Question 1

Find the indicated matrix.
-Let $A = \left[ \begin{array} { l l } - 4 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]$. Find $2 A + 3 B$.

Accepted Answer

A)  $\left[ \begin{array} { l l } - 5 & 4 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } - 8 & 4 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } - 1 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } - 7 & 4 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } - 5 & 4 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } - 8 & 4 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } - 1 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } - 7 & 4 \end{array} \right]$

Question 2

Solve the system graphically.
-$$\begin{array} { l } 
y = \ln ( 3 x - 2 ) \
x ^ { 2 } + 3 y ^ { 2 } = 7
\end{array}$$

Accepted Answer

A)  $\approx ( 5.25,2.62 )$ 
B)  $\approx ( 0.74 , - 1.47 )$ and $\approx ( 1.73,1.16 )$ 
C)  $\approx ( 1.73 , - 1.16 )$ and $\approx ( 0.74,1.47 )$ 
D)  $\approx ( 0.77,1.46 )$ and $\approx ( - 0.59 , - 1.49 )$ 
A)  $\approx ( 5.25,2.62 )$ 
B)  $\approx ( 0.74 , - 1.47 )$ and $\approx ( 1.73,1.16 )$ 
C)  $\approx ( 1.73 , - 1.16 )$ and $\approx ( 0.74,1.47 )$ 
D)  $\approx ( 0.77,1.46 )$ and $\approx ( - 0.59 , - 1.49 )$

Question 3

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 If the graphs of a system of...

Question 4

Find the determinant of the given matrix.
-$\left[ \begin{array} { l l l } 1 & 7 & 0 \ 5 & 6 & 2 \ 5 & 5 & 7 \end{array} \right]$

Accepted Answer

A)  $- 283$ 
B)  367 
C)  $- 143$ 
D)  143 
A)  $- 283$ 
B)  367 
C)  $- 143$ 
D)  143

Question 5

Use the graph to estimate any solutions of the system.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 1 \
y = 1 + x
\end{array}$$

$[ - 5,5 ]$ by $[ - 5,5 ]$

Accepted Answer

A)  $( 1,0 )$ and $( - 1,0 )$ 
B)  $( 0,1 )$ and $( - 1,0 )$ 
C)  $( 0,1 )$ and $( 0 , - 1 )$ 
D)  $( 0,1 )$ and $( 1,0 )$ 
A)  $( 1,0 )$ and $( - 1,0 )$ 
B)  $( 0,1 )$ and $( - 1,0 )$ 
C)  $( 0,1 )$ and $( 0 , - 1 )$ 
D)  $( 0,1 )$ and $( 1,0 )$

Question 6

Perform the indicated elementary row operations.
-$\begin{array}{l}
\text { (6) } \mathrm{R}_{2}+\mathrm{R}_{3}\
\left[\begin{array}{rrr}
-3 & 7 & 1 \
3 & 5 & -10 \
10 & 8 & -5
\end{array}\right]
\end{array}$

Accepted Answer

A) $\left[\begin{array}{rrr}
-3 & 7 & 1 \
63 & 53 & -40 \
10 & 8 & -5
\end{array}\right]$ 
B) $\left[\begin{array}{rrr}
-3 & 7 & 8 \
3 & 5 & -5 \
10 & 8 & 3
\end{array}\right]$ 
C) $\left[\begin{array}{rrr}
-3 & 7 & 43 \
3 & 5 & 20 \
10 & 8 & 43
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
-3 & 7 & 1 \
3 & 5 & -10 \
28 & 38 & -65
\end{array}\right]$ 
A) $\left[\begin{array}{rrr}
-3 & 7 & 1 \
63 & 53 & -40 \
10 & 8 & -5
\end{array}\right]$ 
B) $\left[\begin{array}{rrr}
-3 & 7 & 8 \
3 & 5 & -5 \
10 & 8 & 3
\end{array}\right]$ 
C) $\left[\begin{array}{rrr}
-3 & 7 & 43 \
3 & 5 & 20 \
10 & 8 & 43
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
-3 & 7 & 1 \
3 & 5 & -10 \
28 & 38 & -65
\end{array}\right]$

Question 7

Solve.
-Find the dimensions of a rectangular enclosure with perimeter 40 yd and area 91 yd2.

