Question 1

Simplify. A) B) -4x³z³ C) D)

Accepted Answer

A

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)

Accepted Answer

We can use the factoring techniques of grouping or trial and error to factor the polynomial. One possible method is: 15z² - 11z + 2 = (3z² - 2)(5z² - 1) Then, we check if this factorization is correct by multiplying the factors: (3z² - 2)(5z² - 1) = 15z^2 - 9z - 10z + 2 = 15z^2 - 19z + 2 which matches with the original polynomial. Therefore, the answer is C.

Question 3

Perform the indicated operations and write your result in lowest terms. 
A) 
B) 
C) 
D)

Accepted Answer

D

Question 4

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

Accepted Answer

When substituting x = 13 into the equation -3x - 15, we get -3(13) - 15 = -39 - 15 = -54, which is not equal to -24. Therefore, 13 is not a solution.

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

Accepted Answer

We can use the distributive property and FOIL method to find the product:

(3b + 5)(b + 6) = 3b^2 + 18b + 5b + 30 
= 3b^2 + 23b + 30

Therefore, the best choice is B, which is the only option with the correct product.

Question 6

Simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of 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)

Accepted Answer

The expression 64x^3 + 1 is a sum of cubes, which factors as (a + b)(a^2 - ab + b^2) where a = 4x and b = 1.

Question 8

Solve the given equation. x² + 10x + 24 = 0 A) 4, -6 B) -4, 6 C) -4, -6 D) 4, 6

Accepted Answer

The quadratic equation can be factored as (x + 4)(x + 6) = 0, giving solutions x = -4 and x = -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

Accepted Answer

By simplifying the given equation, 
x + (x + 1) + (x + 2) = 12 inches

3x + 3 = 12 inches
3x = 9 inches
x = 3 inches

Therefore, the sides are x = 3 inches, x + 1 = 4 inches, and x + 2 = 5 inches, which correspond to choice D.

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

Accepted Answer

The answer of Liam invested some money in the Abernathy...

Question 11

Evaluate: -5 + 75 $\div$ 5² A) 220 B) C) -4 D) -2

Accepted Answer

The answer of Evaluate: -5 + 75 $\div$ 5² A)...

Question 12

Solve and write your answer in interval notation. p - 3 < 3p - 13
A) (-∞, 3)
B) (6, ∞)
C) (5, ∞)
D) (3, ∞)

Accepted Answer

We solve the inequality as follows:

p - 3 < 3p - 13

-2p < -10

p > 5

Thus, the solution set is (5, ∞). The correct choice is C.

Question 13

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

Accepted Answer

Substitute x = -15, y = 15 into the inequality: 
y ≥ -12x + 8 
15 ≥ -12(-15) + 8 
15 ≥ 178 
The inequality is not satisfied, so the answer is 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

Accepted Answer

Distributing the negative sign in front of the first expression, we get: -p² - p - 1 - p² - 4p - 5 Combining like terms, we get: -2p² - 5p - 6 Thus, the correct answer is D.

Question 15

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

Accepted Answer

The answer of Find the equation (in standard form) of...

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)

Accepted Answer

The given polynomial can be factored using the grouping method as follows:
yS1U1P13S1S1P0 - 8yS1U1P12S1S1P0 - 9y + 72
= yS1U1P12(y + 3) - 8(y + 3)(y - 3)
= (y + 3)(yS1U1P12 - 8y + 24)
= (y + 3)(yS1U1P12 - 6y - 4y + 24)
= (y + 3)(y - 3)(y - 8)
Therefore, the correct option is B.

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

Accepted Answer

The equation simplifies to 7x = 7x, which is true for all real numbers. Therefore, the solution set is all real numbers and the equation is an identity.

Question 18

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

B)

C)

D)

Accepted Answer

The answer of Which of the following is the correct...

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

Accepted Answer

The answer of The temperature T of a gas sample...

Question 20

Simplify: r - 0.1(r + 400)
A) 0.9r - 40
B) 1.1r + 40
C) 1.1r - 40
D) 0.9r + 40

Accepted Answer

First, distribute the -0.1 across the terms in the parentheses: r - 0.1r - 40. Then, combine like terms: 0.9r - 40.

Quiz 16: Algebraic Equations and Problem Solving

Simplify.

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

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

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

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

Simplify.

Factor. 64x³ + 1

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

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.

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?

Evaluate: -5 + 75 $\div$ 5²

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

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

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

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

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

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

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

Simplify: r - 0.1(r + 400)

Quiz 16: Algebraic Equations and Problem Solving

Simplify.

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

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

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

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

Simplify.

Factor. 64x3 + 1

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

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.

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?

Evaluate: -5 + 75 ÷\div÷ 52

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

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

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

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

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

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

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

Simplify: r - 0.1(r + 400)

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

Factor. 64x³ + 1

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

Evaluate: -5 + 75 $\div$ 5²

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

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

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