Question 1

Answer the question.
-Determine the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ so that its graph contains the points $( - 1,2 ) , ( 0,6 ) , ( 1,16 )$, and $( 2$, 50).

Accepted Answer

A)  $f ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } - 4 x - 6$ 
B)  $f ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } + 4 x + 6$ 
C)  $f ( x ) = 3 x ^ { 3 } + 4 x ^ { 2 } + 3 x + 6$ 
D)  $f ( x ) = 4 x ^ { 3 } + 4 x ^ { 2 } + 4 x + 6$ 
A)  $f ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } - 4 x - 6$ 
B)  $f ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } + 4 x + 6$ 
C)  $f ( x ) = 3 x ^ { 3 } + 4 x ^ { 2 } + 3 x + 6$ 
D)  $f ( x ) = 4 x ^ { 3 } + 4 x ^ { 2 } + 4 x + 6$

Question 2

Determine the order of the matrix.
-$\left[ \begin{array} { r r } 2 & - 4 \ 6 & 0 \ - 6 & 8 \ 4 & - 2 \end{array} \right]$

Accepted Answer

A)  $2 \times 4$ 
B)  8 
C)  2 
D)  $4 \times 2$ 
A)  $2 \times 4$ 
B)  8 
C)  2 
D)  $4 \times 2$

Question 3

Solve the system of equations.
-x + 2y + 2z + w = -3.5 x + y + z + w = -2.5

Accepted Answer

A)  (-w - 1.5, -z - 1, z, w) 
B)  (-w + 1, -z - 3.5, z, w) 
C)  (-w - 1.5, -w - 1, w, w) 
D)  (w - 1.5, z - 1, -z, -w) 
A)  (-w - 1.5, -z - 1, z, w) 
B)  (-w + 1, -z - 3.5, z, w) 
C)  (-w - 1.5, -w - 1, w, w) 
D)  (w - 1.5, z - 1, -z, -w)

Question 4

Determine which inequality matches the graph.
-

Accepted Answer

A)  $y \geq 2 x - 3$ 
B)  $y \geq - 2 x - 3$ 
C)  $y \leq 2 x - 3$ 
D)  $y \leq - 2 x - 3$ 
A)  $y \geq 2 x - 3$ 
B)  $y \geq - 2 x - 3$ 
C)  $y \leq 2 x - 3$ 
D)  $y \leq - 2 x - 3$

Question 5

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

Accepted Answer

A) 
$$\left[ \begin{array} { r r } 
2 & - 6 \
- 3 & - 1
\end{array} \right]$$ 
B) 
$\left[ \begin{array} { r r } 2 & 0 \ - 4 & 2 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 3 & - 1 \ 2 & - 10 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 1 & 3 \ - 10 & 2 \end{array} \right]$ 
A) 
$$\left[ \begin{array} { r r } 
2 & - 6 \
- 3 & - 1
\end{array} \right]$$ 
B) 
$\left[ \begin{array} { r r } 2 & 0 \ - 4 & 2 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 3 & - 1 \ 2 & - 10 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 1 & 3 \ - 10 & 2 \end{array} \right]$

Question 6

Graph the system of inequalities. Shade the region that represents the solution set.
-$\begin{array}{r}
x^{2}-y \leq 7 \
x+y<4
\end{array}$

Accepted Answer

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

Question 7

Solve the problem.
-Zach is planning to invest up to $\$ 45,000$ in corporate and municipal bonds. The least he will invest in corporate bonds is $\$ 9000$ and he does not want to invest more than $\$ 30,000$ in corporate bonds. He also does not want to invest more than $\$ 31,447$ in municipal bonds. The interest is $8.4 \%$ on corporate bonds and $6.5 \%$ on municipal bonds. This is simple interest for one year. What is the maximum income?

