Question 1

Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$2 x ^ { 2 } + y ^ { 2 } = 17$$
$3 x ^ { 2 } - 2 y ^ { 2 } = - 6$

Accepted Answer

A)  $\{ ( 2,3 ) , ( 2 , - 3 ) , ( - 2,3 ) , ( - 2 , - 3 ) \}$ 
B)  $\{ ( 1,3 ) , ( 1 , - 3 ) , ( - 1,3 ) , ( - 1 , - 3 ) \}$ 
C)  $\{ ( 2 , - 3 ) , ( - 2,3 ) \}$ 
D)  $\{ ( 1,3 ) , ( - 1 , - 3 ) \}$ 
A)  $\{ ( 2,3 ) , ( 2 , - 3 ) , ( - 2,3 ) , ( - 2 , - 3 ) \}$ 
B)  $\{ ( 1,3 ) , ( 1 , - 3 ) , ( - 1,3 ) , ( - 1 , - 3 ) \}$ 
C)  $\{ ( 2 , - 3 ) , ( - 2,3 ) \}$ 
D)  $\{ ( 1,3 ) , ( - 1 , - 3 ) \}$

Question 2

Solve the system of equations by the substitution method.
-$$\begin{array} { r } 
x - 3 y = - 30 \
- 5 x - 4 y = - 2
\end{array}$$

Accepted Answer

A)  $\{ ( - 6,8 ) \}$ 
B)  $\{ ( - 7,9 ) \}$ 
C)  $\{ ( 6,9 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( - 6,8 ) \}$ 
B)  $\{ ( - 7,9 ) \}$ 
C)  $\{ ( 6,9 ) \}$ 
D)  $\varnothing$

Question 3

Solve the problem.
-Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 2 times as many dimes as nickels, and the value of the dimes is
$0.90 more than the value of the nickels. How many nickels and dimes does Jamil have?

Accepted Answer

A) 6 nickels and 12 dimes 
B) 7 nickels and 14 dimes 
C) 5 nickels and 10 dimes 
D) 12 nickels and 6 dimes 
A) 6 nickels and 12 dimes 
B) 7 nickels and 14 dimes 
C) 5 nickels and 10 dimes 
D) 12 nickels and 6 dimes

Question 4

Determine whether the given ordered pair is a solution of the system.
-$$\begin{array} { l } 
( 1 , - 6 ) \
3 x + y = 9 \
4 x + 3 y = 22
\end{array}$$

Accepted Answer

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

Question 5

Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$y ^ { 2 } + 3 x ^ { 2 } = 17$$
$y ^ { 2 } - x ^ { 2 } = 1$

Accepted Answer

A)  $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } ) , ( - 2 , \sqrt { 5 } ) , ( - 2 , - \sqrt { 5 } )$ 
B)  $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } )$ 
C)  $( 3 , \sqrt { 5 } ) , ( 3 , - \sqrt { 5 } ) , ( - 3 , \sqrt { 5 } ) , ( - 3 , - \sqrt { 5 } )$ 
D)  $( 3 , \sqrt { 5 } ) , ( 3 , - \sqrt { 5 } )$ 
A)  $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } ) , ( - 2 , \sqrt { 5 } ) , ( - 2 , - \sqrt { 5 } )$ 
B)  $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } )$ 
C)  $( 3 , \sqrt { 5 } ) , ( 3 , - \sqrt { 5 } ) , ( - 3 , \sqrt { 5 } ) , ( - 3 , - \sqrt { 5 } )$ 
D)  $( 3 , \sqrt { 5 } ) , ( 3 , - \sqrt { 5 } )$

Question 6

Solve the problem.
-Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 860 calories. Three servings of ice cream and two servings of blueberry pie provides 1300 calories. Find the
Caloric content of each item.

