These are 18 questions and 18 answers. Each with its justification.

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Question 1 (Multiple Choice Worth 1 points)

Which expression is equivalent to 5x − 2x + 6 and why?

Third option: 6 + 3x, because (5x − 2x) + 6 = 3x + 6 = 6 + 3x

Justification:

These are the steps that proove the equivalence:

Given: 5x - 2x + 6Associative property: (5x - 2x) + 6 ← grouping the first two termsCombine like terms: 3x + 6 ← subtract the terms with common literal partConmutative property: 6 + 3x ← change the order of the summands

Question 2(Multiple Choice Worth 1 points)

Four expressions are shown:

6(5x + 3)

6(6x + 2)

36x + 12

30x + 18

Which two expressions are equivalent to 6(5x + 2 + x)?

B and C

Justification:

Given: 6 (5x + 2 + x)Combine like terms (add 5x and x): 6 (6x + 2) That is the option B.Use distributive property: 6(6x) + 6(2)Due the operations: 36x + 12That is the option C.

Question 3(Multiple Choice Worth 1 points)

Which expression is equal to p + (m + n)?

(p + m) + n

Justification:

This is a direct application of the associative property of the addiction, which states that you can group the addends in any order. So given p + (m + n) you can regroup moving the parenthesis to (p + m) + n.

This numerical example will help you:

assume p = 1, m = 2, n = 3, then:1 + (2 + 3) = ( 1 + 2) + 31 + (5) = (3) + 31+ 5 = 3 + 36 = 6

Question 4(Multiple Choice Worth 1 points)

Which of the following best describes the expression 11(x + 7)?

The product of a constant factor 11 and a 2-term factor x + 7

Justification:

A number or a letter preceding a parenthesis indicates that the former is being multiplied by the amount that is in parentheses.The amounts being multiplied are called factors11 as a number is a constant factorThe amount in the parentheses is other factor. In this case, x and 7 each is a term. So, it is a two-term factor.

Question 5(Multiple Choice Worth 1 points)

The equation below shows the total volume (V), in cubic units, of 6 identical boxes with each side equal to s units:

V = 6s³

If s = 3.1 units, what is the value of V?

178.746 cubic units

Justification:

Given: V = 6s³Substitue s = 3.1 units: V = 6(3.1 units)³Do the operation indicated by the parentheses: V = 6(29.791 unit³)Do the operation 6×29.791 unit³: 178.746

Question 6(Multiple Choice Worth 1 points)

A student attempted to generate an equivalent expression using the distributive property, as shown below:

7(y − 5) = y − 35

What was the mistake made?

7 was not multiplied by y

Justification:

The distributive property states that you must multiply the factor that preceeds the parentheses by all the terms inside the parentheses. this is: 7 (y - 5) = 7y - 7(5) = 7y - 35So, in the correct product 7 must appear as a coefficient of the variable y.

Question 7(Multiple Choice Worth 1 points)

Which expression represents "5 times the sum of 4 and y?"

5(4 + y)

Justification:

The factor 4 + y represents the sum of 4 and y.

The statement indicate 5 times such sum, so you have to multiply the factor 4 + y by the constant factor 5. Mathematically you must use the parentheses to show that 4 and y must be added before the multiplication is performed.

Question 8 (Fill-In-The-Blank Worth 1 points)

If s = 1/2 unit and A = 16s², what is the value of A, in square units? square unit(s). (Input whole number only.)

Answer for Blank 1: 4

Justification:

Given: A = 16s²Substitute s = 1/2: A = 16 (1/2)²(1/2)² = (1/4)A = 16(1/4) = 16 / 4 = 4

Question 9(Multiple Choice Worth 1 points)

Which of these shows 2s + 8 rewritten using the commutative property of addition?

8 + 2s

Justification:

The conmutative property of addition states that the order of the addends do not modificy the sum.This is represented by: a + b = b + c.Hence, 2s + 8 = 8 + 2sFinally a numerical example may help you:

8 + 2(5) = 2(5) + 8

8 + 10 = 10 + 8

18 = 18

Which shows how the sum is not modified when you change the order of the addends.

Question 10(Multiple Choice Worth 1 points)

What is the value of fraction 1/2 x³ + 5.3y, when x = 2 and y = 3?

19.9

Justification:

Given: 1/2 x³ + 5.3y and x = 2 and y = 3Substitute: 1/2 (2³) + 5.3(3) = 1/2 (8) + 15.9 = 8/2 + 15.9 = 4 + 15.9 = 19.9