Question 1

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor
-$$\frac { 2 x - 5 } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$$

Accepted Answer

A)  $\frac { A x + B } { x ^ { 2 } + x + 6 } + \frac { C x + D } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$ 
B)  $\frac { A } { x ^ { 2 } + x + 6 } + \frac { B x + C } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$ 
C)  $\frac { A } { x ^ { 2 } + x + 6 } + \frac { B } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$ 
D)  $\frac { A x + B } { x ^ { 2 } + x + 6 } + \frac { C } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$ 
A)  $\frac { A x + B } { x ^ { 2 } + x + 6 } + \frac { C x + D } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$ 
B)  $\frac { A } { x ^ { 2 } + x + 6 } + \frac { B x + C } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$ 
C)  $\frac { A } { x ^ { 2 } + x + 6 } + \frac { B } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$ 
D)  $\frac { A x + B } { x ^ { 2 } + x + 6 } + \frac { C } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$

Question 2

Solve Problems Using Systems of Linear Equations
-A twin-engined aircraft can fly 1330 miles from city A to city B in 5 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

Accepted Answer

A)  $38 \mathrm { mph }$ 
B)  $19 \mathrm { mph }$ 
C)  $57 \mathrm { mph }$ 
D)  $76 \mathrm { mph }$ 
A)  $38 \mathrm { mph }$ 
B)  $19 \mathrm { mph }$ 
C)  $57 \mathrm { mph }$ 
D)  $76 \mathrm { mph }$

Question 3

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$\begin{array}{l}
y \geq 2 x-4 \
x+2 y \leq 7 \
x \geq-2 \
y \leq 1
\end{array}$

Accepted Answer

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

Question 4

Use Linear Programming to Solve Problems
-Objective Function: $z = 4 x + 8 y$
Find maximum and minimum.

Accepted Answer

A)  maximum value: 104 ; minimum value: 8 
B)  maximum value: 104 ; minimum value: 16 
C)  maximum value: 56 ; minimum value: 8 
D)  maximum value: 56; minimum value: 16 Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points. $$\overbrace { ( 3,3 ) } ^ { ( 2,5 ) }$$ 
A)  maximum value: 104 ; minimum value: 8 
B)  maximum value: 104 ; minimum value: 16 
C)  maximum value: 56 ; minimum value: 8 
D)  maximum value: 56; minimum value: 16 Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points. $$\overbrace { ( 3,3 ) } ^ { ( 2,5 ) }$$

Question 5

Solve Problems Using Systems of Linear Equations
-The Family Fine Arts Center charges $\$ 25$ per adult and $\$ 15$ per senior citizen for its performances. On a recent weekend evening when 502 people paid admission, the total receipts were $\$ 9330$. How many who paid were senior citizens?

Accepted Answer

A)  322 senior citizens 
B)  180 senior citizens 
C)  232 senior citizens 
D)  270 senior citizens 
A)  322 senior citizens 
B)  180 senior citizens 
C)  232 senior citizens 
D)  270 senior citizens

Question 6

Graph a Nonlinear Inequality in Two Variables
-$x^{2}+y^{2} \leq 9$

Accepted Answer

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

Question 7

Use Mathematical Models Involving Linear Inequalities
-The equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2P + 3F ≤ 23, where P is the number of police cars on active duty and F is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation 2P + F ≤ 17 is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so P ≥ 0 and F ≥ 0. Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for P and the vertical axis for F. If 3 police cars are on active duty and 6 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied?

Accepted Answer

A)  No
  
B)  Yes
  
C)  No
  
D)  Yes
  
A)  No
  
B)  Yes
  
C)  No
  
D)  Yes

Question 8

Solve Problems Using Systems of Linear Equations
-An-Mei owns a business making and selling jackets. She has a fixed cost of $\$ 1440$. It costs $\$ 87$ to produce each jacket. The selling price is $\$ 99$ per jacket. Determine the number of jackets that must be made and sold in order to break even.

