Question 1

The temperature T of a gas sample varies jointly as the pressure P and the volume V. If the temperature is 297 kelvin when the volume is 4.6 liters and the pressure is 1.2 atmospheres, then what is its temperature if the gas is compressed to 1.5 liters at 2.9 atmospheres? Round your answer to the nearest tenth of a kelvin. [The unit "kelvin" is simply a temperature unit related to the Celsius degree. The exact relationship between the two plays no part in the solution of this problem.]

Accepted Answer

A)   230.8 kelvin
B)   234.0 kelvin
C)   198.9 kelvin
D)   242.9 kelvin B

Question 2

Does the point (-15, 15) satisfy the inequality y F1F1F1S1F1F1F10 -12x + 8?

Accepted Answer

A)   Yes
B)   No B

Question 3

Sarah has 12 coins (nickels, dimes, and quarters) in her piggy bank with a total value of $1.65. There are 2 more dimes than nickels. How many of each type of coin does Sarah have?

Accepted Answer

A)   2 nickels, 8 dimes, and 3 quarters
B)   3 nickels, 5 dimes, and 4 quarters
C)   0 nickels, 4 dimes, and 5 quarters
D)   4 nickels, 7 dimes, and 3 quarters B

Question 4

Liam invested some money in the Abernathy Fund at 5% simple interest and twice as much at twice the rate in the Carlson Fund. If the simple-interest income from the two funds totalled $3055.75, then how much was invested in each fund?

Accepted Answer

A)   $13,723 in Abernathy and $27,446 in Carlson
B)   $14,323 in Abernathy and $28,646 in Carlson
C)   $10,723 in Abernathy and $21,446 in Carlson
D)   $12,223 in Abernathy and $24,446 in Carlson

Question 5

Factor the given polynomial completely. If the polynomial is prime, say so. y3 - 8y2 - 9y + 72

Accepted Answer

A)   y(y + 3) (y - 8) 
B)   (y - 3) (y + 3) (y - 8) 
C)   The polynomial is prime.
D)   (y - 3) 2(y - 8)

Question 6

Simplify.

Accepted Answer

A)   
B)   
C)   
D)

Question 7

Solve the system of equations. 0.25x + 3.5y = -3.6875
-1)4x - 2.5y = 3.55

Accepted Answer

A)   {(-0.75, -1) }
B)   {(0.75, -1) }
C)   {(-0.25, -0.5) }
D)   {(0.75, 1) }

Question 8

Simplify: r - 0.1(r + 400)

Accepted Answer

A)   0.9r - 40
B)   1.1r + 40
C)   1.1r - 40
D)   0.9r + 40

Question 9

Simplify.

Accepted Answer

A)   
B)   
C)   
D)

Question 10

Solve and write your answer in interval notation. p - 3 < 3p - 13

Accepted Answer

A)   (-∞, 3) 
B)   (6, ∞) 
C)   (5, ∞) 
D)   (3, ∞)

Question 11

Simplify.

Accepted Answer

A)   3z3 
C)     
D)    " class="answers-bank-image d-inline" rel="preload" >
B)   -4x3z3
C)   3z3 
C)     
D)    " class="answers-bank-image d-inline" rel="preload" >
D)   3z3 
C)     
D)    " class="answers-bank-image d-inline" rel="preload" >

Question 12

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 8x - x = 7x

Accepted Answer

A)   All real numbers, identity
B)   {1}, conditional
C)   Ø, inconsistent

Question 13

Factor the given polynomial completely. If the polynomial is prime, say so. 15z2 - 11z + 2

Accepted Answer

A)   (15z - 2) (z - 1) 
B)   The polynomial is prime.
C)   (5z - 2) (3z - 1) 
D)   (5z + 2) (3z - 1)

Question 14

Find the product. (3b + 5)(b + 6)

Accepted Answer

A)   b2 + 23b + 30
B)   3b2 + 23b + 30
C)   3b2 + 11b + 30
D)   b2 + 9b + 18

Question 15

Perform the indicated operation. (p2 - p - 1) - (p2 + 4p + 5)

Accepted Answer

A)   -5p + 4
B)   2p2 - 5p - 6
C)   -5p + 6
D)   -5p - 6

Question 16

A triangle has sides of length x inches, x + 1 inches, and x + 2 inches and its perimeter is given by x + (x + 1) + (x + 2) = 12 inches. Find the measures of the sides by solving the perimeter equation.

Accepted Answer

A)   3 inches, 5 inches, 7 inches
B)   3 inches, 3 inches, 3 inches
C)   4 inches, 5 inches, 6 inches
D)   3 inches, 4 inches, 5 inches

Question 17

Frank rides his bike 10 mph faster than he walks. He can bike from home to work in the same amount of time that it takes him to walk from home to the park. If the distance from Frank's home to work is 6 miles and the distance from his home to the park is 2 miles, what is Frank's walking speed?

