Question 1

Compute the product.
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Accepted Answer

A)    
B)    
C)    
D) not defined 
A)    
B)    
C)    
D) not defined

Question 2

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer.
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Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 3

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer.
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Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

Write the word or phrase that best completes each statement or answers the question.
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Accepted Answer

A) x = -3 - 4w, y = 1 - w, z = 3 + w, where w is any real number 
B) inconsistent 
C) x = -3, y = 1, z = 3, w = 0; (-3, 1, 3, 0) 
D) x = -7, y = 0, z = 4, w = 1; (-7, 0, 4, 1) 
A) x = -3 - 4w, y = 1 - w, z = 3 + w, where w is any real number 
B) inconsistent 
C) x = -3, y = 1, z = 3, w = 0; (-3, 1, 3, 0) 
D) x = -7, y = 0, z = 4, w = 1; (-7, 0, 4, 1)

Question 5

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places.
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Accepted Answer

A) x = 1.18, y = 1.03; x = 1.07, y = 1.52; x = -0.91, y = 2.88 or (1.18, 1.03), (1.07, 1.52), (-0.91,2.88) 
B) x = 1.99, y = 0.13; x = 1.04, y = 1.70; x = -0.91, y = 2.95 or (1.99, 0.13), (1.04, 1.70), (-0.91, 2.95) 
C) x = 1.81, y = 0.28; x = 0.20, y = 2.45; x = -0.20, y = -2.45 or (1.81, 0.28), (0.20, 2.45), (-0.20, -2.45) 
D) No real solution exists. 
A) x = 1.18, y = 1.03; x = 1.07, y = 1.52; x = -0.91, y = 2.88 or (1.18, 1.03), (1.07, 1.52), (-0.91,2.88) 
B) x = 1.99, y = 0.13; x = 1.04, y = 1.70; x = -0.91, y = 2.95 or (1.99, 0.13), (1.04, 1.70), (-0.91, 2.95) 
C) x = 1.81, y = 0.28; x = 0.20, y = 2.45; x = -0.20, y = -2.45 or (1.81, 0.28), (0.20, 2.45), (-0.20, -2.45) 
D) No real solution exists.

Question 6

Write the word or phrase that best completes each statement or answers the question.
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Accepted Answer

A) x = 5, y = -2, z = 2; (5, -2, 2) 
B) x = 2, y = 5, z = 2; (2, 5, 2) 
C) x = 5, y = 2, z = -2; (5, 2, -2) 
D) x = -5, y = -2, z = -2; (-5, -2, -2) 
A) x = 5, y = -2, z = 2; (5, -2, 2) 
B) x = 2, y = 5, z = 2; (2, 5, 2) 
C) x = 5, y = 2, z = -2; (5, 2, -2) 
D) x = -5, y = -2, z = -2; (-5, -2, -2)

Question 7

Solve the system of equations.
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Accepted Answer

A) x = 4, y = 3, z = 5; (4, 3, 5) 
B) x = 4, y = 5, z = 3; (4, 5, 3) 
C) x = 5, y = 3, z = 4; (5, 3, 4) 
D) inconsistent 
A) x = 4, y = 3, z = 5; (4, 3, 5) 
B) x = 4, y = 5, z = 3; (4, 5, 3) 
C) x = 5, y = 3, z = 4; (5, 3, 4) 
D) inconsistent

Question 8

Write the partial fraction decomposition of the rational expression.
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Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Write the word or phrase that best completes each statement or answers the question.
-A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours toprepare, 2 hours to paint, and 10 hours to fire. A tree takes 16 hours to prepare, 3 hours to paint, and 4hours to fire. A sleigh takes 4 hours to prepare, 14 hours to paint, and 7 hours to fire. If the workshop has99 hours for prep time, 58 hours for painting, and 120 hours for firing, how many of each can be made?

Accepted Answer

A) 9 wreaths; 4 trees; 2 sleighs 
B) 4 wreaths; 2 trees; 9 sleighs 
C) 2 wreaths; 9 trees; 4 sleighs 
D) 10 wreaths; 5 trees; 3 sleighs 
A) 9 wreaths; 4 trees; 2 sleighs 
B) 4 wreaths; 2 trees; 9 sleighs 
C) 2 wreaths; 9 trees; 4 sleighs 
D) 10 wreaths; 5 trees; 3 sleighs

Question 10

Solve the linear programming problem.
-A doctor has told a sick patient to take vitamin pills. The patient needs at least 6 units of vitamin A and atleast 6 units of vitamin B. The red vitamin pills cost 10¢ each and contain 1 unit of A and 2 units of B. Theblue vitamin pills cost   each and contain 2 units of A and 1 unit of B. To avoid indigestion, the patientshould take no more than 4 red pills and no more than 7 blue pills. How many pills should the patient takeeach day to minimize costs?