Accepted Answer

A)  120 units 
B)  121 units 
C)  122 units 
D)  13 units 
A)  120 units 
B)  121 units 
C)  122 units 
D)  13 units

Question 9

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
x ^ { 2 } - 2 y ^ { 2 } = 2 \
3 x ^ { 2 } + 2 y ^ { 2 } = 14
\end{array}$$

Accepted Answer

A)  $\{ ( 2,1 ) , ( 2 , - 1 ) , ( - 2,1 ) , ( - 2 , - 1 ) \}$ 
B)  $\{ ( 1,2 ) , ( - 1,2 ) , ( 1 , - 2 ) , ( - 1 , - 2 ) \}$ 
C)  $\{ ( 2,1 ) , ( - 2 , - 1 ) \}$ 
D)  $\{ ( - 1,2 ) , ( 1 , - 2 ) \}$ 
A)  $\{ ( 2,1 ) , ( 2 , - 1 ) , ( - 2,1 ) , ( - 2 , - 1 ) \}$ 
B)  $\{ ( 1,2 ) , ( - 1,2 ) , ( 1 , - 2 ) , ( - 1 , - 2 ) \}$ 
C)  $\{ ( 2,1 ) , ( - 2 , - 1 ) \}$ 
D)  $\{ ( - 1,2 ) , ( 1 , - 2 ) \}$

Question 10

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 16 \
x ^ { 2 } - y ^ { 2 } = 16
\end{array}$$

Accepted Answer

A)  $\{ ( 4,0 ) , ( - 4,0 ) \}$ 
B)  $\{ ( 0,4 ) , ( 0 , - 4 ) \}$ 
C)  $\{ ( 4,0 ) \}$ 
D)  $\{ ( 0,4 ) \}$ 
A)  $\{ ( 4,0 ) , ( - 4,0 ) \}$ 
B)  $\{ ( 0,4 ) , ( 0 , - 4 ) \}$ 
C)  $\{ ( 4,0 ) \}$ 
D)  $\{ ( 0,4 ) \}$

Question 11

Determine whether the given ordered pair is a solution of the system.
-$$\begin{array} { l } 
( 1 , - 2 ) \
x + y = - 1 \
x - y = 3
\end{array}$$

Accepted Answer

A)  solution 
B)  not a solution 
A)  solution 
B)  not a solution

Question 12

Decompose P/Q, Where Q Has Repeated Linear Factors
-$$\frac { 4 x - 2 } { ( x + 1 ) ^ { 2 } }$$

Accepted Answer

A)  $\frac { \mathrm { A } } { \mathrm { x } + 1 } + \frac { \mathrm { B } } { ( \mathrm { x } + 1 ) ^ { 2 } }$ 
B)  $\frac { A } { x + 1 } + \frac { B x + C } { ( x + 1 ) ^ { 2 } }$ 
C)  $\frac { \mathrm { A } } { \mathrm { x } + 1 } + \frac { \mathrm { B } } { \mathrm { x } + 1 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 1 ) ^ { 2 } }$ 
D)  $\frac { A } { x + 1 } + \frac { B } { x + 1 } + \frac { C } { ( x + 1 ) ^ { 2 } }$ 
A)  $\frac { \mathrm { A } } { \mathrm { x } + 1 } + \frac { \mathrm { B } } { ( \mathrm { x } + 1 ) ^ { 2 } }$ 
B)  $\frac { A } { x + 1 } + \frac { B x + C } { ( x + 1 ) ^ { 2 } }$ 
C)  $\frac { \mathrm { A } } { \mathrm { x } + 1 } + \frac { \mathrm { B } } { \mathrm { x } + 1 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 1 ) ^ { 2 } }$ 
D)  $\frac { A } { x + 1 } + \frac { B } { x + 1 } + \frac { C } { ( x + 1 ) ^ { 2 } }$

Question 13

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$\begin{array}{l}
x^{2}+y^{2} \leq 36 \
-5 x+2 y \leq-10
\end{array}$

