Deck 16: Algebraic Equations and Problem Solving

Question 1

Simplify.

A)
B) -4x³z³
C)
D)

Answer 1

Question 2

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

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

Answer 2

(5z - 2)(3z - 1)

Question 3

Perform the indicated operations and write your result in lowest terms.

A)
B)
C)
D)

Answer 3

Question 4

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

A) No
B) Yes

Question 5

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

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

Question 6

Simplify.

A)
B)
C)
D)

Question 7

Factor. 64x³ + 1

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

Question 8

Solve the given equation. x² + 10x + 24 = 0

A) 4, -6
B) -4, 6
C) -4, -6
D) 4, 6

Question 9

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.

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 10

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?

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 11

Evaluate: -5 + 75  5²

A) 220
B)
C) -4
D) -2

Question 12

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

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

Question 13

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

A) Yes
B) No

Question 14

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

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

Question 15

Find the equation (in standard form) of the line through (2, -1) and (4, -2).

A)
B)
C)
D)

Question 16

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

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 17

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

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

Question 18

Which of the following is the correct graph of the line through (2, -2) with slope ?

A)

B)

C)

D)

Question 19

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.]

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

Question 20

Simplify: r - 0.1(r + 400)

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

Question 21

Perform the indicated operations and write your result in lowest terms.

A)
B) 5n + 30p
C)
D) 5n + 6p

Question 22

Simplify.

A)
B)
C)
D)

Question 23

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?

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

Question 24

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

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

Question 25

Perform the indicated operations and write your result in lowest terms.

A) 0
B)
C)
D)

Question 26

A rectangular corral has a perimeter of 64 yards. Its length is 8 yards more than its width. What are the dimensions of the corral?

A) Length 22 yd, width 14 yd
B) Length 40 yd, width 24 yd
C) Length 18 yd, width 14 yd
D) Length 20 yd, width 12 yd

Question 27

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?

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