Question 1

Find the partial fraction decomposition for the rational expression.
-$$\frac { 4 x ^ { 2 } + 20 x - 12 } { \left( 2 x ^ { 2 } + 1 \right) ( 4 - x ) }$$

Accepted Answer

A)  $\frac { 4 x - 4 } { 2 x ^ { 2 } + 1 } + \frac { 4 } { x - 4 }$ 
B)  $\frac { 4 x - 4 } { 2 x ^ { 2 } + 1 } + \frac { - 4 } { x - 4 }$ 
C)  $\frac { 135 x + 120 } { 2 x ^ { 2 } + 1 } + \frac { - 84 } { x - 4 }$ 
D)  $\frac { 135 x - 120 } { 2 x ^ { 2 } + 1 } + \frac { - 84 } { x - 4 }$ 
A)  $\frac { 4 x - 4 } { 2 x ^ { 2 } + 1 } + \frac { 4 } { x - 4 }$ 
B)  $\frac { 4 x - 4 } { 2 x ^ { 2 } + 1 } + \frac { - 4 } { x - 4 }$ 
C)  $\frac { 135 x + 120 } { 2 x ^ { 2 } + 1 } + \frac { - 84 } { x - 4 }$ 
D)  $\frac { 135 x - 120 } { 2 x ^ { 2 } + 1 } + \frac { - 84 } { x - 4 }$

Question 2

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-$$\begin{array} { l } 
y = e ^ { 2 x + 3 } \
2 x + y = 3
\end{array}$$

Accepted Answer

A)  $\{ ( 0.75 , - 4.50 ) \}$ 
B)  $\{ ( - 0.75,4.50 ) \}$ 
C)  $\{ ( - 0.75 , - 4.50 ) \}$ 
D)  $\{ ( 0.75,4.50 ) \}$ 
A)  $\{ ( 0.75 , - 4.50 ) \}$ 
B)  $\{ ( - 0.75,4.50 ) \}$ 
C)  $\{ ( - 0.75 , - 4.50 ) \}$ 
D)  $\{ ( 0.75,4.50 ) \}$

Question 3

Graph the solution set of the system of inequalities.
-$$\begin{array} { l } 
\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } \leq 1 \
\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } \geq 1
\end{array}$$

Accepted Answer

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

Question 4

A triangle with vertices at (x1, y1), (x2, y2), and (x3, y3) has area equal to the absolute value of D, where $$D = \frac { 1 } { 2 } \left| \begin{array} { l l l } 
x _ { 1 } & y _ { 1 } & 1 \
x _ { 2 } & y _ { 2 } & 1 \
x _ { 3 } & y _ { 3 } & 1
\end{array} \right|$$ Find the area of the triangle having vertices at P, Q, and R.
-$P ( 0 , - 4 ) , Q ( 0,5 ) , R ( 5,1 )$

Accepted Answer

A)  3 
B)  45 
C)  $\frac { 45 } { 2 }$ 
D)  0 
A)  3 
B)  45 
C)  $\frac { 45 } { 2 }$ 
D)  0

Question 5

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 7 \
y = \sqrt [ 3 ] { x + 6 }
\end{array}$$

Accepted Answer

A)  $\{ ( - 2.29 , - 1.32 ) , ( 2.29,1.32 ) \}$ 
B)  $\{ ( - 1.76 , - 1.98 ) , ( 2.13 , - 1.57 ) \}$ 
C)  $\{ ( - 2.13,1.57 ) , ( 1.76,1.98 ) \}$ 
D)  $\{ ( - 2.13 , - 1.57 ) , ( 1.76 , - 1.98 ) \}$ 
A)  $\{ ( - 2.29 , - 1.32 ) , ( 2.29,1.32 ) \}$ 
B)  $\{ ( - 1.76 , - 1.98 ) , ( 2.13 , - 1.57 ) \}$ 
C)  $\{ ( - 2.13,1.57 ) , ( 1.76,1.98 ) \}$ 
D)  $\{ ( - 2.13 , - 1.57 ) , ( 1.76 , - 1.98 ) \}$

Question 6

Solve the system by elimination.
-$$\begin{array} { l } 
5 x + 9 y = 81 \
3 x - 3 y = - 27
\end{array}$$

Accepted Answer

A)  $\{ ( 0,10 ) \}$ 
B)  $\{ ( 0,9 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( - 1,10 ) \}$ 
A)  $\{ ( 0,10 ) \}$ 
B)  $\{ ( 0,9 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( - 1,10 ) \}$

Question 7

Solve the problem.
-A basketball fieldhouse seats 15,000 . Courtside seats sell for $\$ 8$, endzone for $\$ 6$, and balcony for $\$ 4$ Total revenue for a sell-out is $\$ 76,000$. If half the courtside and balcony and all the endzone seats are sold, the total revenue is $\$ 44,000$. How many of each type of seat are there in the fieldhouse?

Accepted Answer

A)  4,000 courtside; 3,000 endzone; 8,000 balcony 
B)  3,000 courtside; 2,000 endzone; 10,000 balcony 
C)  2,000 courtside; 5,000 endzone; 8,000 balcony 
D)  3,200 courtside; 1,800 endzone; 10,000 balcony 
A)  4,000 courtside; 3,000 endzone; 8,000 balcony 
B)  3,000 courtside; 2,000 endzone; 10,000 balcony 
C)  2,000 courtside; 5,000 endzone; 8,000 balcony 
D)  3,200 courtside; 1,800 endzone; 10,000 balcony

Question 8

For the equation, determine the constants A and B that make the equation an identity.
-$$\frac { x } { ( x + 8 ) ( x - 8 ) } = \frac { A } { ( x + 8 ) } + \frac { B } { ( x - 8 ) }$$

Accepted Answer

A)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = \frac { 1 } { 2 }$ 
B)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = 1$ 
C)  $A = 1 , B = \frac { 1 } { 2 }$ 
D)  $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = \frac { 1 } { 2 }$ 
A)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = \frac { 1 } { 2 }$ 
B)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = 1$ 
C)  $A = 1 , B = \frac { 1 } { 2 }$ 
D)  $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = \frac { 1 } { 2 }$

Question 9

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the
solution with y arbitrary.
-$$\begin{array} { r } 
9 x + 9 y = 9 \
2 x + 6 y = 2
\end{array}$$

Accepted Answer

A)  $\{ ( 1,1 ) \}$ 
B)  $\{ ( 1,0 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( 0,1 ) \}$ 
A)  $\{ ( 1,1 ) \}$ 
B)  $\{ ( 1,0 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( 0,1 ) \}$

Question 10

Solve the problem.
-Matt bought 3 pounds of oranges and 2 pounds of apples and paid $\$ 4.02$, before tax. Andy bought 4 pounds of oranges and 3 pounds of apples and paid $\$ 5.65$, before tax. Use this information to set up a matrix equation of the form $A X = B$, which can be solved to determine the price per pound for oranges and apples. Solve this matrix equation to find the price per pound of oranges.
Use the fact that for $A = \left[ \begin{array} { l l } 3 & 2 \ 4 & 3 \end{array} \right] , A ^ { - 1 } = \left[ \begin{array} { r r } 3 & - 2 \ - 4 & 3 \end{array} \right]$.

Accepted Answer

A)  $\$ 0.72$ per pound 
B)  $\$ 0.74$ per pound 
C)  $\$ 0.79$ per pound 
D)  $\$ 0.76$ per pound 
A)  $\$ 0.72$ per pound 
B)  $\$ 0.74$ per pound 
C)  $\$ 0.79$ per pound 
D)  $\$ 0.76$ per pound

Question 11

Provide an appropriate response.
-If the graphs of a system of two equations are a line and a parabola, what are the possible
numbers of solutions (with real coordinates) of this system?

Accepted Answer

The answer of Provide an appropriate response.
-If the graphs of...

Question 12

Decide whether or not the matrices are inverses of each other.
-$$\left[ \begin{array} { r r r } 
2 & - 1 & 0 \
- 1 & 1 & - 2 \
1 & 0 & - 1
\end{array} \right] \text { and } \left[ \begin{array} { r r r } 
1 & - 1 & 2 \
- 3 & - 2 & 4 \
- 1 & 1 & 1
\end{array} \right]$$

Accepted Answer

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

Question 13

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { r } 
x + y + z = 9 \
2 x - 3 y + 4 z = 7
\end{array}$$

Accepted Answer

A)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left( \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } - 11 } { 5 } , \mathrm { z } \right\} \right\}$ 
B)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left( \frac { \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } + 11 } { 5 } , \mathrm { z } \right) \right\}$ 
C)  Cramer's rule does not apply since $\mathrm { D } = 0$; $\varnothing$ 
D)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left( \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } + 11 } { 5 } , \mathrm { z } \right) \right\}$ 
A)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left( \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } - 11 } { 5 } , \mathrm { z } \right\} \right\}$ 
B)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left( \frac { \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } + 11 } { 5 } , \mathrm { z } \right) \right\}$ 
C)  Cramer's rule does not apply since $\mathrm { D } = 0$; $\varnothing$ 
D)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left( \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } + 11 } { 5 } , \mathrm { z } \right) \right\}$

Question 14

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the
solution with y arbitrary.
-$$\begin{array} { l } 
4 x - 5 y - 10 = 0 \
8 x + y - 25 = 0
\end{array}$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ \left( \frac { 135 } { 44 } , \frac { 5 } { 11 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 85 } { 44 } , - \frac { 5 } { 11 } \right) \right\}$ 
D)  $\left\{ \left( - \frac { 6 } { 5 } y , y \right) \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ \left( \frac { 135 } { 44 } , \frac { 5 } { 11 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 85 } { 44 } , - \frac { 5 } { 11 } \right) \right\}$ 
D)  $\left\{ \left( - \frac { 6 } { 5 } y , y \right) \right\}$

Question 15

Find the matrix product when possible.
-$$\left[ \begin{array} { r r } 
- 1 & 3 \
2 & 2
\end{array} \right] \left[ \begin{array} { l l } 
- 2 & 0 \
- 1 & 4
\end{array} \right]$$

Accepted Answer

A) 
$\left[\begin{array}{rr}
2 & 0 \
-2 & 8
\end{array}\right]$ 
B) 
$\left[\begin{array}{rr}
2 & -6 \
-1 & 5
\end{array}\right]$ 
C) 
$\left[\begin{array}{rr}
-1 & 12 \
-6 & 8
\end{array}\right]$ 
D) 
$\left[\begin{array}{rr}
12 & -1 \
8 & -6
\end{array}\right]$ 
A) 
$\left[\begin{array}{rr}
2 & 0 \
-2 & 8
\end{array}\right]$ 
B) 
$\left[\begin{array}{rr}
2 & -6 \
-1 & 5
\end{array}\right]$ 
C) 
$\left[\begin{array}{rr}
-1 & 12 \
-6 & 8
\end{array}\right]$ 
D) 
$\left[\begin{array}{rr}
12 & -1 \
8 & -6
\end{array}\right]$

Question 16

Provide an appropriate response.
-For a certain system of two linear equations, the values of the determinants used in Cramer's rule are $\mathrm { D } = 23 , \mathrm { D } _ { \mathrm { x } } = 29$, and $\mathrm { D } _ { \mathrm { y } } = - 13$. What is the solution set of the system?

Accepted Answer

A)  $\{ ( 29 , - 13 ) \}$ 
B)  $\left\{ \left( \frac { 23 } { 29 } , - \frac { 23 } { 13 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 29 } { 23 } , - \frac { 13 } { 23 } \right) \right\}$ 
D)  $\left\{ \left( - \frac { 13 } { 23 } , \frac { 29 } { 23 } \right) \right\}$ 
A)  $\{ ( 29 , - 13 ) \}$ 
B)  $\left\{ \left( \frac { 23 } { 29 } , - \frac { 23 } { 13 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 29 } { 23 } , - \frac { 13 } { 23 } \right) \right\}$ 
D)  $\left\{ \left( - \frac { 13 } { 23 } , \frac { 29 } { 23 } \right) \right\}$

Question 17

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l } 
y = 4 | x | - 4 \
y = x ^ { 2 }
\end{array}$$

Accepted Answer

A)  $\{ ( - 2,4 ) \}$ 
B)  $\{ ( 2,4 ) \}$ 
C)  $\{ ( 2,4 ) , ( - 2,4 ) \}$ 
D)  $\{ ( 0 , - 4 ) , ( - 2,4 ) \}$ 
A)  $\{ ( - 2,4 ) \}$ 
B)  $\{ ( 2,4 ) \}$ 
C)  $\{ ( 2,4 ) , ( - 2,4 ) \}$ 
D)  $\{ ( 0 , - 4 ) , ( - 2,4 ) \}$

Question 18

Find the value of the determinant.
-$$\left| \begin{array} { l l } 
- 5 & - 3 \
- 8 & - 4
\end{array} \right|$$

Accepted Answer

A)  4 
B)  $- 17$ 
C)  44 
D)  $- 4$ 
A)  4 
B)  $- 17$ 
C)  44 
D)  $- 4$

Question 19

Find the values of the variables for which the statement is true, if possible.
-$\left[ \begin{array} { r c c } \mathrm { a } & 1 & - 8 \ - 5 & - 3 & \mathrm { f } \end{array} \right] + \left[ \begin{array} { r r r } 6 & \mathrm {~b} & - 4 \ \mathrm {~d} & - 6 & - 8 \end{array} \right] = \left[ \begin{array} { r r r } 2 & - 9 & \mathrm { c } \ - 1 & \mathrm { e } & 2 \end{array} \right]$

Accepted Answer

A)  $a = 8 ; b = - 8 ; c = 4 ; d = - 6 ; e = 3 ; f = - 6$ 
B)  $\mathrm { a } = \frac { 1 } { 3 } ; \mathrm { b } = - 9 ; \mathrm { c } = 72 ; \mathrm { d } = \frac { 1 } { 5 } ; \mathrm { e } = 18 ; \mathrm { f } = - \frac { 1 } { 4 }$ 
C)  $\mathrm { a } = - 4 ; \mathrm { b } = - 10 ; \mathrm { c } = - 12 ; \mathrm { d } = 4 ; \mathrm { e } = - 9 ; \mathrm { f } = 10$ 
D)  $\mathrm { a } = 4 ; \mathrm { b } = 10 ; \mathrm { c } = - 4 ; \mathrm { d } = - 4 ; \mathrm { e } = - 3 ; \mathrm { f } = - 10$ 
A)  $a = 8 ; b = - 8 ; c = 4 ; d = - 6 ; e = 3 ; f = - 6$ 
B)  $\mathrm { a } = \frac { 1 } { 3 } ; \mathrm { b } = - 9 ; \mathrm { c } = 72 ; \mathrm { d } = \frac { 1 } { 5 } ; \mathrm { e } = 18 ; \mathrm { f } = - \frac { 1 } { 4 }$ 
C)  $\mathrm { a } = - 4 ; \mathrm { b } = - 10 ; \mathrm { c } = - 12 ; \mathrm { d } = 4 ; \mathrm { e } = - 9 ; \mathrm { f } = 10$ 
D)  $\mathrm { a } = 4 ; \mathrm { b } = 10 ; \mathrm { c } = - 4 ; \mathrm { d } = - 4 ; \mathrm { e } = - 3 ; \mathrm { f } = - 10$

Question 20

Perform the operation or operations when possible.
-$$\left[ \begin{array} { r r } 
- 1 & 4 \
0 & 4 \
6 & - 4
\end{array} \right] - \left[ \begin{array} { l l } 
2 & 1 \
7 & 4 \
1 & 2
\end{array} \right]$$

Accepted Answer

A) 
$\left[ \begin{array} { r r } 3 & - 3 \ 7 & 0 \ - 5 & 6 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 1 & 3 \ 7 & 0 \ 5 & - 2 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 1 & 5 \ 7 & 8 \ 7 & - 1 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 3 & 3 \ - 7 & 0 \ 5 & - 6 \end{array} \right]$ 
A) 
$\left[ \begin{array} { r r } 3 & - 3 \ 7 & 0 \ - 5 & 6 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 1 & 3 \ 7 & 0 \ 5 & - 2 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 1 & 5 \ 7 & 8 \ 7 & - 1 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 3 & 3 \ - 7 & 0 \ 5 & - 6 \end{array} \right]$

Find the partial fraction decomposition for the rational expression. - $\frac { 4 x ^ { 2 } + 20 x - 12 } { \left( 2 x ^ { 2 } + 1 \right) ( 4 - x ) }$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y= 2x+y=3

Graph the solution set of the system of inequalities. - +\leq1 +\geq1 $Graph the solution set of the system of inequalities. - \begin{array} { l } \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } \leq 1 \\ \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } \geq 1 \end{array}$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - +=7 y=

Solve the system by elimination. - 5x+9y=81 3x-3y=-27

For the equation, determine the constants A and B that make the equation an identity. - $\frac { x } { ( x + 8 ) ( x - 8 ) } = \frac { A } { ( x + 8 ) } + \frac { B } { ( x - 8 ) }$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 9x+9y=9 2x+6y=2

Provide an appropriate response. -If the graphs of a system of two equations are a line and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r r } 2 & - 1 & 0 \\- 1 & 1 & - 2 \\1 & 0 & - 1\end{array} \right] \text { and } \left[ \begin{array} { r r r } 1 & - 1 & 2 \\- 3 & - 2 & 4 \\- 1 & 1 & 1\end{array} \right]$

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x+y+z=9 2x-3y+4z=7

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 4x-5y-10=0 8x+y-25=0

Find the matrix product when possible. - $\left[ \begin{array} { r r } - 1 & 3 \\2 & 2\end{array} \right] \left[ \begin{array} { l l } - 2 & 0 \\- 1 & 4\end{array} \right]$

Provide an appropriate response. -For a certain system of two linear equations, the values of the determinants used in Cramer's rule are $\mathrm { D } = 23 , \mathrm { D } _ { \mathrm { x } } = 29$ , and $\mathrm { D } _ { \mathrm { y } } = - 13$ . What is the solution set of the system?

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - y=4|x|-4 y=

Find the value of the determinant. - $\left| \begin{array} { l l } - 5 & - 3 \\- 8 & - 4\end{array} \right|$

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } - 1 & 4 \\0 & 4 \\6 & - 4\end{array} \right] - \left[ \begin{array} { l l } 2 & 1 \\7 & 4 \\1 & 2\end{array} \right]$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

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Exam 9: Systems and Matrices

Find the partial fraction decomposition for the rational expression. - 4x2+20x−12(2x2+1)(4−x)\frac { 4 x ^ { 2 } + 20 x - 12 } { \left( 2 x ^ { 2 } + 1 \right) ( 4 - x ) }(2x2+1)(4−x)4x2+20x−12​