Mathematics, 12.12.2019 03:31, jordeng4354

Anumber divided by the sum of 4 and 7 in algebraic expression

Answers: 1

Show answers

Answers

answered: emily0259

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

Since the answer exceeds 5,000 characters I had to add a file.

Please, open the file attached to see all the answers.

I leave here some of the answers (less than 5,000 characters) but the document contain all the answers.

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 + 6

Associative property: (5x - 2x) + 6 ← grouping the first two terms

Combine like terms: 3x + 6 ← subtract the terms with common literal part

Conmutative 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 + 12

That 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) + 3

1 + (5) = (3) + 3

1+ 5 = 3 + 3

6 = 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 factors

11 as a number is a constant factor

The 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 = 6s³

Substitue s = 3.1 units: V = 6(3.1 units)³

Do 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 - 35

So, 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 = 16s²

Substitute 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: