Question 1

Graph the solution set of the inequality. $$6 y \leq 12 x$$

Accepted Answer

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

Question 2

One angle measures 66° more than 2 times another. If the two angles are complementary, find the measures of the angles.

Accepted Answer

A)  10°; 80° 
B)  18°; 72° 
C)  13°; 77° 
D)  8°; 82° 
A)  10°; 80° 
B)  18°; 72° 
C)  13°; 77° 
D)  8°; 82° D

Question 3

Solve the system of equations. $$\begin{array} { c } 
x - 4 y + 5 z = - 8 \
2 x + 5 y - 3 z = - 3 \
3 x - 5 y + 3 z = - 17
\end{array}$$

Accepted Answer

A)  $( - 4,4,5 )$ 
B)  $( 1,1 , - 1 )$ 
C)  $( - 4 , - 4 , - 4 )$ 
D)  $( - 4,1,0 )$ 
A)  $( - 4,4,5 )$ 
B)  $( 1,1 , - 1 )$ 
C)  $( - 4 , - 4 , - 4 )$ 
D)  $( - 4,1,0 )$ D

Question 4

A manufacturer produces two models of desks. Model A requires 5 hr to stain and finish and 4 hr to assemble. Model B requires 4 hr to stain and finish and 1 hr to assemble. The total amount of time available for staining and finishing is 40 hr and for assembling is 16 hr. Let x represent the number of Model A desks produced, and let y represent the number of Model B desks produced.
a. Write two inequalities that express the fact that the number of desks to be produced cannot be negative.
b. Write an inequality in terms of the number of Model A and Model B desks that can be produced if the total time for staining and finishing is at most 24 hr.
c. Write an inequality in terms of the number of Model A and Model B desks that can be produced if the total time for assembly is no more than 16 hr.
d. Graph the feasible region formed by graphing the preceding inequalities.
e. Is the point (1, 5) in the feasible region? What does the point (3, 1) represent in the context of this problem?
f. Is the point (4, 8) in the feasible region? What does the point (5, 4) represent in the context of this problem?

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM&
c. @#LAT-DLM&
d.
@#IMG-DLM&
 e. Yes; The point (1, 5

Question 5

Graph the solution set of the inequality. $$3 y - 2 x > 10$$

Accepted Answer

The answer of Graph the solution set of the inequality....

Question 6

Given the matrix E $$\mathbf { E } = \left[ \begin{array} { c c | c } 
3 & - 2 & 10 \
5 & - 5 & 9
\end{array} \right]$$ a. What is the element in the second row and third column?
b. What is the element in the first row and second column

Accepted Answer

The answer of Given the matrix E \[\mathbf { E...

Question 7

Consider the matrix below.
(a) Determine the order of the matrix.
(b) Determine the order of the matrix and determine if the matrix is a row matrix, a column matrix, a matrix, or none of these.
$$\left[ \begin{array} { c c c } 
- 9 & 3.9 & 8 \
- 8.2 & 7 & - 1 \
7 & 7.7 & - 7
\end{array} \right]$$

Accepted Answer

A)  (a) $1 \times 3$
(b) column matrix 
B)  (a) $3 \times 1$
(b) row matrix 
C)  (a) $3 \times 3$
(b) square matrix 
D)  (a) $3 \times 3$
(b) none of these 
A)  (a) $1 \times 3$
(b) column matrix 
B)  (a) $3 \times 1$
(b) row matrix 
C)  (a) $3 \times 3$
(b) square matrix 
D)  (a) $3 \times 3$
(b) none of these

Question 8

Solve the system by using the Gauss-Jordan method.
$$\begin{aligned}
2 x - 3 y - 9 z & = 12 \
4 x + 5 y - 6 z & = - 14 \
- 5 x + 3 y - 9 z & = 21
\end{aligned}$$

Accepted Answer

A)  $\left( - 6 , - 4 , - \frac { 4 } { 3 } \right)$ 
B)  $\left( - 3 , - 2 , - \frac { 4 } { 3 } \right)$ 
C)  $( - 3,7 , - 5 )$ 
D)  No solution; inconsistent system 
A)  $\left( - 6 , - 4 , - \frac { 4 } { 3 } \right)$ 
B)  $\left( - 3 , - 2 , - \frac { 4 } { 3 } \right)$ 
C)  $( - 3,7 , - 5 )$ 
D)  No solution; inconsistent system

Question 9

Solve the system of equations. $$\begin{aligned}
3 x + 2 z & = - 18 + 5 y \
8 y & = 4 x + 9 y + 6 \
y & = 3 x + 2 z + 10
\end{aligned}$$

Accepted Answer

A)  $( - 2,2 , - 1 )$ 
B)  $( - 2,0 , - 6 )$ 
C)  $( 0,2 , - 4 )$ 
D)  $( - 2,11,7 )$ 
A)  $( - 2,2 , - 1 )$ 
B)  $( - 2,0 , - 6 )$ 
C)  $( 0,2 , - 4 )$ 
D)  $( - 2,11,7 )$

