Question 1

Find which of the following system of inequalities has a right triangle as a graphed solution set. System I:   System II:   System III:

Accepted Answer

A)  No systems have a right triangle as a graphed solution set. 
B)  Only systems II and III have a right triangle as a graphed solution set. 
C)  Only systems I and III have a right triangle as a graphed solution set. 
D)  Only system I has a right triangle as a graphed solution set. 
E)  Only systems I and II have a right triangle as a graphed solution set. 
A)  No systems have a right triangle as a graphed solution set. 
B)  Only systems II and III have a right triangle as a graphed solution set. 
C)  Only systems I and III have a right triangle as a graphed solution set. 
D)  Only system I has a right triangle as a graphed solution set. 
E)  Only systems I and II have a right triangle as a graphed solution set. B

Question 2

Solve the system by the method of substitution.

Accepted Answer

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

Question 3

Graph the solution set of the system of inequalities below.

Accepted Answer

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

Question 4

Find the equation of the circle   that passes through the points

Accepted Answer

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

Question 5

Sketch the graph of the solution set of each system of inequalities.

Accepted Answer

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

Question 6

Solve the system of linear equations.

Accepted Answer

A)    
B)    
C)    
D)    
E)  inconsistent 
A)    
B)    
C)    
D)    
E)  inconsistent

Question 7

Solve the system of equations below:

Accepted Answer

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

Question 8

A dietitian designs a special diet supplement using two different foods.Each ounce of food X contains 10 units of calcium, 15 units of iron, and 20 units of vitamin B.Each ounce of food Y contains 15 units of calcium, 10 units of iron, and 20 units of vitamin B.The minimum daily requirements for the diet are 380 units of calcium, 240 units of iron, and 390 units of vitamin B.Which combinations of foods X and Y below, if any, can be given to the patient to meet the minimum daily requirements? Combination I :
21 ounces of food X and 22 ounces of food Y
Combination II :
16 ounces of food X and 19 ounces of food Y
Combination III :
10 ounces of food X and 10 ounces of food Y

Accepted Answer

A)  Only combinations II and III meet the minimum daily requirement. 
B)  Only combination II meets the minimum daily requirement. 
C)  None of the combinations meet the minimum daily requirement. 
D)  Only combinations I and II meet the minimum daily requirement. 
E)  Only combination III meets the minimum daily requirement. 
A)  Only combinations II and III meet the minimum daily requirement. 
B)  Only combination II meets the minimum daily requirement. 
C)  None of the combinations meet the minimum daily requirement. 
D)  Only combinations I and II meet the minimum daily requirement. 
E)  Only combination III meets the minimum daily requirement.

Question 9

You plan to invest up to $30,000 in two different interest-bearing accounts.Each account is to contain at least $9000.Moreover, one account should have at least three times the amount that is in the other account.Find a system of inequalities that describes the amount that you can invest in each account.

Accepted Answer

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

Question 10

Find the minimum and maximum values of the objective function   and where they occur, subject to the constraints

Accepted Answer

A)  The minimum value is 0 at   and the maximum value is 32 at   
B)  The minimum value is 0 at   and the maximum value is 32 at   
C)  The minimum value is 0 at   and the maximum value is 32 at   
D)  The minimum value is 0 at   and the maximum value is 32 at   
E)  The minimum value is 0 at   and the maximum value is 32 at   
A)  The minimum value is 0 at   and the maximum value is 32 at   
B)  The minimum value is 0 at   and the maximum value is 32 at   
C)  The minimum value is 0 at   and the maximum value is 32 at   
D)  The minimum value is 0 at   and the maximum value is 32 at   
E)  The minimum value is 0 at   and the maximum value is 32 at

Question 11

A furniture company produces tables and chairs.Each table requires 1 hour in the assembly center and 2.25 hours in the finishing center.Each chair requires 0.75 hour in the assembly center and 0.5 hour in the finishing center.The company's assembly center is available 18 hours per day, and its finishing center is available 12 hours per day.Let   and   be the number of tables and chairs produced per day, respectively.Find a system of inequalities describing all possible production levels.

Accepted Answer

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

Question 12

Solve the system of linear equations.

Accepted Answer

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

Question 13

Solve each system of equations by the elimination method.

Accepted Answer

A)    
B)    
C)    
D)    
E)  no solution 
A)    
B)    
C)    
D)    
E)  no solution

Question 14

Sketch the graph of the inequality below.