Accepted Answer

A)  15 yd by 6 yd 
B)  13 yd by 7 yd 
C)  14 yd by 6 yd 
D)  16 yd by 7 yd 
A)  15 yd by 6 yd 
B)  13 yd by 7 yd 
C)  14 yd by 6 yd 
D)  16 yd by 7 yd

Question 8

Graph the system of inequalities. Shade the region that represents the solution set.
-$\begin{aligned}
y & \leq-x^{2}+8 \
x-y &<3
\end{aligned}$

Accepted Answer

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

Question 9

5x + 3y = 19
7x + 8y = 48
If your friend was going to solve this system of equations by first eliminating y, what general suggestions
would you make so your friend could start on this in a systematic way?

Accepted Answer

Answers may vary. One possibility: Multi

Question 10

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$$\begin{array} { l } 
2 x + 4 y + z = - 16 \
2 x - 5 y - z = 3 \
5 x + y + 5 z = - 3
\end{array}$$

Accepted Answer

A)  $( - 4 , - 3,4 )$ 
B)  No solution 
C)  $( - 4,4 , - 3 )$ 
D)  $( 4 , - 3 , - 4 )$ 
A)  $( - 4 , - 3,4 )$ 
B)  No solution 
C)  $( - 4,4 , - 3 )$ 
D)  $( 4 , - 3 , - 4 )$

Question 11

Find the matrix product, if possible.
-$\left[ \begin{array} { l l l } - 8 & 2 & 4 \end{array} \right] \left[ \begin{array} { r } 8 \ 0 \ - 3 \end{array} \right]$

Accepted Answer

A) 
[250] 
B) 
$\left[ \begin{array} { l l l } - 64 & 0 & - 12 \end{array} \right]$ 
C) 
$[ - 76 ]$ 
D) 
$\left[\begin{array}{r}
-64 \
0 \
-12
\end{array}\right]$ 
A) 
[250] 
B) 
$\left[ \begin{array} { l l l } - 64 & 0 & - 12 \end{array} \right]$ 
C) 
$[ - 76 ]$ 
D) 
$\left[\begin{array}{r}
-64 \
0 \
-12
\end{array}\right]$

Question 12

Solve.
-Find the dimensions of a rectangular enclosure with perimeter 34 ft and area 60 ft2.

Accepted Answer

A)  10 ft by 6 ft 
B)  12 ft by 5 ft 
C)  10 ft by 24 ft 
D)  12 ft by 22 ft 
A)  10 ft by 6 ft 
B)  12 ft by 5 ft 
C)  10 ft by 24 ft 
D)  12 ft by 22 ft

Question 13

Use division to write the rational function in the form q(x) + r(x)/d(x), where the degree of r(x) is less than the degree of
d(x). Then find the partial fraction decomposition of r(x)/d(x).
-$\frac { 2 x ^ { 3 } - 3 x ^ { 2 } - 2 x + 27 } { x ^ { 2 } + x - 2 }$

Accepted Answer

A)  $2 x - 9 - \frac { 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }$ 
B)  $2 x - 9 - \frac { 13 } { x + 2 } + \frac { 7 } { x - 1 }$ 
C)  $2 x - 5 - \frac { 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }$ 
D)  $2 x - 5 - \frac { 1 } { x + 2 } + \frac { 8 } { x - 1 }$ 
A)  $2 x - 9 - \frac { 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }$ 
B)  $2 x - 9 - \frac { 13 } { x + 2 } + \frac { 7 } { x - 1 }$ 
C)  $2 x - 5 - \frac { 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }$ 
D)  $2 x - 5 - \frac { 1 } { x + 2 } + \frac { 8 } { x - 1 }$

Question 14

Perform the indicated operation, if possible.
-$\left[ \begin{array} { l l } 4 & 1 \ 4 & 6 \ 8 & 6 \end{array} \right] + \left[ \begin{array} { r r } - 9 & 4 \ - 5 & - 1 \ - 1 & 1 \end{array} \right]$

Accepted Answer

A) 
$\left[ \begin{array} { r r } - 5 & 5 \ - 1 & 5 \ 7 & 7 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } - 5 & 5 \ 1 & 6 \ 7 & - 7 \end{array} \right]$ 
C) 
$\left[\begin{array}{rr}
-5 & 6 \
-1 & 5 \
7 & 7
\end{array}\right]$ 
D) 
 $\left[\begin{array}{rr}
13 & -3 \
9 & 7 \
9 & 8
\end{array}\right]$ 
A) 
$\left[ \begin{array} { r r } - 5 & 5 \ - 1 & 5 \ 7 & 7 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } - 5 & 5 \ 1 & 6 \ 7 & - 7 \end{array} \right]$ 
C) 
$\left[\begin{array}{rr}
-5 & 6 \
-1 & 5 \
7 & 7
\end{array}\right]$ 
D) 
 $\left[\begin{array}{rr}
13 & -3 \
9 & 7 \
9 & 8
\end{array}\right]$