Question 10

Solve the system by the addition method. $$\begin{array} { l } 
\frac { 1 } { 6 } x - \frac { 1 } { 14 } y = 6 \
- \frac { 1 } { 14 } x + \frac { 1 } { 2 } y = 4
\end{array}$$

Accepted Answer

A)  $( 42,14 )$ 
B)  $( - 56,0 )$ 
C)  $( - 42,28 )$ 
D)  $( 0 , - 84 )$ 
A)  $( 42,14 )$ 
B)  $( - 56,0 )$ 
C)  $( - 42,28 )$ 
D)  $( 0 , - 84 )$

Question 11

Solve the system. If there is no unique solution, label the system as either dependent or inconsistent. $$\begin{aligned}
2 x + y + 3 z & = 12 \
x - y + 4 z & = 5 \
- 4 x + 4 y - 4 z & = - 20
\end{aligned}$$

Accepted Answer

A)  $( 4,1,2 )$ 
B)  $( 1,4,2 )$ 
C)  Dependent system (infinitely many solutions) 
D)  Inconsistent system (no solution) 
A)  $( 4,1,2 )$ 
B)  $( 1,4,2 )$ 
C)  Dependent system (infinitely many solutions) 
D)  Inconsistent system (no solution)

Question 12

Solve the system by the addition method. $$\begin{array} { l } 
- 3 x - 4 y = - 21 \
6 x + 8 y = 42
\end{array}$$

Accepted Answer

A)  $( - 1,6 )$ 
B)  $( 2 , - 12 )$ 
C)  Infinitely many solutions; $\left\{ ( x , y ) \mid y = - \frac { 3 } { 4 } x + \frac { 21 } { 4 } \right\}$; dependent system 
D)  No solution; { } ; inconsistent system 
A)  $( - 1,6 )$ 
B)  $( 2 , - 12 )$ 
C)  Infinitely many solutions; $\left\{ ( x , y ) \mid y = - \frac { 3 } { 4 } x + \frac { 21 } { 4 } \right\}$; dependent system 
D)  No solution; { } ; inconsistent system

Question 13

Solve by using the substitution method. $$\begin{array} { l } 
- 5 x - 2 = 13 \
- 4 x + 5 y = 12
\end{array}$$

Accepted Answer

A)  (-3, 0) 
B)  (0, 3) 
C)  (0, -3) 
D)  (3, 0) 
A)  (-3, 0) 
B)  (0, 3) 
C)  (0, -3) 
D)  (3, 0)

Question 14

Solve the system by using the Gauss-Jordan method.
$$\begin{aligned}
- 3 x + y & = - 9 \
- 9 x + 3 y & = 4
\end{aligned}$$

Accepted Answer

A)  $( 1 , - 6 )$ 
B)  $( 0 , - 9 )$ 
C)  No solution; inconsistent system 
D)  Infinitely many solutions; $\{ ( x , y ) \mid y = 3 x - 9 \}$; dependent system 
A)  $( 1 , - 6 )$ 
B)  $( 0 , - 9 )$ 
C)  No solution; inconsistent system 
D)  Infinitely many solutions; $\{ ( x , y ) \mid y = 3 x - 9 \}$; dependent system

Question 15

Suppose Sue has 50 ft of fencing with which she can build a rectangular dog run. Let x represent the length of the dog run and let y represent the width.
a. Write an inequality representing the fact that the total perimeter of the dog run is at most 70 ft.
b. Sketch part of the solution set for this inequality that represents all possible values for the length and width of the dog run. (Hint: Note that both the length and the width must be positive.)

Accepted Answer

The answer of Suppose Sue has 50 ft of fencing...

Question 16

In the next week, Maureen plans to work at most 50 hours, divided between 2 jobs. Let x represent the number of hours spent as a telemarketer, and let y represent the number of hours spent working As a lifeguard. Is the point (19, 14) in the feasible region defining Maureen's work time?

Accepted Answer

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

Question 17

Graph the solution set of the inequality. $$y < - 3 x + 4$$

Accepted Answer

The answer of Graph the solution set of the inequality....

Question 18

Graph the solution set of the inequality. $$0.1 x + 0.5 y \leq 1.5$$

Accepted Answer

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

Question 19

Graph the solution set of the compound inequality. $$2 x - y \leq 2 \text { or } 2 x + 5 y \geq 10$$

Accepted Answer

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

Question 20

A rectangle has the perimeter of 24 inches. The length is 4 in longer than the width. Find the dimensions of the rectangle.

Accepted Answer

A)  2 inches by 6 inches 
B)  7 inches by 11 inches 
C)  5 inches by 9 inches 
D)  4 inches by 8 inches 
A)  2 inches by 6 inches 
B)  7 inches by 11 inches 
C)  5 inches by 9 inches 
D)  4 inches by 8 inches

Graph the solution set of the inequality. $6 y \leq 12 x$

One angle measures 66° more than 2 times another. If the two angles are complementary, find the measures of the angles.