Accepted Answer

A)  $\$ 18,495$ 
B)  $\$ 33,495$ 
C)  $\$ 3495$ 
D)  $\$ 16,545$ 
A)  $\$ 18,495$ 
B)  $\$ 33,495$ 
C)  $\$ 3495$ 
D)  $\$ 16,545$

Question 8

Find the indicated matrix product or state that the product is undefined.
-$$A = \left[ \begin{array} { l l l l } 
0 & 1 & 0 & 0 \
0 & 0 & 0 & 1 \
1 & 0 & 0 & 0 \
0 & 0 & 1 & 0
\end{array} \right] , B = \left[ \begin{array} { r r r r } 
- 2 & 9 & 3 & 1 \
- 3 & 1 & 1 & - 6 \
1 & - 4 & 5 & 0 \
6 & 3 & - 3 & - 1
\end{array} \right]$$
$\mathrm { AB }$

Accepted Answer

A) $\left[\begin{array}{rrrr}
-3 & 1 & 1 & -6 \
6 & 3 & -3 & -1 \
-2 & 9 & 3 & 1 \
1 & -4 & 5 & 0
\end{array}\right]$ 
B) $\left[\begin{array}{rrrr}
3 & -2 & 1 & 9 \
1 & -3 & -6 & 1 \
5 & 1 & 0 & -4 \
-3 & 6 & -1 & 3
\end{array}\right]$ 
C) $\left[\begin{array}{rrrr}
-2 & 9 & 3 & 1 \
-3 & 1 & 1 & -6 \
1 & -4 & 5 & 0 \
6 & 3 & -3 & -1
\end{array}\right]$ 
D) $\left[\begin{array}{rrrr}
0 & 9 & 0 & 0 \
0 & 0 & 0 & -6 \
1 & 0 & 0 & 0 \
0 & 0 & -3 & 0
\end{array}\right]$ 
A) $\left[\begin{array}{rrrr}
-3 & 1 & 1 & -6 \
6 & 3 & -3 & -1 \
-2 & 9 & 3 & 1 \
1 & -4 & 5 & 0
\end{array}\right]$ 
B) $\left[\begin{array}{rrrr}
3 & -2 & 1 & 9 \
1 & -3 & -6 & 1 \
5 & 1 & 0 & -4 \
-3 & 6 & -1 & 3
\end{array}\right]$ 
C) $\left[\begin{array}{rrrr}
-2 & 9 & 3 & 1 \
-3 & 1 & 1 & -6 \
1 & -4 & 5 & 0 \
6 & 3 & -3 & -1
\end{array}\right]$ 
D) $\left[\begin{array}{rrrr}
0 & 9 & 0 & 0 \
0 & 0 & 0 & -6 \
1 & 0 & 0 & 0 \
0 & 0 & -3 & 0
\end{array}\right]$

Question 9

Determine the order of the matrix.
-[7]

Accepted Answer

A)  $0 \times 0$ 
B)  0 
C)  $1 \times 1$ 
D)  1 
A)  $0 \times 0$ 
B)  0 
C)  $1 \times 1$ 
D)  1

Question 10

Perform the indicated elementary row operations.
-$\begin{array} { l } 
\mathrm { R } _ { 1 } + \mathrm { R } _ { 2 } \
{ \left[ \begin{array} { r r } 
9 & 1 \
8 & - 2
\end{array} \right] }
\end{array}$

Accepted Answer

A) $\left[\begin{array}{rr}
17 & -1 \
8 & -2
\end{array}\right]$ 
B) $\left[\begin{array}{rr}
9 & 1 \
17 & -1
\end{array}\right]$ 
C) $\left[\begin{array}{rr}
9 & 10 \
8 & 6
\end{array}\right]$ 
D) $\left[\begin{array}{ll}
17 & -1 \
17 & -1
\end{array}\right]$ 
A) $\left[\begin{array}{rr}
17 & -1 \
8 & -2
\end{array}\right]$ 
B) $\left[\begin{array}{rr}
9 & 1 \
17 & -1
\end{array}\right]$ 
C) $\left[\begin{array}{rr}
9 & 10 \
8 & 6
\end{array}\right]$ 
D) $\left[\begin{array}{ll}
17 & -1 \
17 & -1
\end{array}\right]$

Question 11

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the
matrix product AB, and interpret the significance of the entries of this product.
-