Question 15

Find the partial fraction decomposition.
-$$\frac { - 7 } { x ( 3 x - 1 ) ( x + 1 ) } = \frac { A } { x } + \frac { B } { 3 x - 1 } + \frac { C } { x + 1 }$$

Accepted Answer

A)  $\mathrm { A } = - 7 , \mathrm {~B} = \frac { 63 } { 4 } , \mathrm { C } = \frac { 7 } { 4 }$ 
B)  $\mathrm { A } = 7 , \mathrm {~B} = \frac { 63 } { 4 } , \mathrm { C } = \frac { 7 } { 4 }$ 
C)  $\mathrm { A } = 7 , \mathrm {~B} = - \frac { 63 } { 4 } , \mathrm { C } = - \frac { 7 } { 4 }$ 
D)  $A = - 7 , B = - \frac { 63 } { 4 } , C = - \frac { 7 } { 4 }$ 
A)  $\mathrm { A } = - 7 , \mathrm {~B} = \frac { 63 } { 4 } , \mathrm { C } = \frac { 7 } { 4 }$ 
B)  $\mathrm { A } = 7 , \mathrm {~B} = \frac { 63 } { 4 } , \mathrm { C } = \frac { 7 } { 4 }$ 
C)  $\mathrm { A } = 7 , \mathrm {~B} = - \frac { 63 } { 4 } , \mathrm { C } = - \frac { 7 } { 4 }$ 
D)  $A = - 7 , B = - \frac { 63 } { 4 } , C = - \frac { 7 } { 4 }$

Question 16

Solve the system of equations by using an inverse matrix.
-$$\begin{aligned}
8 x - 9 y - z & = - 12 \
x + 2 y + 7 z & = 64 \
- 7 x + y + z & = - 23
\end{aligned}$$

Accepted Answer

A)  $( - 5,5,10 )$ 
B)  $( 5,7,5 )$ 
C)  $( 5,5,7 )$ 
D)  $\varnothing$ 
A)  $( - 5,5,10 )$ 
B)  $( 5,7,5 )$ 
C)  $( 5,5,7 )$ 
D)  $\varnothing$

Question 17

Solve.
-Find the dimensions of a rectangular garden with perimeter 62 yd and area 220 yd2.

Accepted Answer

A)  10 yd by 11 yd 
B)  20 yd by 11 yd 
C)  10 yd by 22 yd 
D)  20 yd by 22 yd 
A)  10 yd by 11 yd 
B)  20 yd by 11 yd 
C)  10 yd by 22 yd 
D)  20 yd by 22 yd

Question 18

Find the partial fraction decomposition.
-$$\frac { 7 x - 35 } { ( x + 3 ) ( x - 4 ) }$$

Accepted Answer

A)  $\frac { 7 } { x + 3 } - \frac { 35 } { x - 4 }$ 
B)  $\frac { 8 } { x + 3 } + \frac { 1 } { x - 4 }$ 
C)  $\frac { 1 } { x - 4 } - \frac { 8 } { x + 3 }$ 
D)  $\frac { 8 } { x + 3 } - \frac { 1 } { x - 4 }$ 
A)  $\frac { 7 } { x + 3 } - \frac { 35 } { x - 4 }$ 
B)  $\frac { 8 } { x + 3 } + \frac { 1 } { x - 4 }$ 
C)  $\frac { 1 } { x - 4 } - \frac { 8 } { x + 3 }$ 
D)  $\frac { 8 } { x + 3 } - \frac { 1 } { x - 4 }$

Question 19

Answer the question.
-Find $a , b$, and $c$ so that the graph of the equation $y = a x ^ { 2 } + b x + c$ passes through the points $( 4,54 ) , ( 2,20 )$, and $( 3,35 )$.

