Question 1

Write the partial fraction decomposition of the rational expression.
-$\frac { 27 - 5 x } { x ( x - 3 ) ^ { 2 } }$

Accepted Answer

A)  $\frac { 3 } { x } + \frac { 4 } { x - 3 } + \frac { - 3 } { ( x - 3 ) ^ { 2 } }$ 
B)  $\frac { 3 } { x } + \frac { - 3 } { x - 3 } + \frac { 4 } { ( x - 3 ) ^ { 2 } }$ 
C)  $\frac { - 3 } { x } + \frac { 3 } { x - 3 } + \frac { 4 } { ( x - 3 ) ^ { 2 } }$ 
D)  $\frac { 3 } { x } + \frac { - 3 } { x - 3 } + \frac { 8 } { ( x - 3 ) ^ { 2 } }$ 
A)  $\frac { 3 } { x } + \frac { 4 } { x - 3 } + \frac { - 3 } { ( x - 3 ) ^ { 2 } }$ 
B)  $\frac { 3 } { x } + \frac { - 3 } { x - 3 } + \frac { 4 } { ( x - 3 ) ^ { 2 } }$ 
C)  $\frac { - 3 } { x } + \frac { 3 } { x - 3 } + \frac { 4 } { ( x - 3 ) ^ { 2 } }$ 
D)  $\frac { 3 } { x } + \frac { - 3 } { x - 3 } + \frac { 8 } { ( x - 3 ) ^ { 2 } }$ B

Question 2

Solve the system by the addition method.
-$$\begin{array} { l } 
x + y = - 6 \
x - y = 12
\end{array}$$

Accepted Answer

A)  $\{ ( 6 , - 9 ) \}$ 
B)  $\{ ( 6,3 ) \}$ 
C)  $\{ ( 3,9 ) \}$ 
D)  $\{ ( 3 , - 9 ) \}$ 
A)  $\{ ( 6 , - 9 ) \}$ 
B)  $\{ ( 6,3 ) \}$ 
C)  $\{ ( 3,9 ) \}$ 
D)  $\{ ( 3 , - 9 ) \}$ D

Question 3

Write the partial fraction decomposition of the rational expression.
-$\frac { 5 x ^ { 3 } + 19 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Accepted Answer

A)  $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { 4 x + 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
B)  $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
C)  $\frac { 5 x + 1 } { x ^ { 2 } + 3 } + \frac { 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
D)  $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { - 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
A)  $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { 4 x + 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
B)  $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
C)  $\frac { 5 x + 1 } { x ^ { 2 } + 3 } + \frac { 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
D)  $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { - 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ B

Question 4

Solve the problem
-The sum of three numbers is -6. If the second number is subtracted from the sum of the first and third numbers, the result is -4. If the third number is subtracted from the sum of the first and second numbers, the result is -2. Find the three numbers.
[Hint: let x represent the first number, y the second number, and z the third number. Use the given conditions to write and solve a system of equations.]

Accepted Answer

A)  $x = - 3 , y = - 1 , z = - 2$ 
B)  $x = - 2 , y = 0 , z = - 4$ 
C)  $x = - 2 , y = - 1 , z = - 3$ 
D)  $x = - 5 , y = 1 , z = - 2$ 
A)  $x = - 3 , y = - 1 , z = - 2$ 
B)  $x = - 2 , y = 0 , z = - 4$ 
C)  $x = - 2 , y = - 1 , z = - 3$ 
D)  $x = - 5 , y = 1 , z = - 2$

Question 5

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.
  
-Is there a profit when 956 binoculars are produced?

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 6

Solve the system by the substitution method.
-$$\begin{array} { l } 
x ^ { 2 } = y ^ { 2 } + 39 \
x - y = 3
\end{array}$$

Accepted Answer

A)  $\{ ( - 8,5 ) \}$ 
B)  $\{ ( - 8 , - 5 ) \}$ 
C)  $\{ ( 8,5 ) \}$ 
D)  $\{ ( 8 , - 5 ) \}$ 
A)  $\{ ( - 8,5 ) \}$ 
B)  $\{ ( - 8 , - 5 ) \}$ 
C)  $\{ ( 8,5 ) \}$ 
D)  $\{ ( 8 , - 5 ) \}$

Question 7

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { c } 
( - 3 , - 2,5 ) \
x + 3 y + 4 z = - 13 \
2 y + 5 z = - 19 \
z = - 3
\end{array}$$

Accepted Answer

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

Question 8

Solve the problem
-Find the values of $a , b$, and c such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 3 , - 25 ) , ( 2,5 )$, and $( 3 , - 1 )$.

Accepted Answer

A)  $a = 2 ; b = 4 ; c = 5$ 
B)  $a = - 2 ; b = 5 ; c = 4$ 
C)  $a = - 2 ; b = 4 ; c = 5$ 
D)  $a = 2 ; b = 5 ; c = 4$ 
A)  $a = 2 ; b = 4 ; c = 5$ 
B)  $a = - 2 ; b = 5 ; c = 4$ 
C)  $a = - 2 ; b = 4 ; c = 5$ 
D)  $a = 2 ; b = 5 ; c = 4$

Question 9

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$$\frac { 5 x - 3 } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$$

Accepted Answer

A)  $\frac { A } { x - 5 } + \frac { B } { x ^ { 2 } + x + 5 } + \frac { C } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$ 
B)  $\frac { \mathrm { A } } { \mathrm { x } - 5 } + \frac { \mathrm { B } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 5 }$ 
C)  $\frac { A } { x - 5 } + \frac { B x + C } { x ^ { 2 } + x + 5 } + \frac { D } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$ 
D)  $\frac { A } { x - 5 } + \frac { B x + C } { x ^ { 2 } + x + 5 }$ 
A)  $\frac { A } { x - 5 } + \frac { B } { x ^ { 2 } + x + 5 } + \frac { C } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$ 
B)  $\frac { \mathrm { A } } { \mathrm { x } - 5 } + \frac { \mathrm { B } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 5 }$ 
C)  $\frac { A } { x - 5 } + \frac { B x + C } { x ^ { 2 } + x + 5 } + \frac { D } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$ 
D)  $\frac { A } { x - 5 } + \frac { B x + C } { x ^ { 2 } + x + 5 }$

Question 10

Solve the problem.
-A flat rectangular piece of aluminum has a perimeter of 56 inches. The length is 12 inches longer than the width. Find the width.

Accepted Answer

A) 20 inches 
B) 32 inches 
C) 8 inches 
D) 28 inches 
A) 20 inches 
B) 32 inches 
C) 8 inches 
D) 28 inches

Question 11

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.
  
-What is the profit when 963 binoculars are produced?

Accepted Answer

A) $3426 
B) $2352 
C) $426 
D) $5352 
A) $3426 
B) $2352 
C) $426 
D) $5352

Question 12

Write the partial fraction decomposition of the rational expression.
-$$\frac { x - 2 } { ( x - 5 ) ( x - 4 ) }$$

Accepted Answer

A)  $\frac { 3 } { x - 5 } + \frac { - 2 } { x - 4 }$ 
B)  $\frac { 3 } { x - 5 } + \frac { 2 } { x - 4 }$ 
C)  $\frac { - 2 } { x - 5 } + \frac { 3 } { x - 4 }$ 
D)  $\frac { 2 } { x - 5 } + \frac { - 3 } { x - 4 }$ 
A)  $\frac { 3 } { x - 5 } + \frac { - 2 } { x - 4 }$ 
B)  $\frac { 3 } { x - 5 } + \frac { 2 } { x - 4 }$ 
C)  $\frac { - 2 } { x - 5 } + \frac { 3 } { x - 4 }$ 
D)  $\frac { 2 } { x - 5 } + \frac { - 3 } { x - 4 }$