Accepted Answer

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

Question 14

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$\begin{array}{r}
2 x+3 y \geq 6 \
x-y \leq 3 \
y \leq 2
\end{array}$

Accepted Answer

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

Question 15

Determine whether the given ordered pair is a solution of the system.
-$$\begin{array} { l } 
( 2 , - 4 ) \
4 x = 4 - y \
2 x = - 12 - 4 y
\end{array}$$

Accepted Answer

A)  solution 
B)  not a solution 
A)  solution 
B)  not a solution

Question 16

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$\begin{array}{l}
y \geq 1 \
2 \leq x \leq 6 \
x-2 y \geq-2 \
x+y \leq 6
\end{array}$

Accepted Answer

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

Question 17

Solve Problems Using Systems of Linear Equations
-One number is 3 less than a second number. Twice the second number is 18 less than 5 times the first. Find the two numbers.

Accepted Answer

A)  8 and 11 
B)  7 and 10 
C)  9 and 12 
D)  $- 11$ and $- 8$ 
A)  8 and 11 
B)  7 and 10 
C)  9 and 12 
D)  $- 11$ and $- 8$

Question 18

Solve Problems Using Systems in Three Variables
-A deli sells three sizes of roast beef sandwiches: the small roast beef sandwich contains 6 ounces of meat and sells for $3.50; the regular roast beef sandwich contains 9 ounces of meat and sells for $4.00; and the large roast beef sandwich contains 13 ounces of meat and sells for $4.50. A customer requests a selection of each size for a reception. She and the manager agree on a combination of 42 sandwiches made from 23 pounds 10 ounces of roast beef for a total cost of $164. How many of each size sandwich will be in this combination? (Note: 1 pound = 16 ounces)

Accepted Answer

A)  16 small sandwiches, 18 medium sandwiches, 8 large sandwiches. 
B)  18 small sandwiches, 12 medium sandwiches, 12 large sandwiches. 
C)  12 small sandwiches, 14 medium sandwiches, 16 large sandwiches. 
D)  14 small sandwiches, 24 medium sandwiches, 4 large sandwiches. 
A)  16 small sandwiches, 18 medium sandwiches, 8 large sandwiches. 
B)  18 small sandwiches, 12 medium sandwiches, 12 large sandwiches. 
C)  12 small sandwiches, 14 medium sandwiches, 16 large sandwiches. 
D)  14 small sandwiches, 24 medium sandwiches, 4 large sandwiches.

Question 19

Solve Problems Using Systems in Three Variables
-A basketball player scored 27 points in a game. The number of three-point field goals the player made was 25 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals the player made was 10 more than the number of three-point field goals made. Find the number of free-throws, two-point field goals, and three-point field goals that the player made in the game.

Accepted Answer

A)  9 free throws; 6 two-point field goals; 2 three-point field goals 
B)  10 free throws; 6 two-point field goals; 5 three-point field goals 
C)  9 free throws; 7 two-point field goals; 4 three-point field goals 
D)  9 free throws; 2 two-point field goals; 6 three-point field goals 
A)  9 free throws; 6 two-point field goals; 2 three-point field goals 
B)  10 free throws; 6 two-point field goals; 5 three-point field goals 
C)  9 free throws; 7 two-point field goals; 4 three-point field goals 
D)  9 free throws; 2 two-point field goals; 6 three-point field goals

Question 20

Graph the inequality.
-$x-y>-4$

Accepted Answer

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

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor - $\frac { 2 x - 5 } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$

Solve Problems Using Systems of Linear Equations -A twin-engined aircraft can fly 1330 miles from city A to city B in 5 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

Use Linear Programming to Solve Problems -Objective Function: $z = 4 x + 8 y$ Find maximum and minimum.

Solve Problems Using Systems of Linear Equations -The Family Fine Arts Center charges $\$ 25$ per adult and $\$ 15$ per senior citizen for its performances. On a recent weekend evening when 502 people paid admission, the total receipts were $\$ 9330$ . How many who paid were senior citizens?