Accepted Answer

A)  Serving of ice cream: 220 calories
Serving of blueberry pie: 320 calories 
B)  Serving of ice cream: 320 calories
Serving of blueberry pie: 220 calories 
C)  Serving of ice cream: 196 calories
Serving of blueberry pie: 332 calories 
D)  Serving of ice cream: 236 calories
Serving of blueberry pie: 312 calories 
A)  Serving of ice cream: 220 calories
Serving of blueberry pie: 320 calories 
B)  Serving of ice cream: 320 calories
Serving of blueberry pie: 220 calories 
C)  Serving of ice cream: 196 calories
Serving of blueberry pie: 332 calories 
D)  Serving of ice cream: 236 calories
Serving of blueberry pie: 312 calories

Question 7

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.
  
-How many binoculars must be produced and sold for the company to break even?

Accepted Answer

A) 750 binoculars 
B) 2250 binoculars 
C) 1500 binoculars 
D) 2700 binoculars 
A) 750 binoculars 
B) 2250 binoculars 
C) 1500 binoculars 
D) 2700 binoculars

Question 8

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.
  
-More than how many binoculars must be produced and sold for the company to have a profit gain?

Accepted Answer

A) 750 binoculars 
B) 2250 binoculars 
C) 1500 binoculars 
D) 2700 binoculars 
A) 750 binoculars 
B) 2250 binoculars 
C) 1500 binoculars 
D) 2700 binoculars

Question 9

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
-$$\begin{array} { l } 
x + y = - 9 \
x - y = 12
\end{array}$$

Accepted Answer

A)  $\{ ( 1.5 , - 10.5 ) \}$ 
B)  $\{ ( 1.5,10.5 ) \}$ 
C)  $\{ ( x , y ) \mid x + y = - 9 \}$ 
D)  $\varnothing$ 
A)  $\{ ( 1.5 , - 10.5 ) \}$ 
B)  $\{ ( 1.5,10.5 ) \}$ 
C)  $\{ ( x , y ) \mid x + y = - 9 \}$ 
D)  $\varnothing$

Question 10

Solve the problem.
-In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 30 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the
Race, by how many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.)

Accepted Answer

A) 20.04 ft 
B) -10.06 ft 
C) -20.11 ft 
D) 10.02 ft 
A) 20.04 ft 
B) -10.06 ft 
C) -20.11 ft 
D) 10.02 ft

Question 11

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$$\frac { 6 x - 4 } { ( x - 4 ) \left( x ^ { 2 } + x + 6 \right) }$$

Accepted Answer

A)  $\frac { A } { x - 4 } + \frac { B x + C } { x ^ { 2 } + x + 6 }$ 
B)  $\frac { A } { x - 4 } + \frac { B } { x ^ { 2 } + x + 6 }$ 
C)  $\frac { \mathrm { A } } { x - 4 } + \frac { \mathrm { B } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 6 } + \frac { \mathrm { C } } { ( \mathrm { x } - 4 ) \left( \mathrm { x } ^ { 2 } + \mathrm { x } + 6 \right) }$ 
D)  $\frac { \mathrm { A } } { \mathrm { x } - 4 } + \frac { \mathrm { Bx } + \mathrm { C } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 6 } + \frac { \mathrm { D } } { ( \mathrm { x } - 4 ) \left( \mathrm { x } ^ { 2 } + \mathrm { x } + 6 \right) }$ Write the partial fraction decomposition of the rational expression. 
A)  $\frac { A } { x - 4 } + \frac { B x + C } { x ^ { 2 } + x + 6 }$ 
B)  $\frac { A } { x - 4 } + \frac { B } { x ^ { 2 } + x + 6 }$ 
C)  $\frac { \mathrm { A } } { x - 4 } + \frac { \mathrm { B } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 6 } + \frac { \mathrm { C } } { ( \mathrm { x } - 4 ) \left( \mathrm { x } ^ { 2 } + \mathrm { x } + 6 \right) }$ 
D)  $\frac { \mathrm { A } } { \mathrm { x } - 4 } + \frac { \mathrm { Bx } + \mathrm { C } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 6 } + \frac { \mathrm { D } } { ( \mathrm { x } - 4 ) \left( \mathrm { x } ^ { 2 } + \mathrm { x } + 6 \right) }$ Write the partial fraction decomposition of the rational expression.

Question 12

Graph the inequality.
-$y \geq x-4$

Accepted Answer

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

Question 13

Solve the problem.
-Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 6 hours to make a hat and 4 hours to make an afghan, and she has no more than 66 hours available. She has material for no
More than 14 items, and she wants to make at least two afghans. Let x = the number of hats she makes and
Y = the number of afghans she makes. Write a system of inequalities that describes these constraints.

Accepted Answer

A)  $6 x + 4 y \leq 66$
$x + y \leq 14$
$y \geq 2$ 
B)  $6 x + 4 y \leq 66$
$x + y \leq 14$
$x \geq 2$ 
C)  $4 x + 6 y \leq 66$
$x + y \leq 14$
$x \leq 2$ 
D)  $6 x + 4 y \geq 66$
$x + y \leq 14$
$y \geq 2$ 
A)  $6 x + 4 y \leq 66$
$x + y \leq 14$
$y \geq 2$ 
B)  $6 x + 4 y \leq 66$
$x + y \leq 14$
$x \geq 2$ 
C)  $4 x + 6 y \leq 66$
$x + y \leq 14$
$x \leq 2$ 
D)  $6 x + 4 y \geq 66$
$x + y \leq 14$
$y \geq 2$

Question 14

Solve the system by the substitution method.
-$x ^ { 2 } + y ^ { 2 } = 25$ $x - y = 1$

Accepted Answer

A)  $\{ ( 4,3 ) , ( - 3 , - 4 ) \}$ 
B)  $\{ ( - 4,3 ) , ( - 3,4 ) \}$ 
C)  $\{ ( 4 , - 3 ) , ( 3 , - 4 ) \}$ 
D)  $\{ ( - 4 , - 3 ) , ( - 3 , - 4 ) \}$ 
A)  $\{ ( 4,3 ) , ( - 3 , - 4 ) \}$ 
B)  $\{ ( - 4,3 ) , ( - 3,4 ) \}$ 
C)  $\{ ( 4 , - 3 ) , ( 3 , - 4 ) \}$ 
D)  $\{ ( - 4 , - 3 ) , ( - 3 , - 4 ) \}$

Question 15

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { c } 
( 1,4,0 ) \
x - y + 2 z = - 2 \
2 x \quad + z = 1 \
x + 3 y + z = 13
\end{array}$$

Accepted Answer

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

Question 16

Solve the problem.
-Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 5 feet more than 6 times the width. He needs 122 feet of fencing to do the job. Find
The length and width of the garden.

Accepted Answer

A) length: 53 feet; width: 8 feet 
B) length: 105 2 feet; width: 165 feet 7 7 
C) length: 59 feet; width: 9 feet 
D) length: 47 feet; width: 7 feet 
A) length: 53 feet; width: 8 feet 
B) length: 105 2 feet; width: 165 feet 7 7 
C) length: 59 feet; width: 9 feet 
D) length: 47 feet; width: 7 feet

Question 17

Use Linear Programming to Solve Problems
Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of the feasible points.
-Objective Function: z = 5x + 6y Find minimum.

Accepted Answer

A) minimum: 32 
B) minimum: 33 
C) minimum: 40 
D) no minimum 
A) minimum: 32 
B) minimum: 33 
C) minimum: 40 
D) no minimum

Question 18

Solve the problem.
-Benjamin never has more than 23 hours free during the week. He is trying to make a weekly plan for dividing his free time between reading and working out. He wants to spend at least 6 hours per week
Reading. Write a system of inequalities to describe the situation. Let x represent the number of hours for
Reading and y represent the number of hours for working out.

Accepted Answer

A)  $x + y \leq 23$
$x \geq 6$
$y \geq 0$ 
B)  $x + y \leq 23$
$x \geq 6 y$
$x \geq 0$
$y \geq 0$ 
C)  $x + y \leq 23$
$y \geq 6$
$x \geq 0$ 
D)  $x + y \leq 23$
$x \leq 6 y$
$x \geq 0$
$y \geq 0$ 
A)  $x + y \leq 23$
$x \geq 6$
$y \geq 0$ 
B)  $x + y \leq 23$
$x \geq 6 y$
$x \geq 0$
$y \geq 0$ 
C)  $x + y \leq 23$
$y \geq 6$
$x \geq 0$ 
D)  $x + y \leq 23$
$x \leq 6 y$
$x \geq 0$
$y \geq 0$

Question 19

Solve the problem.
-You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball's height
Above the ground, y, after x seconds. Consider the following data:

Find the quadratic function $y = a x ^ { 2 } + b x + c$ whose graph passes through the given points.

