Question 1

Graph the inequality $x^{2}+y^{2} \geq 4$

Accepted Answer

The answer of Graph the inequality $x^{2}+y^{2} \geq 4$
 ...

Question 2

Solve the system by substitution.
$\begin{aligned}
x-y &=4 \
y &=x^{2}-6
\end{aligned}$

Accepted Answer

The answer of Solve the system by substitution.
\(\begin{aligned}
x-y &=4 \
y...

Question 3

Draw a graph representing the solution to the system of inequalities $\begin{aligned}
16 x^{2}+25 y^{2} & \leq 400 \
y & \geq(1 / 3) x-1
\end{aligned}$

Accepted Answer

The answer of Draw a graph representing the solution to...

Question 4

A factory records its inventory in matrix  X , where column 1 represents Model  A  of a product, column 2 represents Model  B  of the same product, and each row represents a color of the product. Matrix  M  is the price of Model A (row 1) and Model B (row 2). Compute matrix  XM  and give its physical interpretation.
$X=\left[\begin{array}{rr}
25 & 10 \
30 & 50 \
15 & 40 \
10 & 5
\end{array}\right] \text { and } M=\left[\begin{array}{c}
220 \
250
\end{array}\right]$

Accepted Answer

represents

Question 5

A company's inventory for two models of televisions and two models of radios is given by the matrix
$\left[\begin{array}{ll}
360 & 300 \
200 & 160
\end{array}\right]$
, where row 1 represents the televisions, row 2 represents the radios, column 1 represents Model A, and column 2 represents Model B. If the company wants to increase inventory by  20%  in the next month, what will be the projected matrix for the inventory? Use matrices and explain.

Accepted Answer

None

Question 6

A company's inventory for two models of computers and two models of palm-pilots is given by the matrix

$\left[\begin{array}{ll}
260 & 400 \
300 & 180
\end{array}\right]$ 
where row 1 represents the computers, row 2 represents the palm-pilots, column 1 represents Model A, and column 2 represents Model B. If the company wants to increase inventory by  15%  in the next month, what will be the projected matrix for the inventory? Use matrices and explain.

Accepted Answer

is  1.15

Question 7

Determine the inequality corresponding to the graph below.

Accepted Answer

The answer of Determine the inequality corresponding to the graph...

Question 8

Determine the number of solutions to the augmented matrix.
$\left[\begin{array}{rrrrr}
1 & 0 & 0 & 4 & 3 \
0 & 1 & 0 & 3 & -1 \
0 & 0 & 1 & 2 & 1 \
0 & 0 & 0 & 1 & 0
\end{array}\right]$

Accepted Answer

A)  infinitely many 
B)  2 solutions 
C)  1 solution 
D)  no solutions 
A)  infinitely many 
B)  2 solutions 
C)  1 solution 
D)  no solutions

Question 9

Write the system of equations for the augmented matrix. Do not solve.
$\left[\begin{array}{rrrr}
2 & 1 & 0 & 3 \
-1 & 3 & 4 & 0 \
0 & -2 & 1 & 5
\end{array}\right]$

Accepted Answer

None

Question 10

Use Gaussian elimination to solve the system. 
$\begin{aligned}
x+2 y-3 z &=3 \
4 x+y+2 z &=-2 \
2 x-3 y+8 z &=5
\end{aligned}$

Accepted Answer

To solve the system of equations using G

Question 11

There are how many solutions of the system?
$\begin{aligned}
x^{2}+y^{2} &=25 \
y &=x^{2}-7
\end{aligned}$

Accepted Answer

A)  None 
B)  One 
C)  Two 
D)  Three 
E)  Four 
A)  None 
B)  One 
C)  Two 
D)  Three 
E)  Four

Question 12

Solve the linear programming problem: Maximize 
$\begin{array}{c}
C=2 x+5 y \text { subject to } \
x+2 y \leq 10 \
3 x+2 y \leq 18 \
x \geq 0 \
y \geq 0
\end{array}$

Accepted Answer

A)  12 
B)  23 
C)  25 
D)  32 
A)  12 
B)  23 
C)  25 
D)  32

Question 13

Solve the linear programming problem. Maximize $C=4 x-3 y$ subject to:
$\begin{array}{r}
x+4 y \leq 32 \
2 x-y \leq 10 \
x \geq 0 \
y \geq 0
\end{array}$

Accepted Answer

The answer of Solve the linear programming problem. Maximize \(C=4...

Question 14

Connor invested a total of  $ 50,000  in three different investments that yield  5%, 7% , and  10%  per year, respectively. The total income per year from the three investments is  $ 3,764 . If the income from the  7%  investment is half the income of the  10%  investment, what amount did Jose invest in each investment?
(a) Write the system of equations that will solve this problem. Do not solve.
(b) Write the system as a matrix equation  A X=B . Do not solve.

