Question 1

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

Accepted Answer

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

Question 2

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is
inconsistent.
-

Accepted Answer

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

Question 3

Verify that the values of the variables listed are solutions of the system of equations.
-  x = -1, y = 2, z = 4

Accepted Answer

A) solution 
B) not a solution 
A) solution 
B) not a solution

Question 4

Write a system of linear inequalities that has the given graph.
-

Accepted Answer

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

Question 5

Write the word or phrase that best completes each statement or answers the question.
-The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ftlonger than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Accepted Answer

A) width = 9.7 ft, length = 22.4 ft 
B) width = 4 ft, length = 11 ft 
C) width = 2 ft, length = 9 ft 
D) width = 3.9 ft, length = 9.7 ft 
A) width = 9.7 ft, length = 22.4 ft 
B) width = 4 ft, length = 11 ft 
C) width = 2 ft, length = 9 ft 
D) width = 3.9 ft, length = 9.7 ft

Question 6

Graph the inequality.
-

Accepted Answer

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

Question 7

Solve the problem.
-An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highwaydriving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

Accepted Answer

A) 153 mi 
B) 147 mi 
C) 132 mi 
D) 168 mi 
A) 153 mi 
B) 147 mi 
C) 132 mi 
D) 168 mi

Question 8

Write the word or phrase that best completes each statement or answers the question.
-Find real numbers a, b, and c such that the graph of the function   contains the points(-2, -4), (1, -1), and (3, -19).

Accepted Answer

a = -2 , b

Question 9

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

Accepted Answer

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

Question 10

Write the word or phrase that best completes each statement or answers the question.
-Melody has $45,000 to invest and wishes to receive an annual income of $4290 from this money. She haschosen investments that pay 5%, 8%, and 12% simple interest. Melody wants to have the amount investedat 12% to be double the amount invested at 8%. How much should she invest at each rate?

Accepted Answer

$9000 at 5

Question 11

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

Accepted Answer

A) x = 1, y = 2, z = 8; (1, 2, 8) 
B) x = 2, y = 8, z = 2; (2, 8, 2) 
C) x = 1, y = -2, z = -8; (1, -2, -8) 
D) x = 2, y = 0, z = 8; (2, 0, 8) 
A) x = 1, y = 2, z = 8; (1, 2, 8) 
B) x = 2, y = 8, z = 2; (2, 8, 2) 
C) x = 1, y = -2, z = -8; (1, -2, -8) 
D) x = 2, y = 0, z = 8; (2, 0, 8)

Question 12

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual
order.
-Use the coding matrix   and its inverse   to decode the cryptogram   .

Accepted Answer

A) GOOD_LUCK 
B) STAY_CALM 
C) LOOK_DOWN 
D) HELP_THEM 
A) GOOD_LUCK 
B) STAY_CALM 
C) LOOK_DOWN 
D) HELP_THEM

Question 13

Solve the system of equations using substitution.
-

Accepted Answer

A) x = 12, y = 5; x = 5, y = 12 or (12, 5), (5, 12) 
B) x = -12, y = 5; x = -5, y = 12 or (-12, 5), (-5, 12) 
C) x = 12, y = -5; x = 5, y = -12 or (12, -5), (5, -12) 
D) x = -12, y = -5; x = -5, y = -12 or (-12, -5), (-5, -12) 
A) x = 12, y = 5; x = 5, y = 12 or (12, 5), (5, 12) 
B) x = -12, y = 5; x = -5, y = 12 or (-12, 5), (-5, 12) 
C) x = 12, y = -5; x = 5, y = -12 or (12, -5), (5, -12) 
D) x = -12, y = -5; x = -5, y = -12 or (-12, -5), (-5, -12)

Question 14

Write the word or phrase that best completes each statement or answers the question.
Graph the equations of the system. Then solve the system to find the points of intersection.
-

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Solve using elimination.
-

Accepted Answer

A) x = -8, y= 0; x = 8, y = 0 or (-8, 0), (8, 0) 
B) x = 0, y= -8; x = 0, y = 8 or (0, -8), (0, 8) 
C) x = 0, y= -3; x = 0, y = 3 or (0, -3), (0, 3) 
D) No real solution exists. 
A) x = -8, y= 0; x = 8, y = 0 or (-8, 0), (8, 0) 
B) x = 0, y= -8; x = 0, y = 8 or (0, -8), (0, 8) 
C) x = 0, y= -3; x = 0, y = 3 or (0, -3), (0, 3) 
D) No real solution exists.

Question 16

Solve for x.
-

Accepted Answer

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

Question 17

An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed
region. Use these values to determine the maximum value of the objective function and the values of x and y for
which the maximum occurs.
C
-

Accepted Answer

A) maximum: 80; at (10, 0) 
B) maximum: 61; at (2, 5) 
C) maximum: 48; at (6, 0) 
D) maximum: -32; at (4, 0) 
A) maximum: 80; at (10, 0) 
B) maximum: 61; at (2, 5) 
C) maximum: 48; at (6, 0) 
D) maximum: -32; at (4, 0)

Question 18

Graph the system of inequalities.
-

Accepted Answer

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

Question 19

Write the word or phrase that best completes each statement or answers the question.
-The liquid portion of a diet is to provide at least 300 calories, 36 units of vitamin A, and 90 units of vitaminC daily. A cup of dietary drink X provides 60 calories, 12 units of vitamin A, and 10 units of vitamin C. Acup of dietary drink Y provides 60 calories, 6 units of vitamin A, and 30 units of vitamin C. Set up a systemof linear inequalities that describes the minimum daily requirements for calories and vitamins. Letx = number of cups of dietary drink X, and y = number of cups of dietary drink Y. Write all the constraintsas a system of linear inequalities.

Accepted Answer

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

Question 20

Graph the inequality.
-

Accepted Answer

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

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

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -

Verify that the values of the variables listed are solutions of the system of equations. - x = -1, y = 2, z = 4

Write a system of linear inequalities that has the given graph. -

Graph the inequality. -

Solve the problem. -An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highwaydriving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

Write the word or phrase that best completes each statement or answers the question. -Find real numbers a, b, and c such that the graph of the function contains the points(-2, -4), (1, -1), and (3, -19).

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

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

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. -Use the coding matrix and its inverse to decode the cryptogram .

Solve the system of equations using substitution. -

Write the word or phrase that best completes each statement or answers the question. Graph the equations of the system. Then solve the system to find the points of intersection. -

Solve using elimination. -

Solve for x. -

Graph the system of inequalities. -

Graph the inequality. -

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

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

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -

Verify that the values of the variables listed are solutions of the system of equations. - x = -1, y = 2, z = 4

Write a system of linear inequalities that has the given graph. -

Graph the inequality. -

Solve the problem. -An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highwaydriving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

Write the word or phrase that best completes each statement or answers the question. -Find real numbers a, b, and c such that the graph of the function contains the points(-2, -4), (1, -1), and (3, -19).

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

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

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. -Use the coding matrix and its inverse to decode the cryptogram .

Solve the system of equations using substitution. -

Write the word or phrase that best completes each statement or answers the question. Graph the equations of the system. Then solve the system to find the points of intersection. -

Solve using elimination. -

Solve for x. -

Graph the system of inequalities. -

Graph the inequality. -

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