Solve the system of equations. x-4y+5z=-8 2x+5y-3z=-3 3x-5y+3z=-17

Graph the solution set of the inequality. $3 y - 2 x > 10$

Given the matrix E $\mathbf { E } = \left[ \begin{array} { c c | c } 3 & - 2 & 10 \\5 & - 5 & 9\end{array} \right]$ a. What is the element in the second row and third column? b. What is the element in the first row and second column

Consider the matrix below. (a) Determine the order of the matrix. (b) Determine the order of the matrix and determine if the matrix is a row matrix, a column matrix, a matrix, or none of these. $\left[ \begin{array} { c c c } - 9 & 3.9 & 8 \\- 8.2 & 7 & - 1 \\7 & 7.7 & - 7\end{array} \right]$

Solve the system by using the Gauss-Jordan method. 2x-3y-9z =12 4x+5y-6z =-14 -5x+3y-9z =21

Solve the system of equations. 3x+2z =-18+5y 8y =4x+9y+6 y =3x+2z+10

Solve the system by the addition method. x-y=6 -x+y=4

Solve the system. If there is no unique solution, label the system as either dependent or inconsistent. 2x+y+3z =12 x-y+4z =5 -4x+4y-4z =-20

Solve the system by the addition method. -3x-4y=-21 6x+8y=42

Solve by using the substitution method. -5x-2=13 -4x+5y=12

Solve the system by using the Gauss-Jordan method. -3x+y =-9 -9x+3y =4

In the next week, Maureen plans to work at most 50 hours, divided between 2 jobs. Let x represent the number of hours spent as a telemarketer, and let y represent the number of hours spent working As a lifeguard. Is the point (19, 14) in the feasible region defining Maureen's work time?

Graph the solution set of the inequality. $y < - 3 x + 4$

Graph the solution set of the inequality. $0.1 x + 0.5 y \leq 1.5$

Graph the solution set of the compound inequality. $2 x - y \leq 2 \text { or } 2 x + 5 y \geq 10$

A rectangle has the perimeter of 24 inches. The length is 4 in longer than the width. Find the dimensions of the rectangle.

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Exam 3: Systems of Linear Equations and Inequalities

Graph the solution set of the inequality. 6y≤12x6 y \leq 12 x6y≤12x

One angle measures 66° more than 2 times another. If the two angles are complementary, find the measures of the angles.

Solve the system of equations. x-4y+5z=-8 2x+5y-3z=-3 3x-5y+3z=-17

Graph the solution set of the inequality. 3y−2x>103 y - 2 x > 103y−2x>10

Given the matrix E E=[3−2105−59]\mathbf { E } = \left[ \begin{array} { c c | c } 3 & - 2 & 10 \\5 & - 5 & 9\end{array} \right]E=[35​−2−5​109​] a. What is the element in the second row and third column? b. What is the element in the first row and second column

Solve the system by using the Gauss-Jordan method. 2x-3y-9z =12 4x+5y-6z =-14 -5x+3y-9z =21

Solve the system of equations. 3x+2z =-18+5y 8y =4x+9y+6 y =3x+2z+10

Solve the system by the addition method. x-y=6 -x+y=4

Solve the system. If there is no unique solution, label the system as either dependent or inconsistent. 2x+y+3z =12 x-y+4z =5 -4x+4y-4z =-20

Solve the system by the addition method. -3x-4y=-21 6x+8y=42

Solve by using the substitution method. -5x-2=13 -4x+5y=12

Solve the system by using the Gauss-Jordan method. -3x+y =-9 -9x+3y =4

In the next week, Maureen plans to work at most 50 hours, divided between 2 jobs. Let x represent the number of hours spent as a telemarketer, and let y represent the number of hours spent working As a lifeguard. Is the point (19, 14) in the feasible region defining Maureen's work time?

Graph the solution set of the inequality. y<−3x+4y < - 3 x + 4y<−3x+4

Graph the solution set of the inequality. 0.1x+0.5y≤1.50.1 x + 0.5 y \leq 1.50.1x+0.5y≤1.5

Graph the solution set of the compound inequality. 2x−y≤2 or 2x+5y≥102 x - y \leq 2 \text { or } 2 x + 5 y \geq 102x−y≤2 or 2x+5y≥10

A rectangle has the perimeter of 24 inches. The length is 4 in longer than the width. Find the dimensions of the rectangle.

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Graph the solution set of the inequality. $6 y \leq 12 x$

Graph the solution set of the inequality. $3 y - 2 x > 10$

Given the matrix E $\mathbf { E } = \left[ \begin{array} { c c | c } 3 & - 2 & 10 \\5 & - 5 & 9\end{array} \right]$ a. What is the element in the second row and third column? b. What is the element in the first row and second column

Graph the solution set of the inequality. $y < - 3 x + 4$

Graph the solution set of the inequality. $0.1 x + 0.5 y \leq 1.5$

Graph the solution set of the compound inequality. $2 x - y \leq 2 \text { or } 2 x + 5 y \geq 10$