Accepted Answer

A) 4 red and 1 blue 
B) 2 red and 2 blue 
C) 0 red and 6 blue 
D) 4 red and 7 blue 
A) 4 red and 1 blue 
B) 2 red and 2 blue 
C) 0 red and 6 blue 
D) 4 red and 7 blue

Question 11

Write the partial fraction decomposition of the rational expression.
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Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Find the value of the determinant.
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Accepted Answer

A) 8 
B) 64 
C) -8 
D) 4 
A) 8 
B) 64 
C) -8 
D) 4

Question 13

Solve using elimination.
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Accepted Answer

A) x = 3, y = 2; x = -3, y = 2 ; x = 3, y = -2; x = -3, y = -2 or (3, 2), (-3, 2), (3, -2), (-3, -2) 
B) x = 3, y = 2; x = 2, y = 3; x = -3, y = -2; x = -2, y = -3 or (3, 2), (2, 3), (-3, -2), (-2, -3) 
C) x = 3, y = -2; x = 3, y = 2 or (3, -2), (3, 2) 
D) x = -3, y = -2; x = -2, y = -3 or (-3, -2), (-2, -3) 
A) x = 3, y = 2; x = -3, y = 2 ; x = 3, y = -2; x = -3, y = -2 or (3, 2), (-3, 2), (3, -2), (-3, -2) 
B) x = 3, y = 2; x = 2, y = 3; x = -3, y = -2; x = -2, y = -3 or (3, 2), (2, 3), (-3, -2), (-2, -3) 
C) x = 3, y = -2; x = 3, y = 2 or (3, -2), (3, 2) 
D) x = -3, y = -2; x = -2, y = -3 or (-3, -2), (-2, -3)

Question 14

Solve the system of equations using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so.
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Accepted Answer

A) not applicable 
B) x = 0, y = 2, z = 0; (0, 2, 0) 
C) x = 5, y = 2, z = 0; (5, 2, 0) 
D) x = 0, y = 0, z = 2; (0, 0, 2) 
A) not applicable 
B) x = 0, y = 2, z = 0; (0, 2, 0) 
C) x = 5, y = 2, z = 0; (5, 2, 0) 
D) x = 0, y = 0, z = 2; (0, 0, 2)

Question 15

Write the word or phrase that best completes each statement or answers the question.
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Accepted Answer

A) x = -1, y = -3, z = 0, w = 3; (-1, -3, 0, 3) 
B) x = 1, y = -3, z = 0, w = 3; (1, -3, 0, 3) 
C) x = -1, y = 3, z = 0, w = -3; (-1, 3, 0, -3) 
D) x = 1, y = 3, z = 0, w = -3; (1, 3, 0, -3) 
A) x = -1, y = -3, z = 0, w = 3; (-1, -3, 0, 3) 
B) x = 1, y = -3, z = 0, w = 3; (1, -3, 0, 3) 
C) x = -1, y = 3, z = 0, w = -3; (-1, 3, 0, -3) 
D) x = 1, y = 3, z = 0, w = -3; (1, 3, 0, -3)

Question 16

Write the word or phrase that best completes each statement or answers the question.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Write the partial fraction decomposition of the rational expression.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

Solve the system of equations by substitution.
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Accepted Answer

A) x = 1, y = -9; (1, -9) 
B) x = -1, y = 9; (-1, 9) 
C) x = 1, y = 18; (1, 18) 
D) x = -1, y = -9; (-1, -9) 
A) x = 1, y = -9; (1, -9) 
B) x = -1, y = 9; (-1, 9) 
C) x = 1, y = 18; (1, 18) 
D) x = -1, y = -9; (-1, -9)

Question 19

Perform the row operation(s)on the given augmented matrix.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 20

Solve the system using the inverse matrix method.
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Accepted Answer

A) x = 1, y = -3; (1, -3) 
B) x = -3, y = 1; (-3, 1) 
C) x = -1, y = 3; (-1, 3) 
D) x = 3, y = -1; (3, -1) 
A) x = 1, y = -3; (1, -3) 
B) x = -3, y = 1; (-3, 1) 
C) x = -1, y = 3; (-1, 3) 
D) x = 3, y = -1; (3, -1)

Compute the product. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Write the word or phrase that best completes each statement or answers the question. -

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. -

Write the word or phrase that best completes each statement or answers the question. -

Solve the system of equations. -

Write the partial fraction decomposition of the rational expression. - $Write the partial fraction decomposition of the rational expression. -$

Write the partial fraction decomposition of the rational expression. - $Write the partial fraction decomposition of the rational expression. -$

Find the value of the determinant. -

Solve using elimination. -

Solve the system of equations using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so. -

Write the word or phrase that best completes each statement or answers the question. -

Write the word or phrase that best completes each statement or answers the question. -

Write the partial fraction decomposition of the rational expression. - $Write the partial fraction decomposition of the rational expression. -$

Solve the system of equations by substitution. -

Perform the row operation(s)on the given augmented matrix. -

Solve the system using the inverse matrix method. -

Equations and Inequalities

Graphs

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

Graphing Utilities

Filters

Exam 8: Systems of Equations and Inequalities

Compute the product. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Write the word or phrase that best completes each statement or answers the question. -

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. -

Write the word or phrase that best completes each statement or answers the question. -

Solve the system of equations. -

Write the partial fraction decomposition of the rational expression. -

Write the partial fraction decomposition of the rational expression. -

Find the value of the determinant. -

Solve using elimination. -

Solve the system of equations using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so. -

Write the word or phrase that best completes each statement or answers the question. -

Write the word or phrase that best completes each statement or answers the question. -

Write the partial fraction decomposition of the rational expression. -

Solve the system of equations by substitution. -

Perform the row operation(s)on the given augmented matrix. -

Solve the system using the inverse matrix method. -

Equations and Inequalities

Graphs

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

Graphing Utilities

Filters

Write the partial fraction decomposition of the rational expression. - $Write the partial fraction decomposition of the rational expression. -$

Write the partial fraction decomposition of the rational expression. - $Write the partial fraction decomposition of the rational expression. -$

Write the partial fraction decomposition of the rational expression. - $Write the partial fraction decomposition of the rational expression. -$