Accepted Answer

A)  $y = 2 x ^ { 2 } + 5 x - 2$ 
B)  $y = 2 x ^ { 2 } - 5 x + 2$ 
C)  $y = 2 x ^ { 2 } + 5 x + 2$ 
D)  $y = - 2 x ^ { 2 } + 5 x + 2$ 
A)  $y = 2 x ^ { 2 } + 5 x - 2$ 
B)  $y = 2 x ^ { 2 } - 5 x + 2$ 
C)  $y = 2 x ^ { 2 } + 5 x + 2$ 
D)  $y = - 2 x ^ { 2 } + 5 x + 2$

Question 20

Solve the system graphically.
-$x^{2}+y^{2}=7$
$y=\sqrt[3]{x+6}$

Accepted Answer

A) $\approx(-2,13,157) \text { and } \approx(1,76 \cdot 1.98)$ 
B) $\approx(-1.76,-1.98) \text { and } \approx(2.13,-1.57)$ 
C) $\approx(-2.13,-1.57) \text { and } \approx(1.76,-1.98)$ 
D) $\approx(-2.29,-1.32) \text { and } \approx(2.29,1.32)$ 
A) $\approx(-2,13,157) \text { and } \approx(1,76 \cdot 1.98)$ 
B) $\approx(-1.76,-1.98) \text { and } \approx(2.13,-1.57)$ 
C) $\approx(-2.13,-1.57) \text { and } \approx(1.76,-1.98)$ 
D) $\approx(-2.29,-1.32) \text { and } \approx(2.29,1.32)$

Find the indicated matrix. -Let $A = \left[ \begin{array} { l l } - 4 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]$ . Find $2 A + 3 B$ .

Solve the system graphically. - y=(3x-2) +3=7

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?

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l } 1 & 7 & 0 \\ 5 & 6 & 2 \\ 5 & 5 & 7 \end{array} \right]$

Use the graph to estimate any solutions of the system. - +=1 y=1+x $Use the graph to estimate any solutions of the system. - \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 1 \\ y = 1 + x \end{array} [ - 5,5 ] by [ - 5,5 ]$ $[ - 5,5 ]$ by $[ - 5,5 ]$

Perform the indicated elementary row operations. - (6) + -3 7 1 3 5 -10 10 8 -5

Solve. -Find the dimensions of a rectangular enclosure with perimeter 40 yd and area 91 yd2.

Graph the system of inequalities. Shade the region that represents the solution set. - y \leq-+8 x-y <3 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{aligned} y & \leq-x^{2}+8 \\ x-y &<3 \end{aligned}$

5x + 3y = 19 7x + 8y = 48 If your friend was going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - 2x+4y+z=-16 2x-5y-z=3 5x+y+5z=-3

Find the matrix product, if possible. - $\left[ \begin{array} { l l l } - 8 & 2 & 4 \end{array} \right] \left[ \begin{array} { r } 8 \\ 0 \\ - 3 \end{array} \right]$

Solve. -Find the dimensions of a rectangular enclosure with perimeter 34 ft and area 60 ft2.

Use division to write the rational function in the form q(x) + r(x)/d(x), where the degree of r(x) is less than the degree of d(x). Then find the partial fraction decomposition of r(x)/d(x). - $\frac { 2 x ^ { 3 } - 3 x ^ { 2 } - 2 x + 27 } { x ^ { 2 } + x - 2 }$

Perform the indicated operation, if possible. - $\left[ \begin{array} { l l } 4 & 1 \\ 4 & 6 \\ 8 & 6 \end{array} \right] + \left[ \begin{array} { r r } - 9 & 4 \\ - 5 & - 1 \\ - 1 & 1 \end{array} \right]$

Find the partial fraction decomposition. - $\frac { - 7 } { x ( 3 x - 1 ) ( x + 1 ) } = \frac { A } { x } + \frac { B } { 3 x - 1 } + \frac { C } { x + 1 }$

Solve the system of equations by using an inverse matrix. - 8x-9y-z =-12 x+2y+7z =64 -7x+y+z =-23

Solve. -Find the dimensions of a rectangular garden with perimeter 62 yd and area 220 yd2.

Find the partial fraction decomposition. - $\frac { 7 x - 35 } { ( x + 3 ) ( x - 4 ) }$

Answer the question. -Find $a , b$ , and $c$ so that the graph of the equation $y = a x ^ { 2 } + b x + c$ passes through the points $( 4,54 ) , ( 2,20 )$ , and $( 3,35 )$ .

Solve the system graphically. - $x^{2}+y^{2}=7$ $y=\sqrt[3]{x+6}$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 7: Systems and Matrices

Find the indicated matrix. -Let A=[−42]A = \left[ \begin{array} { l l } - 4 & 2 \end{array} \right]A=[−4​2​] and B=[10]B = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]B=[1​0​] . Find 2A+3B2 A + 3 B2A+3B .