Accepted Answer

A)   7 mph
B)   6 mph
C)   6.5 mph
D)   5 mph

Question 18

Evaluate: -5 + 75 F1F1F1S1F1F1F10 52

Accepted Answer

A)   220
B)    52 
A)   220 
B)     
C)   -4 
D)   -2" class="answers-bank-image d-inline" rel="preload" >
C)   -4
D)   -2

Question 19

Factor. 64x3 + 1

Accepted Answer

A)   The expression is prime.
B)   (4x + 1) (16x2 + 4x - 1) 
C)   (4x - 1) (16x2 + 4x + 1) 
D)   (4x + 1) (16x2 - 4x + 1)

Question 20

Determine whether 13 is a solution of -3x - 15 = -24.

Accepted Answer

A)   No
B)   Yes

Exam 16: Algebraic Equations and Problem Solving

Does the point (-15, 15) satisfy the inequality y  -12x + 8?

Sarah has 12 coins (nickels, dimes, and quarters) in her piggy bank with a total value of $1.65. There are 2 more dimes than nickels. How many of each type of coin does Sarah have?

Liam invested some money in the Abernathy Fund at 5% simple interest and twice as much at twice the rate in the Carlson Fund. If the simple-interest income from the two funds totalled $3055.75, then how much was invested in each fund?

Factor the given polynomial completely. If the polynomial is prime, say so. y³- 8y² - 9y + 72

Simplify.

Solve the system of equations. 0.25x + 3.5y = -3.6875 -1) 4x - 2.5y = 3.55

Simplify: r - 0.1(r + 400)

Simplify.

Solve and write your answer in interval notation. p - 3 < 3p - 13

Simplify.

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 8x - x = 7x

Factor the given polynomial completely. If the polynomial is prime, say so. 15z² - 11z + 2

Find the product. (3b + 5) (b + 6)

Perform the indicated operation. (p² - p - 1) - (p² + 4p + 5)

A triangle has sides of length x inches, x + 1 inches, and x + 2 inches and its perimeter is given by x + (x + 1) + (x + 2) = 12 inches. Find the measures of the sides by solving the perimeter equation.

Frank rides his bike 10 mph faster than he walks. He can bike from home to work in the same amount of time that it takes him to walk from home to the park. If the distance from Frank's home to work is 6 miles and the distance from his home to the park is 2 miles, what is Frank's walking speed?

Evaluate: -5 + 75  5²

Factor. 64x³ + 1

Determine whether 13 is a solution of -3x - 15 = -24.

Exam 16: Algebraic Equations and Problem Solving

Does the point (-15, 15) satisfy the inequality y  -12x + 8?

Sarah has 12 coins (nickels, dimes, and quarters) in her piggy bank with a total value of $1.65. There are 2 more dimes than nickels. How many of each type of coin does Sarah have?

Liam invested some money in the Abernathy Fund at 5% simple interest and twice as much at twice the rate in the Carlson Fund. If the simple-interest income from the two funds totalled $3055.75, then how much was invested in each fund?

Factor the given polynomial completely. If the polynomial is prime, say so. y3 - 8y2 - 9y + 72

Simplify.

Solve the system of equations. 0.25x + 3.5y = -3.6875 -1) 4x - 2.5y = 3.55

Simplify: r - 0.1(r + 400)

Simplify.

Solve and write your answer in interval notation. p - 3 < 3p - 13

Simplify.

Solve the given equation and identify it as a conditional equation, an inconsistent equation, or an identity. 8x - x = 7x

Factor the given polynomial completely. If the polynomial is prime, say so. 15z2 - 11z + 2

Find the product. (3b + 5) (b + 6)

Perform the indicated operation. (p2 - p - 1) - (p2 + 4p + 5)

A triangle has sides of length x inches, x + 1 inches, and x + 2 inches and its perimeter is given by x + (x + 1) + (x + 2) = 12 inches. Find the measures of the sides by solving the perimeter equation.

Frank rides his bike 10 mph faster than he walks. He can bike from home to work in the same amount of time that it takes him to walk from home to the park. If the distance from Frank's home to work is 6 miles and the distance from his home to the park is 2 miles, what is Frank's walking speed?

Evaluate: -5 + 75  52

Factor. 64x3 + 1

Determine whether 13 is a solution of -3x - 15 = -24.

Factor the given polynomial completely. If the polynomial is prime, say so. y³- 8y² - 9y + 72

Factor the given polynomial completely. If the polynomial is prime, say so. 15z² - 11z + 2

Perform the indicated operation. (p² - p - 1) - (p² + 4p + 5)

Evaluate: -5 + 75  5²

Factor. 64x³ + 1