Question 1

Maximize   with the constraints   . Round answer to the nearest hundredth.

Accepted Answer

A) 59.50 
B) 126.00 
C) 69.00 
D) 40.50 
E) 91.80 
A) 59.50 
B) 126.00 
C) 69.00 
D) 40.50 
E) 91.80 B

Question 2

One acetic acid solution is 80% water and another is 45% water. How many liters of each solution should be mixed to produce 15 liters of a solution that is 59% water?

Accepted Answer

A) 10 liters of the 80% solution and 5 liters of the 45% solution 
B) 13 liters of the 80% solution and 2 liters of the 45% solution 
C) 5 liters of the 80% solution and 10 liters of the 45% solution 
D) 2 liters of the 80% solution and 13 liters of the 45% solution 
E) 6 liters of the 80% solution and 9 liters of the 45% solution 
A) 10 liters of the 80% solution and 5 liters of the 45% solution 
B) 13 liters of the 80% solution and 2 liters of the 45% solution 
C) 5 liters of the 80% solution and 10 liters of the 45% solution 
D) 2 liters of the 80% solution and 13 liters of the 45% solution 
E) 6 liters of the 80% solution and 9 liters of the 45% solution E

Question 3

Minimize   with the constraints

Accepted Answer

A) 59 
B) 52 
C) 41 
D) 44 
E) 56 
A) 59 
B) 52 
C) 41 
D) 44 
E) 56 B

Question 4

The sprinters on a track team use the following system of inequalities to determine their targeted exercise heart rate ranges for their workouts.   In this system, y is the person s exercise heart rate in beats per minute and x is the person s age in years. Use the system of inequalities to determine the targeted exercise heart rate range for a sprinter who is 23 years old. Round the minimum and maximum targeted heart rates to the nearest beat per minute.

Accepted Answer

A) between 197 and 202 beats per minute 
B) between 99 and 108 beats per minute 
C) between 174 and 178 beats per minute 
D) between 87 and 98 beats per minute 
E) between 99 and 108 beats per minute. 
A) between 197 and 202 beats per minute 
B) between 99 and 108 beats per minute 
C) between 174 and 178 beats per minute 
D) between 87 and 98 beats per minute 
E) between 99 and 108 beats per minute.

Question 5

Graph the following inequality   .

Accepted Answer

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

Question 6

Sketch the graph of the inequality.

Accepted Answer

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

Question 7

The number x of picture cell phones a manufacturer is willing to sell at price p is given by   where p is the price, in dollars, per picture cell phone. The number x of picture cell phones a distributor is willing to purchase is given by   where p is the price, in dollars, per picture cell phone. Find the equilibrium price.

Accepted Answer

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

Question 8

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 9

A painter leans a ladder against a vertical wall. The top of the ladder is 11 meters above the ground. When the bottom of the ladder is moved 1 meter farther away from the wall, the top of the ladder is 7 meters above the ground. What is the length of the ladder? Round to the nearest hundredth of a meter.

Accepted Answer

A) 34.07 meters 
B) 27.87 meters 
C) 46.46 meters 
D) 43.36 meters 
E) 37.17 meters 
A) 34.07 meters 
B) 27.87 meters 
C) 46.46 meters 
D) 43.36 meters 
E) 37.17 meters

Question 10

A company makes two types of telephone answering machines: the standard model and the deluxe model. Each machine passes through three processes:   ,   , and   . One standard answering machine requires 1 hour in   , 5 hours in   , and 3 hours in   . One deluxe answering machine requires 3 hours in   , 6 hours in   , and 3 hours in   . Because of employee work schedules,   , is available for 27 hours,   , is available for 63 hours, and   is available for 36 hours. If the profit is $5 for each standard model and $12 for each deluxe model, how many units of each type should the company produce to maximize profit?

