Question 1

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-

Accepted Answer

A) -7 
B) 7 
C) 0 
D) Cannot determine 
A) -7 
B) 7 
C) 0 
D) Cannot determine

Question 2

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is
consistent, give the solution.
-

Accepted Answer

A) consistent; x = 2 + 9z, y = -5 - 9z, z any real number or   , y = -5 - 9z, z any real number} 
B) consistent; x = 2 - 9z, y = -5 + 9z, z any real number or   , y = -5 + 9z, z any real number} 
C) consistent; x = 2, y = -5, z = -9; (2, -5, -9) 
D) inconsistent 
A) consistent; x = 2 + 9z, y = -5 - 9z, z any real number or   , y = -5 - 9z, z any real number} 
B) consistent; x = 2 - 9z, y = -5 + 9z, z any real number or   , y = -5 + 9z, z any real number} 
C) consistent; x = 2, y = -5, z = -9; (2, -5, -9) 
D) inconsistent

Question 3

Solve the system of equations by substitution.
-

Accepted Answer

A) x = 0, y = 1; (0, 1) 
B) x = 1, y = 0; (1, 0) 
C) x = 1, y = 1; (1, 1) 
D) x = 0, y = 0; (0, 0) 
A) x = 0, y = 1; (0, 1) 
B) x = 1, y = 0; (1, 0) 
C) x = 1, y = 1; (1, 1) 
D) x = 0, y = 0; (0, 0)

Question 4

Graph the system of inequalities.
-

Accepted Answer

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

Question 5

Solve the linear programming problem.
-A vineyard produces two special wines, a white and a red. A bottle of the white wine requires 14 poundsof grapes and 1 hour of processing time. A bottle of red wine requires 25 pounds of grapes and 2 hours ofprocessing time. The vineyard has on hand 2,198 pounds of grapes and can allot 160 hours of processingtime to the production of these wines. A bottle of the white wine sells for $11.00, while a bottle of the redwine sells for $20.00. How many bottles of each type should the vineyard produce in order to maximizegross sales?

Accepted Answer

A) 132 bottles of white and 14 bottles of red 
B) 14 bottles of white and 132 bottles of red 
C) 76 bottles of white and 42 bottles of red 
D) 42 bottles of white and 59 bottles of red 
A) 132 bottles of white and 14 bottles of red 
B) 14 bottles of white and 132 bottles of red 
C) 76 bottles of white and 42 bottles of red 
D) 42 bottles of white and 59 bottles of red

Question 6

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 7

Write the word or phrase that best completes each statement or answers the question.
-The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They canproduce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to makeone VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be madedaily to maximize the companyʹs profit, if the profit on a VIP ring is $40 and on an SST ring is $35?

Accepted Answer

A) 12 VIP and 12 SST 
B) 14 VIP and 10 SST 
C) 16 VIP and 8 SST 
D) 18 VIP and 6 SST 
A) 12 VIP and 12 SST 
B) 14 VIP and 10 SST 
C) 16 VIP and 8 SST 
D) 18 VIP and 6 SST

Question 8

Verify that the values of the variables listed are solutions of the system of equations.
-  x = 5, y = -1

Accepted Answer

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

Question 9

Perform the indicated operations and simplify.
-Let   Find AB + BC.

Accepted Answer

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

Question 10

Solve the system of equations. If the system has no solution, say that it is inconsistent.
-

Accepted Answer

A) x = 0, y = 1, z = 0; (0, 1, 0) 
B) x = 4, y = 1, z = 0; (4, 1, 0) 
C) x = 0, y = 0, z = 1; (0, 0, 1) 
D) inconsistent 
A) x = 0, y = 1, z = 0; (0, 1, 0) 
B) x = 4, y = 1, z = 0; (4, 1, 0) 
C) x = 0, y = 0, z = 1; (0, 0, 1) 
D) inconsistent

Question 11

Solve for x.
-

Accepted Answer

A) -2 
B) -4 
C) 2 
D) -5 
A) -2 
B) -4 
C) 2 
D) -5

Question 12

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The Family Arts Center charges $21 for adults, $13 for senior citizens, and $7 for children under 12 fortheir live performances on Sunday afternoon. This past Sunday, the paid revenue was $10,690 for 806tickets sold. There were 44 more children than adults. How many children attended?

