluxe
E)160 standard and 40 deluxe

Free

Multiple Choice

Q 57Q 57

A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.2, and a regular notebook, which sells for $0.85. The production cost is $1.00 for each deluxe notebook and $0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 8,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?
A)2,300 deluxe and 5,000 regular
B)3,000 deluxe and 6,000 regular
C)2,000 deluxe and 6,000 regular
D)3,000 deluxe and 5,000 regular
E)2,500 deluxe and 5,000 regular

Free

Multiple Choice

Q 58Q 58

A small firm manufactures bookshelves and desks for microcomputers. For each product it is necessary to use a table saw and a power router. To manufacture each bookshelf, the saw must be used for hour and the router for 1 hour. A desk requires the use of each machine for 2 hours. The profits are $20 per bookshelf and $50 per desk. If the saw can be used for 8 hours per day and the router for 12 hours per day, how many bookshelves and desks should be manufactured each day to maximize the profit?
A)4 bookshelves and 2 desks
B)4 bookshelves and 4 desks
C)2 bookshelves and 4 desks
D)0 bookshelves and 2 desks
E)4 bookshelves and 0 desks

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Q 64Q 64Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

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Q 65Q 65Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

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Q 66Q 66Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 67Q 67

Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent.
E)The equations are dependent.

Free

Multiple Choice

Q 68Q 68

Three average monthly low temperatures for Detroit are listed in the table. Month
Temperature
Feb)
Aug)
Nov)
45)89° F
97)49° F
76)85° F
Let correspond to January, to February, . . . , and to December. Determine a quadratic function that interpolates the data - that is, determine the constants a, b, and c such that , and .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 69Q 69

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A. (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)
A)
B)
C)
D)
E)

Free

Multiple Choice

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Q 71Q 71

Use Cramer's rule, whenever possible, to solve the system.
A)
B)
C)
D)The equations are dependent.
E)The system is inconsistent.

Free

Multiple Choice

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Multiple Choice

Q 73Q 73

Use the method of substitution to solve the system.
A)( - 1, -12 ), ( 8, 68 )
B)( 9, 68 )
C)( - 1, -12 )
D)( - 1, -12 ), ( 9, 68 )
E)no solution

Free

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Q 75Q 75

The data in the table are generated by the function . Approximate the unknown constants a and b to four decimal places. x
1 2 3 4
F ( x )
0)67654 0.44668 0.29492 0.19472
A)
B)
C)
D)
E)

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Q 77Q 77

Find the maximum and minimum values of the objective function on the region in the figure.
A)The maximum is at
,
The minimum is
at
.
B)The maximum is at
,
The minimum is
at
.
C)The maximum is at
,
The minimum is
at
.
D)The maximum is at
,
The minimum is
at
.
E)The maximum is at
,
The minimum is
at
.

Free

Multiple Choice

Q 78Q 78

A manufacturer of tennis rackets makes a profit of $16 on each oversized racket and $10 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 25 and 80, and production of oversized rackets should be between 8 and 33. To maintain high quality, the total number of rackets produced should not exceed 80 per day. How many of each type should be manufactured daily to maximize the profit?
A)47 standard and 8 oversized
B)33 standard and 47 oversized
C)47 standard and 33 oversized
D)25 standard and 8 oversized
E)25 standard and 33 oversized

Free

Multiple Choice

Q 79Q 79

A hospital dietician wishes to prepare a corn-squash vegetable dish that will provide at least grams of protein and cost no more than cents per serving. An ounce of creamed corn provides gram of protein and costs cents. An ounce of squash supplies gram of protein and costs cents. For taste, there must be at least ounces of corn and at least as much squash as corn. It is important to keep the total number of ounces in a serving as small as possible. Find the combination of corn and squash that will minimize the amount of ingredients used per serving.
A) ounces of corn and ounces of squash
B) ounces of corn and ounces of squash
C) ounces of corn and ounces of squash
D) ounces of corn and ounces of squash
E) ounces of corn and ounces of squash

Free

Multiple Choice

Q 80Q 80

Use matrices to solve the system.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 81Q 81

Use matrices to solve the system.
A)( 0, 0, 0)
B)( 0, - z, z )
C)( 2, 2, 2 )
D)( 0, z, z )
E)The system is inconsistent

Free

Multiple Choice

Q 82Q 82

Three solutions contain a certain acid. The first contains 10% acid, the second 30%, and the third 50%. A chemist wishes to use all three solutions to obtain a 10-liter mixture containing 24% acid. If the chemist wants to use twice as much of the 50% solution as of the 30% solution, how many liters of each solution should be used?
A)2.8 of 10% , 2.4 of 30% , 4.8 of 50%
B)5.8 of 10% , 2.8 of 30% , 1.4 of 50%
C)8.8 of 10% , 0.4 of 30% , 0.8 of 50%
D)4.8 of 10% , 2.4 of 30% , 2.8 of 50%
E)5.8 of 10% , 1.4 of 30% , 2.8 of 50%