Accepted Answer

A) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1074 \
914
\end{array} \right]$$
Tuition for Student 2 is $\$ 1074$ and tuition for Student 1 is $\$ 914$. 
B) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1074 \
914
\end{array} \right]$$
Tuition for Student 1 is $\$ 1074$ and tuition for Student 2 is $\$ 914$. 
C) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1080 \
927
\end{array} \right]$$
Tuition for Student 1 is $\$ 1080$ and tuition for Student 2 is $\$ 927$. 
D) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1080 \
927
\end{array} \right]$$
Tuition for Student 2 is $\$ 1080$ and tuition for Student 1 is $\$ 927 .$ 
A) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1074 \
914
\end{array} \right]$$
Tuition for Student 2 is $\$ 1074$ and tuition for Student 1 is $\$ 914$. 
B) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1074 \
914
\end{array} \right]$$
Tuition for Student 1 is $\$ 1074$ and tuition for Student 2 is $\$ 914$. 
C) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1080 \
927
\end{array} \right]$$
Tuition for Student 1 is $\$ 1080$ and tuition for Student 2 is $\$ 927$. 
D) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1080 \
927
\end{array} \right]$$
Tuition for Student 2 is $\$ 1080$ and tuition for Student 1 is $\$ 927 .$

Question 12

Solve the problem.
-Find the minimum value of $f = 6 x + 8 y$ subject to the following constraints.
$$\begin{array} { l } 
2 x + 4 y \geq 12 \
2 x + y \geq 8 \
x \geq 0 \
y \geq 0
\end{array}$$

Accepted Answer

A)  Minimum of 36 
B)  Minimum of 26 
C)  Minimum of 0 
D)  Minimum of $\frac { 92 } { 3 }$ 
A)  Minimum of 36 
B)  Minimum of 26 
C)  Minimum of 0 
D)  Minimum of $\frac { 92 } { 3 }$

Question 13

Solve the problem.
-Find the equilibrium point for the given demand and supply curve. p = 524 - 3x (demand)
P = 3x - 412 (supply)

Accepted Answer

A)  (-412, 524) 
B)  (56, 156) 
C)  (521, 415) 
D)  (156, 56) 
A)  (-412, 524) 
B)  (56, 156) 
C)  (521, 415) 
D)  (156, 56)

Question 14

Solve the system by elimination.
-x - 3y = -21 5x - 2y = -14

Accepted Answer

A)  (-7, 0) 
B)  No solution 
C)  (0, 7) 
D)  (1, 6) 
A)  (-7, 0) 
B)  No solution 
C)  (0, 7) 
D)  (1, 6)

Question 15

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { l l l } 
1 & 0 & 8 \
1 & 2 & 3 \
2 & 5 & 3
\end{array} \right]$$

Accepted Answer

A)  Inverse does not exist 
B) 
$$\left[ \begin{array} { l l l } 
1 & 1 & 2 \
0 & 2 & 5 \
8 & 3 & 3
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
- 1 & 0 & - 8 \
- 1 & - 2 & - 3 \
- 2 & - 5 & - 3
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { r r r } 
9 & - 40 & 16 \
- 3 & 13 & - 5 \
- 1 & 5 & - 2
\end{array} \right]$$ 
A)  Inverse does not exist 
B) 
$$\left[ \begin{array} { l l l } 
1 & 1 & 2 \
0 & 2 & 5 \
8 & 3 & 3
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
- 1 & 0 & - 8 \
- 1 & - 2 & - 3 \
- 2 & - 5 & - 3
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { r r r } 
9 & - 40 & 16 \
- 3 & 13 & - 5 \
- 1 & 5 & - 2
\end{array} \right]$$

Question 16

Solve the system by elimination.
-$$\begin{array} { l } 
x + 8 y = 12 \
8 x + 7 y = 39
\end{array}$$

Accepted Answer

A)  $( - 4,2 )$ 
B)  $( 4,1 )$ 
C)  No solution 
D)  $( 3,2 )$ 
A)  $( - 4,2 )$ 
B)  $( 4,1 )$ 
C)  No solution 
D)  $( 3,2 )$

Question 17

Graph the system of inequalities. Shade the region that represents the solution set.
-$\begin{array}{r}
y \geq x^{2} \
x+y>3
\end{array}$