Accepted Answer

A) 282 children 
B) 238 children 
C) 286 children 
D) 272 children 
A) 282 children 
B) 238 children 
C) 286 children 
D) 272 children

Question 13

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

Accepted Answer

A) x = 5, y = 4, z = 2; (5, 4, 2) 
B) x = 4, y = 2, z = 4; (4, 2, 4) 
C) x = 5, y = -4, z = -2; (5, -4, -2) 
D) x = 6, y = 2, z = 2; (6, 2, 2) 
A) x = 5, y = 4, z = 2; (5, 4, 2) 
B) x = 4, y = 2, z = 4; (4, 2, 4) 
C) x = 5, y = -4, z = -2; (5, -4, -2) 
D) x = 6, y = 2, z = 2; (6, 2, 2)

Question 14

Solve the problem.
-The area of a triangle with vertices (     where the symbol   indicates that the appropriate sign should be chosen to yield a positive area. Use thisformula to find the area of a triangle whose vertices are (10, 3), (7, -9), and (-5, -2).

Accepted Answer

A)    
B) 165 
C)    
D) 33 
A)    
B) 165 
C)    
D) 33

Question 15

Verify that the values of the variables listed are solutions of the system of equations.
-  x = -6, y = -5

Accepted Answer

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

Question 16

Write the augmented matrix for the system.
-

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 using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so.
-

Accepted Answer

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

Question 19

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

Accepted Answer

A) x = 5, y = - 1; 5, - 1 
B) x = 1, y = 3; 1, 3 
C) x = 10, y = -2; 10, -2 
D) inconsistent 
A) x = 5, y = - 1; 5, - 1 
B) x = 1, y = 3; 1, 3 
C) x = 10, y = -2; 10, -2 
D) inconsistent

Question 20

Solve using elimination.
-

Accepted Answer

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

Use the properties of determinants to find the value of the second determinant, given the value of the first. -

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. -

Solve the system of equations by substitution. -

Graph the system of inequalities. -

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

Verify that the values of the variables listed are solutions of the system of equations. - x = 5, y = -1

Perform the indicated operations and simplify. -Let Find AB + BC.

Solve the system of equations. If the system has no solution, say that it is inconsistent. -

Solve for x. -

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

Solve the problem. -The area of a triangle with vertices ( where the symbol indicates that the appropriate sign should be chosen to yield a positive area. Use thisformula to find the area of a triangle whose vertices are (10, 3), (7, -9), and (-5, -2).

Verify that the values of the variables listed are solutions of the system of equations. - x = -6, y = -5

Write the augmented matrix for the system. -

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

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

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

Solve using elimination. -

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

Use the properties of determinants to find the value of the second determinant, given the value of the first. -

Determine whether the system corresponding to the given augmented matrix is consistent or inconsistent. If it is consistent, give the solution. -

Solve the system of equations by substitution. -

Graph the system of inequalities. -

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

Verify that the values of the variables listed are solutions of the system of equations. - x = 5, y = -1

Perform the indicated operations and simplify. -Let Find AB + BC.

Solve the system of equations. If the system has no solution, say that it is inconsistent. -

Solve for x. -

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

Solve the problem. -The area of a triangle with vertices ( where the symbol indicates that the appropriate sign should be chosen to yield a positive area. Use thisformula to find the area of a triangle whose vertices are (10, 3), (7, -9), and (-5, -2).

Verify that the values of the variables listed are solutions of the system of equations. - x = -6, y = -5

Write the augmented matrix for the system. -

Write the partial fraction decomposition of the rational expression. -

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

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

Solve using elimination. -

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