Free

Multiple Choice

Q 83Q 83

A shop specializes in preparing blends of gourmet coffees. From Colombian, Costa Rican, and Kenyan coffees, the owner wishes to prepare 2-pounds bags that will sell for $8.50. The cost per pound of these coffees is $10, $6, and $8, respectively. The amount of Colombian is to be three times the amount of Costa Rican. Find the amount of each type of coffee in the blend.
A)0.3 lb Colombian , 0.1 lb Costa Rican , 1.6 lb Kenyan
B)1.05 lb Colombian , 0.35 lb Costa Rican , 0.6 lb Kenyan
C)0.6 lb Colombian , 0.2 lb Costa Rican , 1.2 lb Kenyan
D)0.75 lb Colombian , 0.25 lb Costa Rican , 2 lb Kenyan
E)0.75 lb Colombian , 0.25 lb Costa Rican , 1 lb Kenyan

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Q 88Q 88Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 89Q 89

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of .
(In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 90Q 90

Find the determinant of the matrix.
A)- 392,544
B)- 1,570,176
C)- 98,136
D)- 392,545
E)392,544

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Q 93Q 93Use Cramer's rule, whenever possible, to solve the system.
A)
B)
C)
D)The equations are dependent.
E)The system is inconsistent.

Free

Multiple Choice

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Q 98Q 98

Use the method of substitution to solve the system.
A)( - 1, -14 )
B)( - 1, -14 ), ( 9, 66 )
C)( - 1, -14 ), ( 8, 66 )
D)( 9, 66 )
E)no solution

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Q 100Q 100

The data in the table are generated by the function . Approximate the unknown constants a and b to four decimal places. x
1 2 3 4
F ( x )
0)88834 0.44394 0.22186 0.11087
A)
B)
C)
D)
E)

Free

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Q 102Q 102

Find the maximum and minimum values of the objective function on the region in the figure.
A)The maximum is at
,
The minimum is
at
.
B)The maximum is at
,
The minimum is
at
.
C)The maximum is at
,
The minimum is
at
.
D)The maximum is at
,
The minimum is
at
.
E)The maximum is at
,
The minimum is
at
.

Free

Multiple Choice

Q 103Q 103

A manufacturer of tennis rackets makes a profit of $14 on each oversized racket and $8 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 25 and 77, and production of oversized rackets should be between 10 and 30. To maintain high quality, the total number of rackets produced should not exceed 77 per day. How many of each type should be manufactured daily to maximize the profit?
A)25 standard and 10 oversized
B)30 standard and 47 oversized
C)25 standard and 30 oversized
D)47 standard and 10 oversized
E)47 standard and 30 oversized

Free

Multiple Choice

Q 104Q 104

A hospital dietician wishes to prepare a corn-squash vegetable dish that will provide at least grams of protein and cost no more than cents per serving. An ounce of creamed corn provides gram of protein and costs cents. An ounce of squash supplies gram of protein and costs cents. For taste, there must be at least ounces of corn and at least as much squash as corn. It is important to keep the total number of ounces in a serving as small as possible. Find the combination of corn and squash that will minimize the amount of ingredients used per serving.
A) ounces of corn and ounces of squash
B) ounces of corn and ounces of squash
C) ounces of corn and ounces of squash
D) ounces of corn and ounces of squash
E) ounces of corn and ounces of squash

Free

Multiple Choice

Q 105Q 105

Use matrices to solve the system.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 106Q 106

Use matrices to solve the system.
A)( 0, z, z )
B)( 0, - z, z )
C)( 5, 8, 2 )
D)( 0, 0, 0)
E)The system is inconsistent

Free

Multiple Choice

Q 107Q 107

Three solutions contain a certain acid. The first contains 10% acid, the second 30%, and the third 50%. A chemist wishes to use all three solutions to obtain a 90-liter mixture containing 26% acid. If the chemist wants to use twice as much of the 50% solution as of the 30% solution, how many liters of each solution should be used?
A)43.8 of 10% , 15.4 of 30% , 30.8 of 50%
B)46.8 of 10% , 14.4 of 30% , 28.8 of 50%
C)49.8 of 10% , 13.4 of 30% , 26.8 of 50%
D)45.8 of 10% , 15.4 of 30% , 28.8 of 50%
E)46.8 of 10% , 28.8 of 30% , 14.4 of 50%

Free

Multiple Choice

Q 108Q 108

A shop specializes in preparing blends of gourmet coffees. From Colombian, Costa Rican, and Kenyan coffees, the owner wishes to prepare 3-pounds bags that will sell for $8.50. The cost per pound of these coffees is $10, $6, and $8, respectively. The amount of Colombian is to be three times the amount of Costa Rican. Find the amount of each type of coffee in the blend.
A)0.825 lb Colombian , 0.275 lb Costa Rican , 1.9 lb Kenyan
B)0.675 lb Colombian , 0.225 lb Costa Rican , 2.1 lb Kenyan
C)1.125 lb Colombian , 0.375 lb Costa Rican , 1.5 lb Kenyan
D)1.125 lb Colombian , 0.375 lb Costa Rican , 3 lb Kenyan
E)1.275 lb Colombian , 0.425 lb Costa Rican , 1.3 lb Kenyan

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Q 113Q 113Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 114Q 114

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of .
(In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 115Q 115

Find the determinant of the matrix.
A)- 311,324
B)- 933,969
C)- 311,323
D)311,323
E)- 103,774

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Q 118Q 118Use Cramer's rule, whenever possible, to solve the system.
A)
B)
C)
D)The equations are dependent.
E)The system is inconsistent.