Accepted Answer

A)  $y = - 16 x ^ { 2 } + 90 x + 20$ 
B)  $y = - 12 x ^ { 2 } + 90 x + 16$ 
C)  $y = - 16 x ^ { 2 } + 80 x + 30$ 
D)  $y = - 10 x ^ { 2 } + 100 x + 4$ 
A)  $y = - 16 x ^ { 2 } + 90 x + 20$ 
B)  $y = - 12 x ^ { 2 } + 90 x + 16$ 
C)  $y = - 16 x ^ { 2 } + 80 x + 30$ 
D)  $y = - 10 x ^ { 2 } + 100 x + 4$

Question 20

Solve the system of equations.
-$$\begin{array} { l } 
2 x + 3 y + z = - 5 \
3 x - 4 y - z = 22 \
5 x + y + 3 z = - 2
\end{array}$$

Accepted Answer

A)  $\{ ( 3 , - 2 , - 5 ) \}$ 
B)  $\{ ( 3 , - 5 , - 2 ) \}$ 
C)  $\{ ( - 5 , - 2,3 ) \}$ 
D)  $\{ ( - 2,3 , - 5 ) \}$ 
A)  $\{ ( 3 , - 2 , - 5 ) \}$ 
B)  $\{ ( 3 , - 5 , - 2 ) \}$ 
C)  $\{ ( - 5 , - 2,3 ) \}$ 
D)  $\{ ( - 2,3 , - 5 ) \}$

Solve Nonlinear Systems By Addition Solve the system by the addition method. - $2 x ^ { 2 } + y ^ { 2 } = 17$ $3 x ^ { 2 } - 2 y ^ { 2 } = - 6$

Solve the system of equations by the substitution method. - x-3y=-30 -5x-4y=-2

Determine whether the given ordered pair is a solution of the system. - (1,-6) 3x+y=9 4x+3y=22

Solve Nonlinear Systems By Addition Solve the system by the addition method. - $y ^ { 2 } + 3 x ^ { 2 } = 17$ $y ^ { 2 } - x ^ { 2 } = 1$

Solve the problem. -Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 860 calories. Three servings of ice cream and two servings of blueberry pie provides 1300 calories. Find the Caloric content of each item.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -How many binoculars must be produced and sold for the company to break even?

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -More than how many binoculars must be produced and sold for the company to have a profit gain?

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - x+y=-9 x-y=12

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. - $\frac { 6 x - 4 } { ( x - 4 ) \left( x ^ { 2 } + x + 6 \right) }$

Graph the inequality. - $y \geq x-4$ $Graph the inequality. - y \geq x-4$

Solve the system by the substitution method. - $x ^ { 2 } + y ^ { 2 } = 25$ $x - y = 1$

Determine if the given ordered triple is a solution of the system. - (1,4,0) x-y+2z=-2 2x+z=1 x+3y+z=13

Solve the problem. -Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 5 feet more than 6 times the width. He needs 122 feet of fencing to do the job. Find The length and width of the garden.

Use Linear Programming to Solve Problems Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. -Objective Function: z = 5x + 6y Find minimum.

Solve the system of equations. - 2x+3y+z=-5 3x-4y-z=22 5x+y+3z=-2

Equations and Inequalities

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Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

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Exam 5: Systems of Equations and Inequalities

Solve Nonlinear Systems By Addition Solve the system by the addition method. - 2x2+y2=172 x ^ { 2 } + y ^ { 2 } = 172x2+y2=17 3x2−2y2=−63 x ^ { 2 } - 2 y ^ { 2 } = - 63x2−2y2=−6