Question 1

Find the inverse of the matrix.
-$$\left[ \begin{array} { l l l } 
1 & 3 & 2 \
1 & 3 & 3 \
2 & 7 & 8
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } - 1 & - 3 & - 2 \ - 1 & - 3 & - 3 \ - 2 & - 7 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \ 1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \ \frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 3 & 10 & - 3 \ 2 & - 4 & 1 \ - 1 & 1 & 0 \end{array} \right]$ 
D)  No inverse 
A)  $\left[ \begin{array} { l l l } - 1 & - 3 & - 2 \ - 1 & - 3 & - 3 \ - 2 & - 7 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \ 1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \ \frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 3 & 10 & - 3 \ 2 & - 4 & 1 \ - 1 & 1 & 0 \end{array} \right]$ 
D)  No inverse

Question 2

Solve the problem.
-Let $A = \left[ \begin{array} { r r } - 2 & 3 \ 3 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { c c } - 2 & 0 \ - 1 & 4 \end{array} \right]$. Find $A B$.

Accepted Answer

A)  $\left[ \begin{array} { r r } 12 & 1 \ 8 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 4 & - 6 \ - 4 & 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 4 & 0 \ - 3 & 8 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 1 & 12 \ - 8 & 8 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 12 & 1 \ 8 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 4 & - 6 \ - 4 & 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 4 & 0 \ - 3 & 8 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 1 & 12 \ - 8 & 8 \end{array} \right]$

Question 3

Verify that the values of the variables listed are solutions of the system of equations.
-$$\left\{ \begin{array} { c } 
x + y + z = - 1 \
x - y + 3 z = - 13 \
4 x + y + z = 8 \
\end{array} \right.$$

x = 3 , y = 1 , z = - 5

Accepted Answer

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

Question 4

Write the augmented matrix for the system.
-$$\left\{ \begin{array} { l } 
2 x + 8 y = 64 \
5 x + 7 y = 69
\end{array} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { l l | l } 2 & 8 & 64 \ 5 & 7 & 69 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l | l } 2 & 5 & 64 \ 8 & 7 & 69 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l | l } 2 & 8 & 69 \ 7 & 5 & 64 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l | l } 64 & 8 & 2 \ 69 & 5 & 7 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l | l } 2 & 8 & 64 \ 5 & 7 & 69 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l | l } 2 & 5 & 64 \ 8 & 7 & 69 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l | l } 2 & 8 & 69 \ 7 & 5 & 64 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l | l } 64 & 8 & 2 \ 69 & 5 & 7 \end{array} \right]$

Question 5

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places.
-$$\left\{ \begin{array} { r } 
3 x ^ { 3 } + y ^ { 2 } = 6 \
x ^ { 4 } y = 2
\end{array} \right.$$

Accepted Answer

A)  $x = 1.18 , y = 1.03 ; x = 1.07 , y = 1.52 ; x = - 0.91 , y = 2.88$ 
B)  no solution 
C)  $x = 1.81 , y = 0.28 ; x = 0.20 , y = 2.45 ; x = - 0.20 , y = - 2.45$ 
D)  $x = 1.99 , y = 0.13 ; x = 1.04 , y = 1.70 ; x = - 0.91 , y = 2.95$ 
A)  $x = 1.18 , y = 1.03 ; x = 1.07 , y = 1.52 ; x = - 0.91 , y = 2.88$ 
B)  no solution 
C)  $x = 1.81 , y = 0.28 ; x = 0.20 , y = 2.45 ; x = - 0.20 , y = - 2.45$ 
D)  $x = 1.99 , y = 0.13 ; x = 1.04 , y = 1.70 ; x = - 0.91 , y = 2.95$

Question 6

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the
systems of equations. Are the points of intersection solutions to the system of equations (Y/N)?
-  $$\begin{array} { l } 
x ^ { 2 } = y - 1 \
y = - 2 x + 4
\end{array}$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 7

Find the inverse of the matrix.
-$$\left[ \begin{array} { l l } 
1 & - 2 \
0 & - 2
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } - \frac { 1 } { 2 } & - 1 \ 0 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 0 & - \frac { 1 } { 2 } \ 1 & - 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 1 & 1 \ 0 & - \frac { 1 } { 2 } \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 1 & - 1 \ 0 & - \frac { 1 } { 2 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } - \frac { 1 } { 2 } & - 1 \ 0 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 0 & - \frac { 1 } { 2 } \ 1 & - 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 1 & 1 \ 0 & - \frac { 1 } { 2 } \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 1 & - 1 \ 0 & - \frac { 1 } { 2 } \end{array} \right]$

Question 8

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary.
-$$\left\{ \begin{array} { r } 
2 x + 4 y - 5 z = - 8 \
x + 5 y + 2 z = - 1 \
3 x + 3 y + 3 z = 15
\end{array} \right.$$

Accepted Answer

A)  $x = 5 , y = - 2 , z = 2$ 
B)  $x = - 5 , y = - 2 , z = - 2$ 
C)  $x = 2 , y = 5 , z = 2$ 
D)  $x = 5 , y = 2 , z = - 2$ 
A)  $x = 5 , y = - 2 , z = 2$ 
B)  $x = - 5 , y = - 2 , z = - 2$ 
C)  $x = 2 , y = 5 , z = 2$ 
D)  $x = 5 , y = 2 , z = - 2$

Question 9

Solve the problem.
-A company has sales (measured in millions of dollars) of 50, 60, and 75 during the first three consecutive years.Find a quadratic function that fits these data, and use the result to predict the sales during the fourth year. Assume that the quadratic function is of the form y = ax2 + bx + c

Accepted Answer

A)  $y = \frac { 15 } { 2 } x ^ { 2 } - \frac { 25 } { 2 } x + \frac { 325 } { 4 }$; sales during the fourth year $= \$ 151.25$ million 
B)  $y = 5 x ^ { 2 } + 5 x + 40$; sales during the fourth year $= \$ 180$ million 
C)  $y = - 5 x ^ { 2 } + 40 x + 15$; sales during the fourth year $= \$ 95$ million 
D)  $y = \frac { 5 } { 2 } x ^ { 2 } + \frac { 5 } { 2 } x + 45$; sales during the fourth year $= \$ 95$ million 
A)  $y = \frac { 15 } { 2 } x ^ { 2 } - \frac { 25 } { 2 } x + \frac { 325 } { 4 }$; sales during the fourth year $= \$ 151.25$ million 
B)  $y = 5 x ^ { 2 } + 5 x + 40$; sales during the fourth year $= \$ 180$ million 
C)  $y = - 5 x ^ { 2 } + 40 x + 15$; sales during the fourth year $= \$ 95$ million 
D)  $y = \frac { 5 } { 2 } x ^ { 2 } + \frac { 5 } { 2 } x + 45$; sales during the fourth year $= \$ 95$ million

Question 10

Find the inverse of the matrix.
-$$\left[ \begin{array} { l l l } 
1 & 0 & 8 \
1 & 2 & 3 \
2 & 5 & 3
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } 1 & 1 & 2 \ 0 & 2 & 5 \ 8 & 3 & 3 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 1 & 0 & - 8 \ - 1 & - 2 & - 3 \ - 2 & - 5 & - 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 9 & - 40 & 16 \ - 3 & 13 & - 5 \ - 1 & 5 & - 2 \end{array} \right]$ 
D)  No inverse 
A)  $\left[ \begin{array} { l l l } 1 & 1 & 2 \ 0 & 2 & 5 \ 8 & 3 & 3 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 1 & 0 & - 8 \ - 1 & - 2 & - 3 \ - 2 & - 5 & - 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 9 & - 40 & 16 \ - 3 & 13 & - 5 \ - 1 & 5 & - 2 \end{array} \right]$ 
D)  No inverse

Question 11

Graph the inequality.
-$$x ^ { 2 } + y ^ { 2 } > 49$$

Accepted Answer

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

Question 12

Graph the inequality.
-x > -1

Accepted Answer

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

Question 13

Find the inverse of the matrix.
-$$\left[ \begin{array} { c c } 
- 2 & - 2 \
- 6 & - 6
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } \frac { 3 } { 16 } & \frac { 1 } { 16 } \ \frac { 3 } { 16 } & \frac { 1 } { 16 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - \frac { 3 } { 16 } & \frac { 1 } { 16 } \ \frac { 3 } { 16 } & - \frac { 1 } { 16 } \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } \frac { 3 } { 16 } & - \frac { 1 } { 16 } \ - \frac { 3 } { 16 } & \frac { 1 } { 16 } \end{array} \right]$ 
D)  No inverse 
A)  $\left[ \begin{array} { c c } \frac { 3 } { 16 } & \frac { 1 } { 16 } \ \frac { 3 } { 16 } & \frac { 1 } { 16 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - \frac { 3 } { 16 } & \frac { 1 } { 16 } \ \frac { 3 } { 16 } & - \frac { 1 } { 16 } \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } \frac { 3 } { 16 } & - \frac { 1 } { 16 } \ - \frac { 3 } { 16 } & \frac { 1 } { 16 } \end{array} \right]$ 
D)  No inverse

Question 14

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c } 
x & y & z \
u & v & w \
1 & 3 & - 2
\end{array} \right| = 14 \quad \left| \begin{array} { c c c } 
1 & 3 & - 2 \
u & v & w \
x & y & z
\end{array} \right| = ?$$

Accepted Answer

A)  14 
B)  -14 
C)  0 
D)  Cannot determine 
A)  14 
B)  -14 
C)  0 
D)  Cannot determine

Question 15

Graph the inequality.
-$y \leq x^{2}-1$

Accepted Answer

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

Question 16

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
5 x ^ { 2 } - 2 y ^ { 2 } = 37 \
2 x ^ { 2 } + 2 y ^ { 2 } = 26
\end{array} \right.$$

Accepted Answer

A)  $x = 3 , y = 2 ; x = - 3 , y = 2 ; x = 3 , y = - 2 ; x = - 3 , y = - 2$ 
B)  $x = 3 , y = 2 ; x = 2 , y = 3 ; x = - 3 , y = - 2 ; x = - 2 , y = - 3$ 
C)  $x = - 3 , y = - 2 ; x = - 2 , y = - 3$ 
D)  $x = 3 , y = - 2 ; x = 3 , y = 2$ 
A)  $x = 3 , y = 2 ; x = - 3 , y = 2 ; x = 3 , y = - 2 ; x = - 3 , y = - 2$ 
B)  $x = 3 , y = 2 ; x = 2 , y = 3 ; x = - 3 , y = - 2 ; x = - 2 , y = - 3$ 
C)  $x = - 3 , y = - 2 ; x = - 2 , y = - 3$ 
D)  $x = 3 , y = - 2 ; x = 3 , y = 2$

Question 17

Write the partial fraction decomposition of the rational expression.
-$$\frac { x + 1 } { ( x - 2 ) ^ { 2 } ( x + 4 ) }$$

Accepted Answer

A)  $\frac { - 1 } { x - 2 } + \frac { \frac { 1 } { 4 } x } { ( x - 2 ) ^ { 2 } } + \frac { - \frac { 1 } { 4 } } { x + 4 }$ 
B)  $\frac { 12 } { x - 2 } + \frac { 2 } { ( x - 2 ) ^ { 2 } } + \frac { - 12 } { x + 4 }$ 
C)  $\frac { \frac { 1 } { 12 } } { x - 2 } + \frac { \frac { 1 } { 2 } } { ( x - 2 ) ^ { 2 } } + \frac { - \frac { 1 } { 12 } } { x + 4 }$ 
D)  $\frac { \frac { 1 } { 2 } } { ( x - 2 ) ^ { 2 } } + \frac { - \frac { 1 } { 12 } } { x + 4 }$ 
A)  $\frac { - 1 } { x - 2 } + \frac { \frac { 1 } { 4 } x } { ( x - 2 ) ^ { 2 } } + \frac { - \frac { 1 } { 4 } } { x + 4 }$ 
B)  $\frac { 12 } { x - 2 } + \frac { 2 } { ( x - 2 ) ^ { 2 } } + \frac { - 12 } { x + 4 }$ 
C)  $\frac { \frac { 1 } { 12 } } { x - 2 } + \frac { \frac { 1 } { 2 } } { ( x - 2 ) ^ { 2 } } + \frac { - \frac { 1 } { 12 } } { x + 4 }$ 
D)  $\frac { \frac { 1 } { 2 } } { ( x - 2 ) ^ { 2 } } + \frac { - \frac { 1 } { 12 } } { x + 4 }$

Question 18

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-x2 + y2 = 49
5x + 6y = 9

Accepted Answer

Substitution should be used, b

Question 19

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
y = 6 x ^ { 2 } - 5 x \
y = 2 x + 3
\end{array} \right.$$

Accepted Answer

A)  $x = \frac { 1 } { 6 } , y = \frac { 10 } { 3 } ; x = 1 , y = 5$ 
B)  $x = - \frac { 1 } { 2 } , y = 2 ; x = 1 , y = 5$ 
C)  $x = \frac { 3 } { 2 } , y = 6 ; x = - \frac { 1 } { 3 } , y = - \frac { 7 } { 3 }$ 
D)  $x = \frac { 1 } { 3 } , y = \frac { 11 } { 3 } ; x = - \frac { 3 } { 2 } , y = 0$ 
A)  $x = \frac { 1 } { 6 } , y = \frac { 10 } { 3 } ; x = 1 , y = 5$ 
B)  $x = - \frac { 1 } { 2 } , y = 2 ; x = 1 , y = 5$ 
C)  $x = \frac { 3 } { 2 } , y = 6 ; x = - \frac { 1 } { 3 } , y = - \frac { 7 } { 3 }$ 
D)  $x = \frac { 1 } { 3 } , y = \frac { 11 } { 3 } ; x = - \frac { 3 } { 2 } , y = 0$

Question 20

Write the partial fraction decomposition of the rational expression.
-$$\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$$

Accepted Answer

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

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

Solve the problem. -Let $A = \left[ \begin{array} { r r } - 2 & 3 \\ 3 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { c c } - 2 & 0 \\ - 1 & 4 \end{array} \right]$ . Find $A B$ .

Verify that the values of the variables listed are solutions of the system of equations. - $\left\{ \begin{array} { c } x + y + z = - 1 \\x - y + 3 z = - 13 \\4 x + y + z = 8 \\\end{array} \right.$ x = 3 , y = 1 , z = - 5

Write the augmented matrix for the system. - $\left\{ \begin{array} { l } 2 x + 8 y = 64 \\5 x + 7 y = 69\end{array} \right.$

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. - $\left\{ \begin{array} { r } 3 x ^ { 3 } + y ^ { 2 } = 6 \\x ^ { 4 } y = 2\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { l l } 1 & - 2 \\0 & - 2\end{array} \right]$

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left\{ \begin{array} { r } 2 x + 4 y - 5 z = - 8 \\x + 5 y + 2 z = - 1 \\3 x + 3 y + 3 z = 15\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\1 & 2 & 3 \\2 & 5 & 3\end{array} \right]$

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } > 49$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } > 49$

Graph the inequality. -x > -1

Find the inverse of the matrix. - $\left[ \begin{array} { c c } - 2 & - 2 \\- 6 & - 6\end{array} \right]$

Use the properties of determinants to find the value of the second determinant, given the value of the first. - $\left| \begin{array} { c c c } x & y & z \\u & v & w \\1 & 3 & - 2\end{array} \right| = 14 \quad \left| \begin{array} { c c c } 1 & 3 & - 2 \\u & v & w \\x & y & z\end{array} \right| = ?$

Graph the inequality. - $y \leq x^{2}-1$ $Graph the inequality. - y \leq x^{2}-1$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } 5 x ^ { 2 } - 2 y ^ { 2 } = 37 \\2 x ^ { 2 } + 2 y ^ { 2 } = 26\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { x + 1 } { ( x - 2 ) ^ { 2 } ( x + 4 ) }$

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² + y² = 49 5x + 6y = 9

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } y = 6 x ^ { 2 } - 5 x \\y = 2 x + 3\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 6: Systems of Equations and Inequalities

Find the inverse of the matrix. - [132133278]\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]​112​337​238​​

Solve the problem. -Let A=[−2332]A = \left[ \begin{array} { r r } - 2 & 3 \\ 3 & 2 \end{array} \right]A=[−23​32​] and B=[−20−14]B = \left[ \begin{array} { c c } - 2 & 0 \\ - 1 & 4 \end{array} \right]B=[−2−1​04​] . Find ABA BAB .

Verify that the values of the variables listed are solutions of the system of equations. - {x+y+z=−1x−y+3z=−134x+y+z=8\left\{ \begin{array} { c } x + y + z = - 1 \\x - y + 3 z = - 13 \\4 x + y + z = 8 \\\end{array} \right.⎩⎨⎧​x+y+z=−1x−y+3z=−134x+y+z=8​ x = 3 , y = 1 , z = - 5

Write the augmented matrix for the system. - {2x+8y=645x+7y=69\left\{ \begin{array} { l } 2 x + 8 y = 64 \\5 x + 7 y = 69\end{array} \right.{2x+8y=645x+7y=69​

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. - {3x3+y2=6x4y=2\left\{ \begin{array} { r } 3 x ^ { 3 } + y ^ { 2 } = 6 \\x ^ { 4 } y = 2\end{array} \right.{3x3+y2=6x4y=2​

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - =y-1 y=-2x+4

Find the inverse of the matrix. - [1−20−2]\left[ \begin{array} { l l } 1 & - 2 \\0 & - 2\end{array} \right][10​−2−2​]

Find the inverse of the matrix. - [108123253]\left[ \begin{array} { l l l } 1 & 0 & 8 \\1 & 2 & 3 \\2 & 5 & 3\end{array} \right]​112​025​833​​

Graph the inequality. - x2+y2>49x ^ { 2 } + y ^ { 2 } > 49x2+y2>49

Graph the inequality. -x > -1

Find the inverse of the matrix. - [−2−2−6−6]\left[ \begin{array} { c c } - 2 & - 2 \\- 6 & - 6\end{array} \right][−2−6​−2−6​]

Graph the inequality. - y≤x2−1y \leq x^{2}-1y≤x2−1

Solve the system of equations using elimination. - {5x2−2y2=372x2+2y2=26\left\{ \begin{array} { l } 5 x ^ { 2 } - 2 y ^ { 2 } = 37 \\2 x ^ { 2 } + 2 y ^ { 2 } = 26\end{array} \right.{5x2−2y2=372x2+2y2=26​

Write the partial fraction decomposition of the rational expression. - x+1(x−2)2(x+4)\frac { x + 1 } { ( x - 2 ) ^ { 2 } ( x + 4 ) }(x−2)2(x+4)x+1​

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x2 + y2 = 49 5x + 6y = 9

Solve the system of equations using substitution. - {y=6x2−5xy=2x+3\left\{ \begin{array} { l } y = 6 x ^ { 2 } - 5 x \\y = 2 x + 3\end{array} \right.{y=6x2−5xy=2x+3​

Write the partial fraction decomposition of the rational expression. - 12x+3(x−1)(x2+x+1)\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }(x−1)(x2+x+1)12x+3​

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

Solve the problem. -Let $A = \left[ \begin{array} { r r } - 2 & 3 \\ 3 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { c c } - 2 & 0 \\ - 1 & 4 \end{array} \right]$ . Find $A B$ .

Verify that the values of the variables listed are solutions of the system of equations. - $\left\{ \begin{array} { c } x + y + z = - 1 \\x - y + 3 z = - 13 \\4 x + y + z = 8 \\\end{array} \right.$ x = 3 , y = 1 , z = - 5

Write the augmented matrix for the system. - $\left\{ \begin{array} { l } 2 x + 8 y = 64 \\5 x + 7 y = 69\end{array} \right.$

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. - $\left\{ \begin{array} { r } 3 x ^ { 3 } + y ^ { 2 } = 6 \\x ^ { 4 } y = 2\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { l l } 1 & - 2 \\0 & - 2\end{array} \right]$

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\1 & 2 & 3 \\2 & 5 & 3\end{array} \right]$

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } > 49$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } > 49$

Find the inverse of the matrix. - $\left[ \begin{array} { c c } - 2 & - 2 \\- 6 & - 6\end{array} \right]$

Graph the inequality. - $y \leq x^{2}-1$ $Graph the inequality. - y \leq x^{2}-1$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } 5 x ^ { 2 } - 2 y ^ { 2 } = 37 \\2 x ^ { 2 } + 2 y ^ { 2 } = 26\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { x + 1 } { ( x - 2 ) ^ { 2 } ( x + 4 ) }$

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² + y² = 49 5x + 6y = 9

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } y = 6 x ^ { 2 } - 5 x \\y = 2 x + 3\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$