Question 1

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

Accepted Answer

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

Question 2

Derive a set of inequalities to describe the region. Triangle: vertices at (0, 0), (3, 0), (3, 4)

Accepted Answer

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

Question 3

Solve the system by the method of substitution.

Accepted Answer

A)  (7, -5), (-7, 5) 
B)  (7, -5) 
C)  (0, 7) 
D)  (0, 0) 
E)  no real solution 
A)  (7, -5), (-7, 5) 
B)  (7, -5) 
C)  (0, 7) 
D)  (0, 0) 
E)  no real solution

Question 4

Use a graphing utility to solve the system of equations. Find the solution accurate to two decimal places.

Accepted Answer

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

Question 5

Write the partial fraction decomposition of the improper rational expression.

Accepted Answer

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

Question 6

Write the partial fraction decomposition of the rational expression.

Accepted Answer

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

Question 7

Solve the system of linear equations.

Accepted Answer

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

Question 8

Sketch the graph and label the vertices of the solution set of the system of inequalities. Shade the solution set.

Accepted Answer

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

Question 9

Write an inequality for the shaded region shown in the figure.

Accepted Answer

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

Question 10

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.

Accepted Answer

A)  (0, 0) 
B)  (-1, 4) 
C)  (3, -3) 
D)  (-9, 7) 
E)  (9, 6) 
A)  (0, 0) 
B)  (-1, 4) 
C)  (3, -3) 
D)  (-9, 7) 
E)  (9, 6)

Question 11

Solve using any method.

Accepted Answer

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

Question 12

An airplane flying into a headwind travels 216 miles in 2 hours and 42 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

Accepted Answer

A)  plane speed = 71 mph; wind speed = 83 mph 
B)  plane speed = 109 mph; wind speed = 14 mph 
C)  plane speed = 94 mph; wind speed = 14 mph 
D)  plane speed = 71 mph; wind speed = 14 mph 
E)  plane speed = 109 mph; wind speed = 101 mph 
A)  plane speed = 71 mph; wind speed = 83 mph 
B)  plane speed = 109 mph; wind speed = 14 mph 
C)  plane speed = 94 mph; wind speed = 14 mph 
D)  plane speed = 71 mph; wind speed = 14 mph 
E)  plane speed = 109 mph; wind speed = 101 mph

Question 13

Solve the system by the method of substitution.

Accepted Answer

A)  (3, 4) 
B)  (-3, 4) 
C)  (4, 3) 
D)  (-4, 3) 
E)  (4, -3) 
A)  (3, 4) 
B)  (-3, 4) 
C)  (4, 3) 
D)  (-4, 3) 
E)  (4, -3)

Question 14

Solve using any method.

Accepted Answer

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

Question 15

Find the least squares regression line   for the points   by solving the system for a and b.   Points:   space

Accepted Answer

A)  y = 3.93x -4.21 
B)  y = 2.80x -3.20 
C)  y = -2.66x +2.80 
D)  y = -3.47x -4.21 
E)  y = -3.20x +2.80 
A)  y = 3.93x -4.21 
B)  y = 2.80x -3.20 
C)  y = -2.66x +2.80 
D)  y = -3.47x -4.21 
E)  y = -3.20x +2.80

Question 16

Determine which ordered pair is a solution of the system.

Accepted Answer

A)  (1, -2) 
B)  (-5, 4) 
C)  (2, 1) 
D)  (-2, 1) 
E)  (-4, -5) 
A)  (1, -2) 
B)  (-5, 4) 
C)  (2, 1) 
D)  (-2, 1) 
E)  (-4, -5)

Question 17

An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet
At t = 2 seconds, s = 98 feet
At t = 3 seconds, s = 3 feet

Accepted Answer

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

Question 18

Solve the system of linear equations.

Accepted Answer

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

Question 19

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

Accepted Answer

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

Question 20

During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 200 tickets and collected $1372. If adult tickets sold for $8 and children's tickets sold for $6, how many of each type of ticket were sold?

Accepted Answer

A)  adult tickets sold = 86; children's tickets sold = 114 
B)  adult tickets sold = 97; children's tickets sold = 125 
C)  adult tickets sold = 114; children's tickets sold = 86 
D)  adult tickets sold = 97; children's tickets sold = 99 
E)  adult tickets sold = 125; children's tickets sold = 97 
A)  adult tickets sold = 86; children's tickets sold = 114 
B)  adult tickets sold = 97; children's tickets sold = 125 
C)  adult tickets sold = 114; children's tickets sold = 86 
D)  adult tickets sold = 97; children's tickets sold = 99 
E)  adult tickets sold = 125; children's tickets sold = 97

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

Derive a set of inequalities to describe the region. Triangle: vertices at (0, 0), (3, 0), (3, 4)

Solve the system by the method of substitution.

Use a graphing utility to solve the system of equations. Find the solution accurate to two decimal places.

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

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

Solve the system of linear equations.

Sketch the graph and label the vertices of the solution set of the system of inequalities. Shade the solution set.

Write an inequality for the shaded region shown in the figure.

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.

Solve using any method.

An airplane flying into a headwind travels 216 miles in 2 hours and 42 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

Solve the system by the method of substitution.

Solve using any method.

Find the least squares regression line for the points by solving the system for a and b. Points: space

Determine which ordered pair is a solution of the system.

An object moving vertically is at the given heights at the specified times. Find the position equation for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet

Solve the system of linear equations.

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. $Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.$

During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 200 tickets and collected $1372. If adult tickets sold for $8 and children's tickets sold for $6, how many of each type of ticket were sold?

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Filters

Exam 9: Systems of Equations and Inequalities

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

Derive a set of inequalities to describe the region. Triangle: vertices at (0, 0), (3, 0), (3, 4)

Solve the system by the method of substitution.

Use a graphing utility to solve the system of equations. Find the solution accurate to two decimal places.

Write the partial fraction decomposition of the improper rational expression.

Write the partial fraction decomposition of the rational expression.

Solve the system of linear equations.

Sketch the graph and label the vertices of the solution set of the system of inequalities. Shade the solution set.

Write an inequality for the shaded region shown in the figure.

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.

Solve using any method.

An airplane flying into a headwind travels 216 miles in 2 hours and 42 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

Solve the system by the method of substitution.

Solve using any method.

Find the least squares regression line for the points by solving the system for a and b. Points: space

Determine which ordered pair is a solution of the system.

An object moving vertically is at the given heights at the specified times. Find the position equation for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet

Solve the system of linear equations.

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 200 tickets and collected $1372. If adult tickets sold for $8 and children's tickets sold for $6, how many of each type of ticket were sold?

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Filters

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

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

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. $Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.$