Free

Multiple Choice

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Q 123Q 123

Use the method of substitution to solve the system.
A)( - 3, -16 )
B)( - 3, -16 ), ( 6, 11 )
C)( 6, 11 )
D)( - 3, -16 ), ( 5, 11 )
E)no solution

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Q 125Q 125

The data in the table are generated by the function . Approximate the unknown constants a and b to four decimal places. x
1 2 3 4
F ( x )
0)71939 0.41687 0.24157 0.13998
A)
B)
C)
D)
E)

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Q 127Q 127

Find the maximum and minimum values of the objective function on the region in the figure.
A)The maximum is at
,
The minimum is
at
.
B)The maximum is at
,
The minimum is
at
.
C)The maximum is at
,
The minimum is
at
.
D)The maximum is at
,
The minimum is
at
.
E)The maximum is at
,
The minimum is
at
.

Free

Multiple Choice

Q 128Q 128

A manufacturer of tennis rackets makes a profit of $15 on each oversized racket and $10 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 25 and 75, and production of oversized rackets should be between 8 and 27. To maintain high quality, the total number of rackets produced should not exceed 75 per day. How many of each type should be manufactured daily to maximize the profit?
A)25 standard and 8 oversized
B)25 standard and 27 oversized
C)27 standard and 48 oversized
D)48 standard and 27 oversized
E)48 standard and 8 oversized

Free

Multiple Choice

Q 129Q 129

A hospital dietician wishes to prepare a corn-squash vegetable dish that will provide at least grams of protein and cost no more than cents per serving. An ounce of creamed corn provides gram of protein and costs cents. An ounce of squash supplies gram of protein and costs cents. For taste, there must be at least ounces of corn and at least as much squash as corn. It is important to keep the total number of ounces in a serving as small as possible. Find the combination of corn and squash that will minimize the amount of ingredients used per serving.
A) ounces of corn and ounces of squash
B) ounces of corn and ounces of squash
C) ounces of corn and ounces of squash
D) ounces of corn and ounces of squash
E) ounces of corn and ounces of squash

Free

Multiple Choice

Q 130Q 130

Use matrices to solve the system.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

Free

Multiple Choice

Q 131Q 131

Use matrices to solve the system.
A)( 0, 0, 0)
B)( 0, z, z )
C)( 0, - z, z )
D)( 2, 8, 4 )
E)The system is inconsistent

Free

Multiple Choice

Q 132Q 132

Three solutions contain a certain acid. The first contains 10% acid, the second 30%, and the third 50%. A chemist wishes to use all three solutions to obtain a 100-liter mixture containing 28% acid. If the chemist wants to use twice as much of the 50% solution as of the 30% solution, how many liters of each solution should be used?
A)49 of 10% , 17 of 30% , 34 of 50%
B)46 of 10% , 36 of 30% , 18 of 50%
C)45 of 10% , 19 of 30% , 36 of 50%
D)46 of 10% , 18 of 30% , 36 of 50%
E)43 of 10% , 19 of 30% , 38 of 50%

Free

Multiple Choice

Q 133Q 133

A shop specializes in preparing blends of gourmet coffees. From Colombian, Costa Rican, and Kenyan coffees, the owner wishes to prepare 3-pounds bags that will sell for $8.50. The cost per pound of these coffees is $10, $6, and $8, respectively. The amount of Colombian is to be three times the amount of Costa Rican. Find the amount of each type of coffee in the blend.
A)1.275 lb Colombian , 0.425 lb Costa Rican , 1.3 lb Kenyan
B)1.575 lb Colombian , 0.525 lb Costa Rican , 0.9 lb Kenyan
C)1.125 lb Colombian , 0.375 lb Costa Rican , 1.5 lb Kenyan
D)1.125 lb Colombian , 0.375 lb Costa Rican , 3 lb Kenyan
E)1.425 lb Colombian , 0.475 lb Costa Rican , 1.1 lb Kenyan

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Q 138Q 138Solve the system using the inverse method.
A)
B)
C)
D)The system is inconsistent
E)The equations are dependent

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Q 139Q 139

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of .
(In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)
A)
B)
C)
D)
E)

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Q 140Q 140

Find the determinant of the matrix.
A)- 89,090
B)- 1,425,432
C)- 356,359
D)356,358
E)- 356,358

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Q 143Q 143Use Cramer's rule, whenever possible, to solve the system.
A)
B)
C)
D)The equations are dependent.
E)The system is inconsistent.

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