Accepted Answer

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

Question 18

Find the determinant of the given matrix.
-$$\left[ \begin{array} { r r r } 
1 & 0 & 0 \
7 & - 3 & 0 \
- 3 & 7 & 7
\end{array} \right]$$

Accepted Answer

A)  21 
B)  $- 28$ 
C)  $- 21$ 
D)  $- 70$ 
A)  21 
B)  $- 28$ 
C)  $- 21$ 
D)  $- 70$

Question 19

Solve the system by substitution.
-x + 3y = 15 2x + 3y = 24

Accepted Answer

A)  (10, 1) 
B)  (10, 9) 
C)  No solution 
D)  (9, 2) 
A)  (10, 1) 
B)  (10, 9) 
C)  No solution 
D)  (9, 2)

Question 20

Write a system of inequalities whose solution set is the region shown.
-

Accepted Answer

A)  $y \leq 0$
$x ^ { 2 } + y ^ { 2 } \geq 16$ 
B)  $y \geq 0$
$x ^ { 2 } + y ^ { 2 } \geq 16$ 
C)  $\mathrm { y } \geq 0$
$x ^ { 2 } + y ^ { 2 } \leq 16$ 
D)  $y \leq 0$
$x ^ { 2 } + y ^ { 2 } \leq 16$ 
A)  $y \leq 0$
$x ^ { 2 } + y ^ { 2 } \geq 16$ 
B)  $y \geq 0$
$x ^ { 2 } + y ^ { 2 } \geq 16$ 
C)  $\mathrm { y } \geq 0$
$x ^ { 2 } + y ^ { 2 } \leq 16$ 
D)  $y \leq 0$
$x ^ { 2 } + y ^ { 2 } \leq 16$

Answer the question. -Determine the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ so that its graph contains the points $( - 1,2 ) , ( 0,6 ) , ( 1,16 )$ , and $( 2$ , 50).

Determine the order of the matrix. - $\left[ \begin{array} { r r } 2 & - 4 \\ 6 & 0 \\ - 6 & 8 \\ 4 & - 2 \end{array} \right]$

Solve the system of equations. -x + 2y + 2z + w = -3.5 x + y + z + w = -2.5

Determine which inequality matches the graph. -

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

Graph the system of inequalities. Shade the region that represents the solution set. - -y\leq7 x+y<4 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{array}{r} x^{2}-y \leq 7 \\ x+y<4 \end{array}$

Determine the order of the matrix. -[7]

Perform the indicated elementary row operations. - + 9 1 8 -2

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Solve the problem. -Find the minimum value of $f = 6 x + 8 y$ subject to the following constraints. 2x+4y\geq12 2x+y\geq8 x\geq0 y\geq0

Solve the problem. -Find the equilibrium point for the given demand and supply curve. p = 524 - 3x (demand) P = 3x - 412 (supply)

Solve the system by elimination. -x - 3y = -21 5x - 2y = -14

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { l l l } 1 & 0 & 8 \\1 & 2 & 3 \\2 & 5 & 3\end{array} \right]$

Solve the system by elimination. - x+8y=12 8x+7y=39

Graph the system of inequalities. Shade the region that represents the solution set. - y\geq x+y>3 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{array}{r} y \geq x^{2} \\ x+y>3 \end{array}$

Find the determinant of the given matrix. - $\left[ \begin{array} { r r r } 1 & 0 & 0 \\7 & - 3 & 0 \\- 3 & 7 & 7\end{array} \right]$

Solve the system by substitution. -x + 3y = 15 2x + 3y = 24

Write a system of inequalities whose solution set is the region shown. -

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

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An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

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Exam 7: Systems and Matrices

Answer the question. -Determine the function f(x)=ax3+bx2+cx+df ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + df(x)=ax3+bx2+cx+d so that its graph contains the points (−1,2),(0,6),(1,16)( - 1,2 ) , ( 0,6 ) , ( 1,16 )(−1,2),(0,6),(1,16) , and (2( 2(2 , 50).

Determine the order of the matrix. - [2−460−684−2]\left[ \begin{array} { r r } 2 & - 4 \\ 6 & 0 \\ - 6 & 8 \\ 4 & - 2 \end{array} \right]​26−64​−408−2​​