Question 13

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.
-$$\begin{array} { r } 
x - 6 y = 13 \
2 x - 7 y = 21
\end{array}$$

Accepted Answer

A)  $\{ ( 7 , - 1 ) \}$ 
B)  $\{ ( 6,0 ) \}$ 
C)  $\{ ( x , y ) \mid x - 6 y = 13 \}$ 
D)  $\varnothing$ 
A)  $\{ ( 7 , - 1 ) \}$ 
B)  $\{ ( 6,0 ) \}$ 
C)  $\{ ( x , y ) \mid x - 6 y = 13 \}$ 
D)  $\varnothing$

Question 14

Solve the system of equations.
-$$\begin{array} { c } 
x - y + 5 z = 13 \
5 x + y + z = - 19
\end{array}$$

Accepted Answer

A)  $\{ ( - 5,2,4 ) \}$ 
B)  $\{ ( 2 , - 5,4 ) \}$ 
C)  $\{ ( 4 , - 5,2 ) \}$ 
D)  $\{ ( 4,2 , - 5 ) \}$ 
A)  $\{ ( - 5,2,4 ) \}$ 
B)  $\{ ( 2 , - 5,4 ) \}$ 
C)  $\{ ( 4 , - 5,2 ) \}$ 
D)  $\{ ( 4,2 , - 5 ) \}$

Question 15

Determine whether the given ordered pair is a solution of the system
-(5, 6) 4x + y = 26
2x + 4y = 34

Accepted Answer

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

Question 16

Write the partial fraction decomposition of the rational expression.
-$\frac { 2 x ^ { 2 } - x - 19 } { x ( x + 1 ) ( x - 1 ) }$

Accepted Answer

A)  $\frac { 19 } { x } + \frac { - 8 } { x + 1 } + \frac { - 9 } { x - 1 }$ 
B)  $\frac { 19 } { x } + \frac { - 9 } { x + 1 } + \frac { 8 } { x - 1 }$ 
C)  $\frac { 19 } { x } + \frac { - 8 } { x + 1 } + \frac { 9 } { x - 1 }$ 
D)  $\frac { 19 } { x } + \frac { 8 } { x + 1 } + \frac { - 9 } { x - 1 }$ 
A)  $\frac { 19 } { x } + \frac { - 8 } { x + 1 } + \frac { - 9 } { x - 1 }$ 
B)  $\frac { 19 } { x } + \frac { - 9 } { x + 1 } + \frac { 8 } { x - 1 }$ 
C)  $\frac { 19 } { x } + \frac { - 8 } { x + 1 } + \frac { 9 } { x - 1 }$ 
D)  $\frac { 19 } { x } + \frac { 8 } { x + 1 } + \frac { - 9 } { x - 1 }$

Question 17

Solve the problem.
-You invested $16,000 and started a business selling vases. Supplies cost $10 per vase and you are selling each vase for $26. Let x represent the number of vases produced and sold and write the cost function, C, and revenue function, R.

Accepted Answer

A)  $C ( x ) = 10 x + 26$
$R ( x ) = 16,000 x$ 
B)  $C ( x ) = 10 x + 16,000$
$R ( x ) = 26 x$ 
C)  $C ( x ) = 10 x + 16,000$
$R ( x ) = 26$ 
D)  $C ( x ) = 10 x + 16,000 x$
$R ( x ) = 26 x$ 
A)  $C ( x ) = 10 x + 26$
$R ( x ) = 16,000 x$ 
B)  $C ( x ) = 10 x + 16,000$
$R ( x ) = 26 x$ 
C)  $C ( x ) = 10 x + 16,000$
$R ( x ) = 26$ 
D)  $C ( x ) = 10 x + 16,000 x$
$R ( x ) = 26 x$

Question 18

Write the partial fraction decomposition of the rational expression.
-$$\frac { 8 x ^ { 2 } - 8 x + 5 } { ( x - 1 ) ^ { 3 } }$$