Accepted Answer

None

Question 15

Jose invested a total of $ \$ 40,000 $ in three different investments that yield $ 6 \%, 8 \% $, and $ 10 \% $ per year, respectively. The total income per year from the three investments is $ \$ 3,240 $. If the income from the $ 8 \% $ investment is half the income of the $ 10 \% $ investment, what amount did Jose invest in each investment?
(a) Write the system of equations that will solve this problem. Do not solve.
(b) Write the system as a matrix equation $ A X=B $. Do not solve.

Accepted Answer

None

Question 16

The inverse of matrix $\left[\begin{array}{lll}
1 & 1 & 0 \
1 & 2 & 1 \
2 & 3 & 2
\end{array}\right] \text { is }\left[\begin{array}{rrr}
1 & -2 & 1 \
0 & 2 & -1 \
-1 & -1 & 1
\end{array}\right]$
Solve the following system by the method of inverse matrix.
$\begin{array}{r}
x+y=15 \
x+2 y+z=20 \
2 x+3 y+2 z=12
\end{array}$

Accepted Answer

The answer of The inverse of matrix \(\left[\begin{array}{lll}
1 & 1...

Question 17

What is the partial fraction decomposition of 
$\frac{2 x}{x^{2}-2 x-3} ?$

Accepted Answer

The answer of What is the partial fraction decomposition of...

Question 18

Show that matrix $A=\left[\begin{array}{crc}
1 / 2 & 3 / 2 & -1 / 2 \
0 & 1 & 0 \
0 & -3 & 1
\end{array}\right]$  is the inverse of the matrix $B=\left[\begin{array}{lll}
2 & 0 & 1 \
0 & 1 & 0 \
0 & 3 & 1
\end{array}\right]$

Accepted Answer

The answer of Show that matrix \(A=\left[\begin{array}{crc}
1 / 2 &...

Question 19

Tell what elementary row operation can be applied to
$\left[\begin{array}{rrrr}
3 & 6 & -2 & 5 \
4 & 7 & 5 & -2 \
-3 & 2 & 0 & 3
\end{array}\right]$ to obtain $\left[\begin{array}{rrrr}
3 & 6 & -2 & 5 \
10 & 3 & 5 & -8 \
-3 & 2 & 0 & 3
\end{array}\right]$

Accepted Answer

A)  $-2 R_{2}+R_{3}$ 
B)  $\frac{10}{4} R_{2}$ 
C)  $-2 R_{3}+R_{2}$ 
D)  $2 R_{1}+R_{2}$ 
A)  $-2 R_{2}+R_{3}$ 
B)  $\frac{10}{4} R_{2}$ 
C)  $-2 R_{3}+R_{2}$ 
D)  $2 R_{1}+R_{2}$

Question 20

Write the system of equations as a matrix equation  AX=B , with  A  as the coefficient matrix.
$\begin{aligned}
x+2 y-3 z &=19 \
2 x-3 y+4 z &=-17 \
3 x-y &=4
\end{aligned}$

Accepted Answer

None

Graph the inequality $x^{2}+y^{2} \geq 4$ $Graph the inequality x^{2}+y^{2} \geq 4$

Solve the system by substitution. x-y =4 y =-6

Draw a graph representing the solution to the system of inequalities 16+25 \leq400 y \geq(1/3)x-1 $Draw a graph representing the solution to the system of inequalities \begin{aligned} 16 x^{2}+25 y^{2} & \leq 400 \\ y & \geq(1 / 3) x-1 \end{aligned}$

Determine the inequality corresponding to the graph below.

Determine the number of solutions to the augmented matrix. $\left[\begin{array}{rrrrr}1 & 0 & 0 & 4 & 3 \\0 & 1 & 0 & 3 & -1 \\0 & 0 & 1 & 2 & 1 \\0 & 0 & 0 & 1 & 0\end{array}\right]$

Write the system of equations for the augmented matrix. Do not solve. $\left[\begin{array}{rrrr}2 & 1 & 0 & 3 \\-1 & 3 & 4 & 0 \\0 & -2 & 1 & 5\end{array}\right]$

Use Gaussian elimination to solve the system. x+2y-3z =3 4x+y+2z =-2 2x-3y+8z =5

There are how many solutions of the system? + =25 y =-7

Solve the linear programming problem: Maximize C=2x+5y subject to x+2y\leq10 3x+2y\leq18 x\geq0 y\geq0