Accepted Answer

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

Question 15

The sales of various types of lawn and garden items vary according to the season.At a certain home improvement store, the monthly sales H of garden hoses (hoses sold per month) declines from July to October whereas the monthly sales of lawn rakes R (rakes sold per month) increase during this same interval.The sales of these two items during the calendar months July-October are modeled by the equations: H(t) = 64 - 6t
R(t) = 17t - 97,
Where t is the month (t = 7 corresponds to July).In which month does the number of rakes sold equal the number of hoses sold?

Accepted Answer

A)  August 
B)  September 
C)  October 
D)  November 
E)  July 
A)  August 
B)  September 
C)  October 
D)  November 
E)  July

Question 16

Solve the system by the method of substitution.

Accepted Answer

A)  (12, 5), (-12, -5) 
B)  (12, 5) 
C)  (12, 5), (-12, 5), (-12, -5), (12, -5) 
D)  (5, 12), (5, -12) 
E)  no real solution 
A)  (12, 5), (-12, -5) 
B)  (12, 5) 
C)  (12, 5), (-12, 5), (-12, -5), (12, -5) 
D)  (5, 12), (5, -12) 
E)  no real solution

Question 17

Solve the system below by method of substitution, if possible.

Accepted Answer

A)  no solution 
B)    
C)    
D)    ,   
E)    
A)  no solution 
B)    
C)    
D)    ,   
E)

Question 18

An ice cream supplier has two machines that produce vanilla and chocolate ice cream.To meet one of its contractual obligations, the company must produce at least 11 gallons of vanilla ice cream and 90 gallons of chocolate ice cream per day.One machine makes 5 gallons of vanilla and 6 gallons of chocolate ice cream per hour.The second machine makes 1 gallons of vanilla and 14 gallons of chocolate ice cream per hour.It costs $21 per hour to run machine 1 and $26 per hour to run machine 2.How many hours should each machine be operated to fulfill the contract at the least expense?

Accepted Answer

A)  Machine 1 for 6 hours and machine 2 for 1 hour. 
B)  Machine 1 for 1 hour and machine 2 for no hours. 
C)  Machine 1 for 1 hour and machine 2 for 6 hours. 
D)  Machine 1 for 6 hours and machine 2 for no hours. 
E)  Machine 1 for no hours and machine 2 for 1 hour. 
A)  Machine 1 for 6 hours and machine 2 for 1 hour. 
B)  Machine 1 for 1 hour and machine 2 for no hours. 
C)  Machine 1 for 1 hour and machine 2 for 6 hours. 
D)  Machine 1 for 6 hours and machine 2 for no hours. 
E)  Machine 1 for no hours and machine 2 for 1 hour.

Question 19

Maximize the object function   subject to the constraints

Accepted Answer

A)  The maximum value is 90 at   
B)  The maximum value is 122 at   
C)  The maximum value is 130 at   
D)  The maximum value is 86 at   
E)  The maximum value is 56 at   
A)  The maximum value is 90 at   
B)  The maximum value is 122 at   
C)  The maximum value is 130 at   
D)  The maximum value is 86 at   
E)  The maximum value is 56 at

Question 20

Use a graphing utility to graph the inequality.Shade the region representing the solution.

Accepted Answer

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

Find which of the following system of inequalities has a right triangle as a graphed solution set. System I: System II: System III:

Solve the system by the method of substitution.

Graph the solution set of the system of inequalities below.

Find the equation of the circle that passes through the points

Sketch the graph of the solution set of each system of inequalities.

Solve the system of linear equations.

Solve the system of equations below:

Find the minimum and maximum values of the objective function and where they occur, subject to the constraints

Solve the system of linear equations.

Solve each system of equations by the elimination method.

Sketch the graph of the inequality below.

Solve the system by the method of substitution.

Solve the system below by method of substitution, if possible.

Maximize the object function subject to the constraints

Use a graphing utility to graph the inequality.Shade the region representing the solution.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants

Sequences, Series, and Probability

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Exam 5: Systems of Equations and Inequalities

Find which of the following system of inequalities has a right triangle as a graphed solution set. System I: System II: System III:

Solve the system by the method of substitution.

Graph the solution set of the system of inequalities below.

Find the equation of the circle that passes through the points

Sketch the graph of the solution set of each system of inequalities.

Solve the system of linear equations.

Solve the system of equations below:

Find the minimum and maximum values of the objective function and where they occur, subject to the constraints

Solve the system of linear equations.

Solve each system of equations by the elimination method.

Sketch the graph of the inequality below.

Solve the system by the method of substitution.

Solve the system below by method of substitution, if possible.

Maximize the object function subject to the constraints

Use a graphing utility to graph the inequality.Shade the region representing the solution.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants

Sequences, Series, and Probability

Filters