Graph a Nonlinear Inequality in Two Variables - $x^{2}+y^{2} \leq 9$ $Graph a Nonlinear Inequality in Two Variables - x^{2}+y^{2} \leq 9$

Solve Nonlinear Systems By Addition - -2=2 3+2=14

Solve Nonlinear Systems By Addition - +=16 -=16

Determine whether the given ordered pair is a solution of the system. - (1,-2) x+y=-1 x-y=3

Decompose P/Q, Where Q Has Repeated Linear Factors - $\frac { 4 x - 2 } { ( x + 1 ) ^ { 2 } }$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - +\leq36 -5x+2y\leq-10 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{l} x^{2}+y^{2} \leq 36 \\ -5 x+2 y \leq-10 \end{array}$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 2x+3y\geq6 x-y\leq3 y\leq2 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{r} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ y \leq 2 \end{array}$

Determine whether the given ordered pair is a solution of the system. - (2,-4) 4x=4-y 2x=-12-4y

Solve Problems Using Systems of Linear Equations -One number is 3 less than a second number. Twice the second number is 18 less than 5 times the first. Find the two numbers.

Graph the inequality. - $x-y>-4$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 8: Systems of Equations and Inequalities

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor - 2x−5(x2+x+6)2\frac { 2 x - 5 } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }(x2+x+6)22x−5​

Solve Problems Using Systems of Linear Equations -A twin-engined aircraft can fly 1330 miles from city A to city B in 5 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y\geq2x-4 x+2y\leq7 x\geq-2 y\leq1

Use Linear Programming to Solve Problems -Objective Function: z=4x+8yz = 4 x + 8 yz=4x+8y Find maximum and minimum.

Graph a Nonlinear Inequality in Two Variables - x2+y2≤9x^{2}+y^{2} \leq 9x2+y2≤9

Solve Nonlinear Systems By Addition - -2=2 3+2=14

Solve Nonlinear Systems By Addition - +=16 -=16

Determine whether the given ordered pair is a solution of the system. - (1,-2) x+y=-1 x-y=3

Decompose P/Q, Where Q Has Repeated Linear Factors - 4x−2(x+1)2\frac { 4 x - 2 } { ( x + 1 ) ^ { 2 } }(x+1)24x−2​

Graph the solution set of the system of inequalities or indicate that the system has no solution. - +\leq36 -5x+2y\leq-10

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 2x+3y\geq6 x-y\leq3 y\leq2

Determine whether the given ordered pair is a solution of the system. - (2,-4) 4x=4-y 2x=-12-4y

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y\geq1 2\leqx\leq6 x-2y\geq-2 x+y\leq6

Solve Problems Using Systems of Linear Equations -One number is 3 less than a second number. Twice the second number is 18 less than 5 times the first. Find the two numbers.

Graph the inequality. - x−y>−4x-y>-4x−y>−4

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor - $\frac { 2 x - 5 } { \left( x ^ { 2 } + x + 6 \right) ^ { 2 } }$

Use Linear Programming to Solve Problems -Objective Function: $z = 4 x + 8 y$ Find maximum and minimum.

Graph a Nonlinear Inequality in Two Variables - $x^{2}+y^{2} \leq 9$ $Graph a Nonlinear Inequality in Two Variables - x^{2}+y^{2} \leq 9$

Decompose P/Q, Where Q Has Repeated Linear Factors - $\frac { 4 x - 2 } { ( x + 1 ) ^ { 2 } }$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - +\leq36 -5x+2y\leq-10 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{l} x^{2}+y^{2} \leq 36 \\ -5 x+2 y \leq-10 \end{array}$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 2x+3y\geq6 x-y\leq3 y\leq2 $Graph the solution set of the system of inequalities or indicate that the system has no solution. - \begin{array}{r} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ y \leq 2 \end{array}$

Graph the inequality. - $x-y>-4$