Solve the linear programming problem. Maximize $C=4 x-3 y$ subject to: x+4y\leq32 2x-y\leq10 x\geq0 y\geq0

The inverse of matrix $\left[\begin{array}{lll}1 & 1 & 0 \\1 & 2 & 1 \\2 & 3 & 2\end{array}\right] \text { is }\left[\begin{array}{rrr}1 & -2 & 1 \\0 & 2 & -1 \\-1 & -1 & 1\end{array}\right]$ Solve the following system by the method of inverse matrix. x+y=15 x+2y+z=20 2x+3y+2z=12

What is the partial fraction decomposition of $\frac{2 x}{x^{2}-2 x-3} ?$

Show that matrix $A=\left[\begin{array}{crc}1 / 2 & 3 / 2 & -1 / 2 \\0 & 1 & 0 \\0 & -3 & 1\end{array}\right]$ is the inverse of the matrix $B=\left[\begin{array}{lll}2 & 0 & 1 \\0 & 1 & 0 \\0 & 3 & 1\end{array}\right]$

Tell what elementary row operation can be applied to $\left[\begin{array}{rrrr}3 & 6 & -2 & 5 \\4 & 7 & 5 & -2 \\-3 & 2 & 0 & 3\end{array}\right]$ to obtain $\left[\begin{array}{rrrr}3 & 6 & -2 & 5 \\10 & 3 & 5 & -8 \\-3 & 2 & 0 & 3\end{array}\right]$

Write the system of equations as a matrix equation AX=B , with A as the coefficient matrix. x+2y-3z =19 2x-3y+4z =-17 3x-y =4

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

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

Filters

Exam 7: Systems and Matrices

Graph the inequality x2+y2≥4x^{2}+y^{2} \geq 4x2+y2≥4

Solve the system by substitution. x-y =4 y =-6

Draw a graph representing the solution to the system of inequalities 16+25 \leq400 y \geq(1/3)x-1

Determine the inequality corresponding to the graph below.

Determine the number of solutions to the augmented matrix. [100430103−10012100010]\left[\begin{array}{rrrrr}1 & 0 & 0 & 4 & 3 \\0 & 1 & 0 & 3 & -1 \\0 & 0 & 1 & 2 & 1 \\0 & 0 & 0 & 1 & 0\end{array}\right]​1000​0100​0010​4321​3−110​​

Write the system of equations for the augmented matrix. Do not solve. [2103−13400−215]\left[\begin{array}{rrrr}2 & 1 & 0 & 3 \\-1 & 3 & 4 & 0 \\0 & -2 & 1 & 5\end{array}\right]​2−10​13−2​041​305​​

Use Gaussian elimination to solve the system. x+2y-3z =3 4x+y+2z =-2 2x-3y+8z =5

There are how many solutions of the system? + =25 y =-7

Solve the linear programming problem: Maximize C=2x+5y subject to x+2y\leq10 3x+2y\leq18 x\geq0 y\geq0

Solve the linear programming problem. Maximize C=4x−3yC=4 x-3 yC=4x−3y subject to: x+4y\leq32 2x-y\leq10 x\geq0 y\geq0

What is the partial fraction decomposition of 2xx2−2x−3?\frac{2 x}{x^{2}-2 x-3} ?x2−2x−32x​?

Write the system of equations as a matrix equation AX=B , with A as the coefficient matrix. x+2y-3z =19 2x-3y+4z =-17 3x-y =4

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

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

Filters

Graph the inequality $x^{2}+y^{2} \geq 4$ $Graph the inequality x^{2}+y^{2} \geq 4$

Draw a graph representing the solution to the system of inequalities 16+25 \leq400 y \geq(1/3)x-1 $Draw a graph representing the solution to the system of inequalities \begin{aligned} 16 x^{2}+25 y^{2} & \leq 400 \\ y & \geq(1 / 3) x-1 \end{aligned}$

Determine the number of solutions to the augmented matrix. $\left[\begin{array}{rrrrr}1 & 0 & 0 & 4 & 3 \\0 & 1 & 0 & 3 & -1 \\0 & 0 & 1 & 2 & 1 \\0 & 0 & 0 & 1 & 0\end{array}\right]$

Write the system of equations for the augmented matrix. Do not solve. $\left[\begin{array}{rrrr}2 & 1 & 0 & 3 \\-1 & 3 & 4 & 0 \\0 & -2 & 1 & 5\end{array}\right]$

Solve the linear programming problem. Maximize $C=4 x-3 y$ subject to: x+4y\leq32 2x-y\leq10 x\geq0 y\geq0

What is the partial fraction decomposition of $\frac{2 x}{x^{2}-2 x-3} ?$