Accepted Answer

A)  $\frac { 8 } { x - 1 } + \frac { 8 } { ( x - 1 ) ^ { 2 } } + \frac { 5 } { ( x - 1 ) ^ { 3 } }$ 
B)  $\frac { 8 } { x - 1 } + \frac { x + 8 } { ( x - 1 ) ^ { 2 } } + \frac { x ^ { 2 } + 5 } { ( x - 1 ) ^ { 3 } }$ 
C)  $\frac { 8 } { x - 1 } - \frac { 8 } { ( x - 1 ) ^ { 2 } } + \frac { 5 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { 8 } { x - 1 } + \frac { 8 } { ( x - 1 ) ^ { 2 } }$ 
A)  $\frac { 8 } { x - 1 } + \frac { 8 } { ( x - 1 ) ^ { 2 } } + \frac { 5 } { ( x - 1 ) ^ { 3 } }$ 
B)  $\frac { 8 } { x - 1 } + \frac { x + 8 } { ( x - 1 ) ^ { 2 } } + \frac { x ^ { 2 } + 5 } { ( x - 1 ) ^ { 3 } }$ 
C)  $\frac { 8 } { x - 1 } - \frac { 8 } { ( x - 1 ) ^ { 2 } } + \frac { 5 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { 8 } { x - 1 } + \frac { 8 } { ( x - 1 ) ^ { 2 } }$

Question 19

Solve the problem
-The Little Town Arts Center charges $24 for adults, $13 for senior citizens, and $9 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,903 for 854 tickets sold. There were 45 more children than adults. How many children attended?

Accepted Answer

A) 283 children 
B) 243 children 
C) 328 children 
D) 318 children 
A) 283 children 
B) 243 children 
C) 328 children 
D) 318 children

Question 20

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.
  
-Is there a profit when 395 binoculars are produced?

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Write the partial fraction decomposition of the rational expression. - $\frac { 27 - 5 x } { x ( x - 3 ) ^ { 2 } }$

Solve the system by the addition method. - x+y=-6 x-y=12

Write the partial fraction decomposition of the rational expression. - $\frac { 5 x ^ { 3 } + 19 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

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. -Is there a profit when 956 binoculars are produced?

Solve the system by the substitution method. - =+39 x-y=3

Determine if the given ordered triple is a solution of the system. - (-3,-2,5) x+3y+4z=-13 2y+5z=-19 z=-3

Solve the problem -Find the values of $a , b$ , and c such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 3 , - 25 ) , ( 2,5 )$ , and $( 3 , - 1 )$ .

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. - $\frac { 5 x - 3 } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 56 inches. The length is 12 inches longer than the width. Find the width.

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. -What is the profit when 963 binoculars are produced?

Write the partial fraction decomposition of the rational expression. - $\frac { x - 2 } { ( x - 5 ) ( x - 4 ) }$

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-6y=13 2x-7y=21

Solve the system of equations. - x-y+5z=13 5x+y+z=-19

Determine whether the given ordered pair is a solution of the system -(5, 6) 4x + y = 26 2x + 4y = 34

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 2 } - x - 19 } { x ( x + 1 ) ( x - 1 ) }$

Solve the problem. -You invested $16,000 and started a business selling vases. Supplies cost $10 per vase and you are selling each vase for $26. Let x represent the number of vases produced and sold and write the cost function, C, and revenue function, R.

Write the partial fraction decomposition of the rational expression. - $\frac { 8 x ^ { 2 } - 8 x + 5 } { ( x - 1 ) ^ { 3 } }$

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. -Is there a profit when 395 binoculars are produced?

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Exam 5: Systems of Equations and Inequalities

Write the partial fraction decomposition of the rational expression. - 27−5xx(x−3)2\frac { 27 - 5 x } { x ( x - 3 ) ^ { 2 } }x(x−3)227−5x​