Accepted Answer

A) 9 standard models and 0 deluxe models 
B) 0 standard models and 9 deluxe models 
C) 9 standard models and 3 deluxe models 
D) 12 standard models and 0 deluxe models 
E) 3 standard models and 8 deluxe models 
A) 9 standard models and 0 deluxe models 
B) 0 standard models and 9 deluxe models 
C) 9 standard models and 3 deluxe models 
D) 12 standard models and 0 deluxe models 
E) 3 standard models and 8 deluxe models

Question 11

Solve the system of equations below:

Accepted Answer

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

Question 12

A rectangular brochure is designed so that it has an area of 17.5 square inches and a perimeter of 17 inches. Find the width of the brochure. Assume the height is greater than the width.

Accepted Answer

A) 7 inches 
B) 2.5 inches 
C) 1.75 inches 
D) 10 inches 
E) 3.5 inches 
A) 7 inches 
B) 2.5 inches 
C) 1.75 inches 
D) 10 inches 
E) 3.5 inches

Question 13

A company sells a large globe and a small globe. The volume of the large globe is four times the volume of the small globe. The difference between the volumes is 1161.36 cubic inches. Find the radius of the small globe. Round to the nearest tenth of an inch.

Accepted Answer

A) 2.3 inches 
B) 4.5 inches 
C) 10.4 inches 
D) 7.2 inches 
E) 3.6 inches 
A) 2.3 inches 
B) 4.5 inches 
C) 10.4 inches 
D) 7.2 inches 
E) 3.6 inches

Question 14

Solve each system of equations by the elimination method.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Solve each system of equations by the substitution method.

Accepted Answer

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

Question 17

Find the center of the circle whose graph passes through the points   and

Accepted Answer

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

Question 18

Minimize   with the constraints   Round answer to the nearest hundredth.

Accepted Answer

A) 45.89 
B) 70.80 
C) 78.00 
D) 48.00 
E) 45.50 
A) 45.89 
B) 70.80 
C) 78.00 
D) 48.00 
E) 45.50

Question 19

Find an equation of the form   whose graph passes through the points   and   .

Accepted Answer

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

Question 20

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

Accepted Answer

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

Maximize with the constraints . Round answer to the nearest hundredth.

One acetic acid solution is 80% water and another is 45% water. How many liters of each solution should be mixed to produce 15 liters of a solution that is 59% water?

Minimize with the constraints

Graph the following inequality .

Sketch the graph of the inequality.

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

Solve the system of equations below:

A rectangular brochure is designed so that it has an area of 17.5 square inches and a perimeter of 17 inches. Find the width of the brochure. Assume the height is greater than the width.

A company sells a large globe and a small globe. The volume of the large globe is four times the volume of the small globe. The difference between the volumes is 1161.36 cubic inches. Find the radius of the small globe. Round to the nearest tenth of an inch.

Solve each system of equations by the elimination method.

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

Solve each system of equations by the substitution method.

Find the center of the circle whose graph passes through the points and

Minimize with the constraints Round answer to the nearest hundredth.

Find an equation of the form whose graph passes through the points and .

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

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters

Exam 9: Systems of Equations and Inequalities

Maximize with the constraints . Round answer to the nearest hundredth.

One acetic acid solution is 80% water and another is 45% water. How many liters of each solution should be mixed to produce 15 liters of a solution that is 59% water?

Minimize with the constraints

Graph the following inequality .

Sketch the graph of the inequality.

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

Solve the system of equations below:

A rectangular brochure is designed so that it has an area of 17.5 square inches and a perimeter of 17 inches. Find the width of the brochure. Assume the height is greater than the width.

A company sells a large globe and a small globe. The volume of the large globe is four times the volume of the small globe. The difference between the volumes is 1161.36 cubic inches. Find the radius of the small globe. Round to the nearest tenth of an inch.

Solve each system of equations by the elimination method.

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

Solve each system of equations by the substitution method.

Find the center of the circle whose graph passes through the points and

Minimize with the constraints Round answer to the nearest hundredth.

Find an equation of the form whose graph passes through the points and .

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

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters