Question 1

Graph the inequality.
--3x - 4y ≤-12

Accepted Answer

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

Question 2

Graph the inequality.
-x - y > -5

Accepted Answer

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

Question 3

Solve the problem.
-The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Accepted Answer

A)  width = 4 ft, length = 11 ft 
B)  width = 9.7 ft, length = 22.4 ft 
C)  width = 2 ft, length = 9 ft 
D)  width = 3.9 ft, length = 9.7 ft 
A)  width = 4 ft, length = 11 ft 
B)  width = 9.7 ft, length = 22.4 ft 
C)  width = 2 ft, length = 9 ft 
D)  width = 3.9 ft, length = 9.7 ft

Question 4

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

Accepted Answer

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

Question 5

Solve the problem.
-The sum of the squares of two numbers is 85. The sum of the two numbers is 13. Find the two numbers.

Accepted Answer

A)  -7 and -6 
B)  -7 and 6; or -6 and 7 
C)  6 and 7; or -7 and -6 
D)  6 and 7 
A)  -7 and -6 
B)  -7 and 6; or -6 and 7 
C)  6 and 7; or -7 and -6 
D)  6 and 7

Question 6

Write the partial fraction decomposition of the rational expression.
-$$\frac { 9 x ^ { 2 } + 21 x + 11 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$$

Accepted Answer

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

Question 7

Graph the inequality.
-$$y > x ^ { 2 } - 4$$

Accepted Answer

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

Question 8

Solve the problem.
-$\text { Let } \mathrm { A } = \left[ \begin{array} { l } 
- 2 \
1 \
- 1
\end{array} \right] \text { and } \mathrm { B } = \left[ \begin{array} { l l l } 
1 & - 1 & 0
\end{array} \right] \text {. Find } \mathrm { AB } \text {. }$

Accepted Answer

None

Question 9

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
2 x ^ { 2 } + y ^ { 2 } = 17 \
3 x ^ { 2 } - 2 y ^ { 2 } = - 6
\end{array} \right.$$

Accepted Answer

A)  $x = 2 , y = 3 ; x = 2 , y = - 3 ; x = - 2 , y = 3 ; x = - 2 , y = - 3$ 
B)  $x = 2 , y = - 3 ; x = - 2 , y = 3$ 
C)  $x = 1 , y = 3 ; x = - 1 , y = - 3$ 
D)  $\mathrm { x } = 1 , \mathrm { y } = 3 ; \mathrm { x } = 1 , \mathrm { y } = - 3 ; \mathrm { x } = - 1 , \mathrm { y } = 3 ; \mathrm { x } = - 1 , \mathrm { y } = - 3$ 
A)  $x = 2 , y = 3 ; x = 2 , y = - 3 ; x = - 2 , y = 3 ; x = - 2 , y = - 3$ 
B)  $x = 2 , y = - 3 ; x = - 2 , y = 3$ 
C)  $x = 1 , y = 3 ; x = - 1 , y = - 3$ 
D)  $\mathrm { x } = 1 , \mathrm { y } = 3 ; \mathrm { x } = 1 , \mathrm { y } = - 3 ; \mathrm { x } = - 1 , \mathrm { y } = 3 ; \mathrm { x } = - 1 , \mathrm { y } = - 3$

Question 10

Find the value of the determinant.
-$$\left\{ \begin{aligned}
6 x - 2 z & = 16 \
2 x + 9 y - 5 z & = 64 \
- 8 x - 5 y & = - 59
\end{aligned} \right.$$

Accepted Answer

A)  x = 3, y = 7, z = 1 
B)  x = 3, y = -7, z = -1 
C)  x = 4, y = 5, z = 1 
D)  x = 7, y = 1, z = 7 
A)  x = 3, y = 7, z = 1 
B)  x = 3, y = -7, z = -1 
C)  x = 4, y = 5, z = 1 
D)  x = 7, y = 1, z = 7

Question 11

Solve the problem.
-A right triangle has an area of 40 square inches. The square of the hypotenuse is 164. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Accepted Answer

A)  16 in. and 5 in. 
B)  8 in. and 10 in. 
C)  64 in. and 100 in. 
D)  4 in. and 20 in. 
A)  16 in. and 5 in. 
B)  8 in. and 10 in. 
C)  64 in. and 100 in. 
D)  4 in. and 20 in.

Question 12

Find the inverse of the matrix.
-$\left[ \begin{array} { r r } 1 & - 2 \ 6 & 2 \end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { c c } \frac { 1 } { 7 } & \frac { 1 } { 7 } \ - \frac { 3 } { 7 } & \frac { 1 } { 14 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - \frac { 3 } { 7 } & \frac { 1 } { 14 } \ \frac { 1 } { 7 } & \frac { 1 } { 7 } \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } \frac { 1 } { 7 } & - \frac { 1 } { 7 } \ \frac { 3 } { 7 } & \frac { 1 } { 14 } \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } \frac { 1 } { 14 } & \frac { 1 } { 7 } \ - \frac { 3 } { 7 } & \frac { 1 } { 7 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } \frac { 1 } { 7 } & \frac { 1 } { 7 } \ - \frac { 3 } { 7 } & \frac { 1 } { 14 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - \frac { 3 } { 7 } & \frac { 1 } { 14 } \ \frac { 1 } { 7 } & \frac { 1 } { 7 } \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } \frac { 1 } { 7 } & - \frac { 1 } { 7 } \ \frac { 3 } { 7 } & \frac { 1 } { 14 } \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } \frac { 1 } { 14 } & \frac { 1 } { 7 } \ - \frac { 3 } { 7 } & \frac { 1 } { 7 } \end{array} \right]$

Question 13

Which method should be used to solve the system? Explain your answer, including a description of the first step.
--7x2 - 6y2 = 81
x - 2y = -5

Accepted Answer

Substitution should be used, b

Question 14

Graph the system of inequalities.
-$\begin{array}{l}
x^{2}+y^{2} \leq 36 \
10 x+4 y \leq 40
\end{array}$

Accepted Answer

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

Question 15

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

Accepted Answer

A)  $x = 2 , y = - 1 ; x = 1 , y = 2 ; x = - 1 , y = 2 ; x = - 2 , y = - 1$ 
B)  $x = 1 , y = 4 ; x = 4 , y = 19$ 
C)  $x = 1 , y = 2 ; x = - 1 , y = 2$ 
D)  $x = 2 , y = - 1 ; x = - 2 , y = - 1$ 
A)  $x = 2 , y = - 1 ; x = 1 , y = 2 ; x = - 1 , y = 2 ; x = - 2 , y = - 1$ 
B)  $x = 1 , y = 4 ; x = 4 , y = 19$ 
C)  $x = 1 , y = 2 ; x = - 1 , y = 2$ 
D)  $x = 2 , y = - 1 ; x = - 2 , y = - 1$

Question 16

Solve the problem.
-Lexie wants to have an income of $9000 per year from investments. To that end she is going to invest $90,000 in
three different accounts. These accounts pay 7%, 10%, and 14% simple interest. If she wants to have $10,000
more in the account paying 7% simple interest than she has in the account paying 14% simple interest, how
much should go into each account?

Accepted Answer

$40,000 at

Question 17

Solve the problem.
-The sum of the squares of two numbers is 52. The difference of the two numbers is 10. Find the two numbers.

Accepted Answer

A)  -6 and 4 
B)  -6 and -4; or 4 and 6 
C)  -4 and 6 
D)  -4 and 6; or -6 and 4 
A)  -6 and 4 
B)  -6 and -4; or 4 and 6 
C)  -4 and 6 
D)  -4 and 6; or -6 and 4

Question 18

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)?
-  2x2 = y + 5 y = -10x + 3

Accepted Answer

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

Question 19

Verify that the values of the variables listed are solutions of the system of equations.
-$$\left\{ \begin{array} { c } 
x - y + 3 z = - 20 \
4 x + z = - 5 \
x + 2 y + z = 5 \
\end{array} \right.$$

x = 0 , y = 5 , z = - 5

Accepted Answer

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

Question 20

Find the value of the determinant.
-$$\left| \begin{array} { r r r } 
- 2 & 5 & 4 \
3 & - 2 & 1 \
1 & 6 & - 3
\end{array} \right|$$

Accepted Answer

A)  -12 
B)  -90 
C)  130 
D)  80 
A)  -12 
B)  -90 
C)  130 
D)  80

Graph the inequality. --3x - 4y ≤-12

Graph the inequality. -x - y > -5

Solve the problem. -The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

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

Solve the problem. -The sum of the squares of two numbers is 85. The sum of the two numbers is 13. Find the two numbers.

Write the partial fraction decomposition of the rational expression. - $\frac { 9 x ^ { 2 } + 21 x + 11 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$

Graph the inequality. - $y > x ^ { 2 } - 4$ $Graph the inequality. - y > x ^ { 2 } - 4$

Solve the problem. - $\text { Let } \mathrm { A } = \left[ \begin{array} { l } - 2 \\1 \\- 1\end{array} \right] \text { and } \mathrm { B } = \left[ \begin{array} { l l l } 1 & - 1 & 0\end{array} \right] \text {. Find } \mathrm { AB } \text {. }$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array} \right.$

Find the value of the determinant. - $\left\{ \begin{aligned}6 x - 2 z & = 16 \\2 x + 9 y - 5 z & = 64 \\- 8 x - 5 y & = - 59\end{aligned} \right.$

Solve the problem. -A right triangle has an area of 40 square inches. The square of the hypotenuse is 164. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 1 & - 2 \\ 6 & 2 \end{array} \right]$

Which method should be used to solve the system? Explain your answer, including a description of the first step. --7x² - 6y² = 81 x - 2y = -5

Graph the system of inequalities. - +\leq36 10x+4y\leq40 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 36 \\ 10 x+4 y \leq 40 \end{array}$

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

Solve the problem. -The sum of the squares of two numbers is 52. The difference of the two numbers is 10. Find the two numbers.

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)? - 2x² = y + 5 y = -10x + 3

Verify that the values of the variables listed are solutions of the system of equations. - $\left\{ \begin{array} { c } x - y + 3 z = - 20 \\4 x + z = - 5 \\x + 2 y + z = 5 \\\end{array} \right.$ x = 0 , y = 5 , z = - 5

Find the value of the determinant. - $\left| \begin{array} { r r r } - 2 & 5 & 4 \\3 & - 2 & 1 \\1 & 6 & - 3\end{array} \right|$

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

Graph the inequality. --3x - 4y ≤-12

Graph the inequality. -x - y > -5

Solve the problem. -The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Find the inverse of the matrix. - [100−110111]\left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]​1−11​011​001​​

Solve the problem. -The sum of the squares of two numbers is 85. The sum of the two numbers is 13. Find the two numbers.

Write the partial fraction decomposition of the rational expression. - 9x2+21x+11(x+2)(x+1)2\frac { 9 x ^ { 2 } + 21 x + 11 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }(x+2)(x+1)29x2+21x+11​

Graph the inequality. - y>x2−4y > x ^ { 2 } - 4y>x2−4

Solve the system of equations using elimination. - {2x2+y2=173x2−2y2=−6\left\{ \begin{array} { l } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array} \right.{2x2+y2=173x2−2y2=−6​

Find the value of the determinant. - {6x−2z=162x+9y−5z=64−8x−5y=−59\left\{ \begin{aligned}6 x - 2 z & = 16 \\2 x + 9 y - 5 z & = 64 \\- 8 x - 5 y & = - 59\end{aligned} \right.⎩⎨⎧​6x−2z2x+9y−5z−8x−5y​=16=64=−59​

Solve the problem. -A right triangle has an area of 40 square inches. The square of the hypotenuse is 164. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Find the inverse of the matrix. - [1−262]\left[ \begin{array} { r r } 1 & - 2 \\ 6 & 2 \end{array} \right][16​−22​]

Which method should be used to solve the system? Explain your answer, including a description of the first step. --7x2 - 6y2 = 81 x - 2y = -5

Graph the system of inequalities. - +\leq36 10x+4y\leq40

Solve the system of equations using substitution. - {y=−x2+3x2+y2=5\left\{ \begin{array} { l } y = - x ^ { 2 } + 3 \\x ^ { 2 } + y ^ { 2 } = 5\end{array} \right.{y=−x2+3x2+y2=5​

Solve the problem. -The sum of the squares of two numbers is 52. The difference of the two numbers is 10. Find the two numbers.

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)? - 2x2 = y + 5 y = -10x + 3

Verify that the values of the variables listed are solutions of the system of equations. - {x−y+3z=−204x+z=−5x+2y+z=5\left\{ \begin{array} { c } x - y + 3 z = - 20 \\4 x + z = - 5 \\x + 2 y + z = 5 \\\end{array} \right.⎩⎨⎧​x−y+3z=−204x+z=−5x+2y+z=5​ x = 0 , y = 5 , z = - 5

Find the value of the determinant. - ∣−2543−2116−3∣\left| \begin{array} { r r r } - 2 & 5 & 4 \\3 & - 2 & 1 \\1 & 6 & - 3\end{array} \right|​−231​5−26​41−3​​

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. - $\left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]$

Write the partial fraction decomposition of the rational expression. - $\frac { 9 x ^ { 2 } + 21 x + 11 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$

Graph the inequality. - $y > x ^ { 2 } - 4$ $Graph the inequality. - y > x ^ { 2 } - 4$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array} \right.$

Find the value of the determinant. - $\left\{ \begin{aligned}6 x - 2 z & = 16 \\2 x + 9 y - 5 z & = 64 \\- 8 x - 5 y & = - 59\end{aligned} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 1 & - 2 \\ 6 & 2 \end{array} \right]$

Which method should be used to solve the system? Explain your answer, including a description of the first step. --7x² - 6y² = 81 x - 2y = -5

Graph the system of inequalities. - +\leq36 10x+4y\leq40 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 36 \\ 10 x+4 y \leq 40 \end{array}$

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

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)? - 2x² = y + 5 y = -10x + 3

Verify that the values of the variables listed are solutions of the system of equations. - $\left\{ \begin{array} { c } x - y + 3 z = - 20 \\4 x + z = - 5 \\x + 2 y + z = 5 \\\end{array} \right.$ x = 0 , y = 5 , z = - 5

Find the value of the determinant. - $\left| \begin{array} { r r r } - 2 & 5 & 4 \\3 & - 2 & 1 \\1 & 6 & - 3\end{array} \right|$