Question 1

Solve the system by the substitution method.
-$$\begin{array} { l } 
y = - ( x + 3 ) ^ { 2 } + 5 \
y = - 2 x - 1
\end{array}$$

Accepted Answer

A)  $\{ ( - 3,5 ) , \{ - 1,1 ) \}$ 
B)  $\{ ( 3,5 ) , \{ - 5,1 ) \}$ 
C)  $\{ ( - 3,5 ) , \{ - 5,1 ) \}$ 
D)  $\{ ( 3,5 ) , \{ - 1,1 ) \}$ 
A)  $\{ ( - 3,5 ) , \{ - 1,1 ) \}$ 
B)  $\{ ( 3,5 ) , \{ - 5,1 ) \}$ 
C)  $\{ ( - 3,5 ) , \{ - 5,1 ) \}$ 
D)  $\{ ( 3,5 ) , \{ - 1,1 ) \}$

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The region in the plane that represents the solution set to a system of constraints is called the________region.

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

Solve the system of equations by using the substitution method.
-$$\begin{array} { l } 
3 ( x + y ) = - 7 - y \
9 x - 1 = 8 + 3 y
\end{array}$$

Accepted Answer

A)  $\left\{ \left( - \frac { 7 } { 3 } , 0 \right) \right\}$ 
B)  $\left\{ \left( - \frac { 7 } { 3 } , - \frac { 1 } { 3 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 1 } { 3 } , - 2 \right) \right\}$ 
D)  $\left\{ \left( 0 , - \frac { 1 } { 3 } \right) \right\}$ 
A)  $\left\{ \left( - \frac { 7 } { 3 } , 0 \right) \right\}$ 
B)  $\left\{ \left( - \frac { 7 } { 3 } , - \frac { 1 } { 3 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 1 } { 3 } , - 2 \right) \right\}$ 
D)  $\left\{ \left( 0 , - \frac { 1 } { 3 } \right) \right\}$

Question 4

Solve the problem.
-An electronic sign for a grocery store is in the shape of a rectangle. The perimeter of the sign is 88 ft and the area is $480 \mathrm { ft } ^ { 2 }$ . Find the length and width of the sign.

Accepted Answer

A)  The sign is 22 ft by 22 ft. 
B)  The sign is 12 ft by 10 ft. 
C)  The sign is 24 ft by 20 ft. 
D)  The sign is 48 ft by 40 ft. 
A)  The sign is 22 ft by 22 ft. 
B)  The sign is 12 ft by 10 ft. 
C)  The sign is 24 ft by 20 ft. 
D)  The sign is 48 ft by 40 ft.

Question 5

Determine the maximum value of the objective function on the given feasible region.
-Maximize: $z = 4 x + 3 y$

Accepted Answer

A)  Maximum value: 26 
B)  Maximum value: 32 
C)  Maximum value: 33 
D)  Maximum value: 38 
A)  Maximum value: 26 
B)  Maximum value: 32 
C)  Maximum value: 33 
D)  Maximum value: 38

Question 6

For parts (a) and (b), write an inequality to represent the given statement.
-Let x represent the number of hours that Emily spends studying algebra, and let y represent the number of hours she spends studying history.
a. Emily will spend no more than 2 hr studying history.
b. The number of hours spent studying algebra cannot be negative.

Accepted Answer

A) a. $x > 2$; b. $y \geq 0$ B) a. $y \leq 2$; b. $x \geq 0$ C) a. $y < 2$; b. $x \geq 0$ D) a. $x \leq 2$; b. $y \geq 0$ A) a. $x > 2$; b. $y \geq 0$ B) a. $y \leq 2$; b. $x \geq 0$ C) a. $y < 2$; b. $x \geq 0$ D) a. $x \leq 2$; b. $y \geq 0$

Question 7

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The process that maximizes or minimizes a function subject to linear constraints is called________programming.

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$$y \leq \sqrt { x - 2 }$$

Accepted Answer

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

Question 9

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.
-$$\begin{array} { l } 
3 x + 1 = 1 - 4 y \
- 2 + 5 ( x + y ) = 4 y - 2
\end{array}$$

Accepted Answer

A)  $\left\{ \left( 1 , - \frac { 3 } { 4 } \right) \right\}$ 
B)  $\{ ( 0,0 ) \}$ 
C) { } ; The system is inconsistent 
D)  $\{ ( x , y ) \mid 3 x = - 4 y \}$; The equations are dependent. 
A)  $\left\{ \left( 1 , - \frac { 3 } { 4 } \right) \right\}$ 
B)  $\{ ( 0,0 ) \}$ 
C) { } ; The system is inconsistent 
D)  $\{ ( x , y ) \mid 3 x = - 4 y \}$; The equations are dependent.

Question 10

Find the partial fraction decomposition.
-$$\frac { 2 x ^ { 2 } - 6 x - 12 } { 3 x ^ { 3 } + 9 x }$$

Accepted Answer

A)  $\frac { - 4 } { 3 x } + \frac { 2 x } { x ^ { 2 } + 3 }$ 
B)  $\frac { - 4 } { 3 x } + \frac { 2 x - 2 } { x ^ { 2 } + 3 }$ 
C)  $\frac { - 4 } { x } + \frac { 2 x } { x ^ { 2 } + 3 }$ 
D)  $\frac { - 4 } { x } + \frac { 2 x - 2 } { x ^ { 2 } + 3 }$ 
A)  $\frac { - 4 } { 3 x } + \frac { 2 x } { x ^ { 2 } + 3 }$ 
B)  $\frac { - 4 } { 3 x } + \frac { 2 x - 2 } { x ^ { 2 } + 3 }$ 
C)  $\frac { - 4 } { x } + \frac { 2 x } { x ^ { 2 } + 3 }$ 
D)  $\frac { - 4 } { x } + \frac { 2 x - 2 } { x ^ { 2 } + 3 }$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-When setting up a partial fraction decomposition, if the denominator is a quadratic polynomial
irreducible over the integers, then the numerator should be (constant/linear). That is, should the
numerator be set up as A or Ax + B?

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$$- \frac { 1 } { 2 } y - 2 \leq - 3$$

Accepted Answer

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

Question 13

Solve the problem.
-The motion of an object traveling along a straight path is given by $s ( t ) = \frac { 1 } { 2 } a t ^ { 2 } + v _ { 0 } t + s _ { 0 }$, where $s ( t )$ is the position relative to the origin at time $t$. Three observed data points are given. Find the values of $a , v _ { 0 }$, and $s _ { 0 }$.
$$s ( 1 ) = 19 , s ( 3 ) = 87 , s ( 5 ) = 171$$

Accepted Answer

A)  $a = 2 , v _ { 0 } = 87 , s _ { 0 } = - 9$ 
B)  $a = 4 , v _ { 0 } = 26 , s _ { 0 } = - 9$ 
C)  $a = 4 , v _ { 0 } = 87 , s _ { 0 } = 171$ 
D)  $a = 2 , v _ { 0 } = 26 , s _ { 0 } = 171$ 
A)  $a = 2 , v _ { 0 } = 87 , s _ { 0 } = - 9$ 
B)  $a = 4 , v _ { 0 } = 26 , s _ { 0 } = - 9$ 
C)  $a = 4 , v _ { 0 } = 87 , s _ { 0 } = 171$ 
D)  $a = 2 , v _ { 0 } = 26 , s _ { 0 } = 171$

Question 14

Solve the problem.
-Franco borrows a total of $\$ 5,000$ in student loan from two lenders. One charges $4.1 \%$ simple interest and the other charges $6.1 \%$ simple interest. He is not required to pay off the principal for $3 \mathrm { yr }$.
However, at the end of $3 \mathrm { yr }$, he will owe a total of $\$ 825.00$ for interest from both loans. How much did he borrow from each lender?

Accepted Answer

A)  She borrowed $\$ 3,900$ at $4.1 \%$ and $\$ 1,100$ at $6.1 \%$. 
B)  She borrowed $\$ 1,100$ at $4.1 \%$ and $\$ 3,900$ at $6.1 \%$. 
C)  She borrowed $\$ 1,500$ at $4.1 \%$ and $\$ 3,500$ at $6.1 \%$. 
D)  She borrowed $\$ 3,500$ at $4.1 \%$ and $\$ 1,500$ at $6.1 \%$. 
A)  She borrowed $\$ 3,900$ at $4.1 \%$ and $\$ 1,100$ at $6.1 \%$. 
B)  She borrowed $\$ 1,100$ at $4.1 \%$ and $\$ 3,900$ at $6.1 \%$. 
C)  She borrowed $\$ 1,500$ at $4.1 \%$ and $\$ 3,500$ at $6.1 \%$. 
D)  She borrowed $\$ 3,500$ at $4.1 \%$ and $\$ 1,500$ at $6.1 \%$.

Question 15

Solve the problem.
-Abram and Fred leave opposite ends of a bike trail 8.5 miles apart and travel toward each other. Abram is traveling 3 mph faster than Fred. Find each of their speeds if they meet after 30 minutes.

Accepted Answer

A)  Abram: 17 mph; Fred: 20 mph 
B)  Abram: 10 mph; Fred: 7 mph 
C)  Abram: 7 mph; Fred: 10 mph 
D)  Abram: 20 mph; Fred: 17 mph 
A)  Abram: 17 mph; Fred: 20 mph 
B)  Abram: 10 mph; Fred: 7 mph 
C)  Abram: 7 mph; Fred: 10 mph 
D)  Abram: 20 mph; Fred: 17 mph

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given the inequality $$y \leq 2 x + 1$$ + 1, the bounding line y = 2x + 1 is drawn as a (dashed/solid) line.

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

Solve the problem.
-Find the area of the triangle bounded by the lines $$y = x + 2 , y = - \frac { 1 } { 6 } x + 2$$ , and the x-axis.

Accepted Answer

A)  4 square units 
B)  2 square units 
C)  28 square units 
D)  14 square units 
A)  4 square units 
B)  2 square units 
C)  28 square units 
D)  14 square units

Question 18

Solve the system by the substitution method.
-$$\begin{array} { l } 
x ^ { 2 } + ( y - 7 ) ^ { 2 } = 4 \
y = x + 3
\end{array}$$

Accepted Answer

A)  $\{ ( 2,5 ) , ( - 2 , - 5 ) \}$ 
B)  { } 
C)  $\{ ( 2 \sqrt { 2 } , 7 + 2 \sqrt { 2 } ) , ( - 2 \sqrt { 2 } , 7 - 2 \sqrt { 2 } )$ 
D)  $\{ ( 2,5 ) \}$ 
A)  $\{ ( 2,5 ) , ( - 2 , - 5 ) \}$ 
B)  { } 
C)  $\{ ( 2 \sqrt { 2 } , 7 + 2 \sqrt { 2 } ) , ( - 2 \sqrt { 2 } , 7 - 2 \sqrt { 2 } )$ 
D)  $\{ ( 2,5 ) \}$

Question 19

For parts (a) and (b), write an inequality to represent the given statement.
-Let x represent the number of hours that Trenton spends studying algebra, and let y represent the number of hours he spends studying history.
a. Trenton has a total of at most 12 hr to study for both algebra and history combined.
b. Trenton will spend at least 5 hr studying algebra.

Accepted Answer

A)  a. $x + y \leq 12$;
b. $x \leq 5$ 
B)  a. $x + y \geq 12$;
b. $x \leq 5$ 
C)  a. $x + y \geq 12$;
b. $x \geq 5$ 
D)  a. $x + y \leq 12$;
b. $x \geq 5$ 
A)  a. $x + y \leq 12$;
b. $x \leq 5$ 
B)  a. $x + y \geq 12$;
b. $x \leq 5$ 
C)  a. $x + y \geq 12$;
b. $x \geq 5$ 
D)  a. $x + y \leq 12$;
b. $x \geq 5$

Question 20

Solve the problem.
-A helicopter flies 168 miles against the wind in 2 hours; with the wind, it can fly 252 miles in the same amount of time. Find the speed of the helicopter in still air.

Accepted Answer

A)  21 miles per hour 
B)  63 miles per hour 
C)  105 miles per hour 
D)  84 miles per hour 
A)  21 miles per hour 
B)  63 miles per hour 
C)  105 miles per hour 
D)  84 miles per hour

Solve the system by the substitution method. - y=-(x+3+5 y=-2x-1

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The region in the plane that represents the solution set to a system of constraints is called the________region.

Solve the system of equations by using the substitution method. - 3(x+y)=-7-y 9x-1=8+3y

Solve the problem. -An electronic sign for a grocery store is in the shape of a rectangle. The perimeter of the sign is 88 ft and the area is $480 \mathrm { ft } ^ { 2 }$ . Find the length and width of the sign.

Determine the maximum value of the objective function on the given feasible region. -Maximize: $z = 4 x + 3 y$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The process that maximizes or minimizes a function subject to linear constraints is called________programming.

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $y \leq \sqrt { x - 2 }$

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - 3x+1=1-4y -2+5(x+y)=4y-2

Find the partial fraction decomposition. - $\frac { 2 x ^ { 2 } - 6 x - 12 } { 3 x ^ { 3 } + 9 x }$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- \frac { 1 } { 2 } y - 2 \leq - 3$

Solve the problem. -Abram and Fred leave opposite ends of a bike trail 8.5 miles apart and travel toward each other. Abram is traveling 3 mph faster than Fred. Find each of their speeds if they meet after 30 minutes.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given the inequality $y \leq 2 x + 1$ + 1, the bounding line y = 2x + 1 is drawn as a (dashed/solid) line.

Solve the problem. -Find the area of the triangle bounded by the lines $y = x + 2 , y = - \frac { 1 } { 6 } x + 2$ , and the x-axis.

Solve the system by the substitution method. - +(y-7=4 y=x+3

Solve the problem. -A helicopter flies 168 miles against the wind in 2 hours; with the wind, it can fly 252 miles in the same amount of time. Find the speed of the helicopter in still air.

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 5: Systems of Equations and Inequalities

Solve the system by the substitution method. - y=-(x+3+5 y=-2x-1

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The region in the plane that represents the solution set to a system of constraints is called the________region.

Solve the system of equations by using the substitution method. - 3(x+y)=-7-y 9x-1=8+3y

Solve the problem. -An electronic sign for a grocery store is in the shape of a rectangle. The perimeter of the sign is 88 ft and the area is 480ft2480 \mathrm { ft } ^ { 2 }480ft2 . Find the length and width of the sign.

Determine the maximum value of the objective function on the given feasible region. -Maximize: z=4x+3yz = 4 x + 3 yz=4x+3y

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The process that maximizes or minimizes a function subject to linear constraints is called________programming.

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - y≤x−2y \leq \sqrt { x - 2 }y≤x−2​

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - 3x+1=1-4y -2+5(x+y)=4y-2

Find the partial fraction decomposition. - 2x2−6x−123x3+9x\frac { 2 x ^ { 2 } - 6 x - 12 } { 3 x ^ { 3 } + 9 x }3x3+9x2x2−6x−12​

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - −12y−2≤−3- \frac { 1 } { 2 } y - 2 \leq - 3−21​y−2≤−3

Solve the problem. -Abram and Fred leave opposite ends of a bike trail 8.5 miles apart and travel toward each other. Abram is traveling 3 mph faster than Fred. Find each of their speeds if they meet after 30 minutes.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given the inequality y≤2x+1y \leq 2 x + 1y≤2x+1 + 1, the bounding line y = 2x + 1 is drawn as a (dashed/solid) line.

Solve the problem. -Find the area of the triangle bounded by the lines y=x+2,y=−16x+2y = x + 2 , y = - \frac { 1 } { 6 } x + 2y=x+2,y=−61​x+2 , and the x-axis.

Solve the system by the substitution method. - +(y-7=4 y=x+3

Solve the problem. -A helicopter flies 168 miles against the wind in 2 hours; with the wind, it can fly 252 miles in the same amount of time. Find the speed of the helicopter in still air.

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Solve the problem. -An electronic sign for a grocery store is in the shape of a rectangle. The perimeter of the sign is 88 ft and the area is $480 \mathrm { ft } ^ { 2 }$ . Find the length and width of the sign.

Determine the maximum value of the objective function on the given feasible region. -Maximize: $z = 4 x + 3 y$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $y \leq \sqrt { x - 2 }$

Find the partial fraction decomposition. - $\frac { 2 x ^ { 2 } - 6 x - 12 } { 3 x ^ { 3 } + 9 x }$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- \frac { 1 } { 2 } y - 2 \leq - 3$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given the inequality $y \leq 2 x + 1$ + 1, the bounding line y = 2x + 1 is drawn as a (dashed/solid) line.

Solve the problem. -Find the area of the triangle bounded by the lines $y = x + 2 , y = - \frac { 1 } { 6 } x + 2$ , and the x-axis.