Expand 4(3z − 7) .

Answer 1

4(3z − 7) can be expanded by distributing the 4 to each term inside the parentheses:

4(3z) − 4(7)

Simplifying further:

12z − 28

Answer 2

show me how to do that

Answer 3

To expand 4(3z - 7), you distribute the 4 to each term inside the parentheses:

First, distribute the 4 to the first term, 3z, in the parentheses:

4 * 3z = 12z

Next, distribute the 4 to the second term, -7, in the parentheses:

4 * -7 = -28

Finally, combine the terms to get the expanded form:

12z - 28

So, the expanded form of 4(3z - 7) is 12z - 28.

Answer 4

Expand −5(2q + 8) .(1 point)

Answer 5

To expand -5(2q + 8), you distribute the -5 to each term inside the parentheses:

First, distribute the -5 to the first term, 2q, in the parentheses:

-5 * 2q = -10q

Next, distribute the -5 to the second term, 8, in the parentheses:

-5 * 8 = -40

Finally, combine the terms to get the expanded form:

-10q - 40

So, the expanded form of -5(2q + 8) is -10q - 40.

Answer 6

Expand 710(5d+6) .

Answer 7

To expand 710(5d + 6), you distribute the 710 to each term inside the parentheses:

First, distribute the 710 to the first term, 5d, in the parentheses:

710 * 5d = 3550d

Next, distribute the 710 to the second term, 6, in the parentheses:

710 * 6 = 4260

Finally, combine the terms to get the expanded form:

3550d + 4260

So, the expanded form of 710(5d + 6) is 3550d + 4260.

Answer 8

Expand 7/10(5d+6) .

Answer 9

To expand 7/10(5d + 6), you distribute the 7/10 to each term inside the parentheses:

First, distribute 7/10 to the first term, 5d, in the parentheses:

(7/10) * 5d = (35/10)d = 3.5d

Next, distribute 7/10 to the second term, 6, in the parentheses:

(7/10) * 6 = (42/10) = 4.2

Finally, combine the terms to get the expanded form:

3.5d + 4.2

So, the expanded form of 7/10(5d + 6) is 3.5d + 4.2.

Answer 10

−5/8(3p+8) .

Answer 11

To expand -5/8(3p + 8), you distribute the -5/8 to each term inside the parentheses:

First, distribute -5/8 to the first term, 3p, in the parentheses:

(-5/8) * 3p = -15/8 * p = -15p/8

Next, distribute -5/8 to the second term, 8, in the parentheses:

(-5/8) * 8 = -40/8 = -5

Finally, combine the terms to get the expanded form:

-15p/8 - 5

So, the expanded form of -5/8(3p + 8) is -15p/8 - 5.

Answer 12

Use the Order of Operations to simplify (solve) the expression: 24 ÷ 23
- 4 • 5

Answer 13

To simplify the expression 24 ÷ 23 - 4 • 5 using the Order of Operations (also known as PEMDAS), we first perform the multiplication/division from left to right and then the addition/subtraction from left to right.

Step 1: Solve the multiplication and division:

24 ÷ 23 = 1.0435 (approximately)

4 • 5 = 20

Step 2: Perform the subtraction:

1.0435 - 20 = -18.9565 (approximately)

So, the simplified expression is approximately -18.9565.

Answer 14

Part A) Jacqueline has two part-time jobs. She earns $15 per hour, b, working as a lab assistant, and $12 per hour, c, working as a cashier. Which algebraic expression below shows how much money Jacqueline earns altogether at her two jobs?(1 point)

Answer 15

The algebraic expression that shows how much money Jacqueline earns altogether at her two jobs is:

15b + 12c

Answer 16

Part B) If Jacqueline works 2 hours working as a lab assistant and 4 hours as a cashier, how much money will she earn altogether? b = 2 and c = 4(1 point)

Answer 17

To find out how much money Jacqueline will earn altogether if she works 2 hours as a lab assistant (b = 2) and 4 hours as a cashier (c = 4), we substitute the values into the algebraic expression:

15b + 12c

15(2) + 12(4)

30 + 48

78

So, Jacqueline will earn a total of $78 altogether from her two jobs.

Answer 18

Simplify by combining like terms: 5a − 8c + b + 3c −9a + 6b

Type out your answer in the text box.

(1 point)

Answer 19

To simplify by combining like terms:

5a - 8c + b + 3c - 9a + 6b,

we can combine the terms with the same variables:

(5a - 9a) + (- 8c + 3c) + (b + 6b),

which simplifies to:

-4a - 5c + 7b.

Therefore, the simplified expression is:

-4a - 5c + 7b.

Answer 20

-3(m + 6)

Answer 21

To simplify -3(m + 6), you can distribute the -3 to each term inside the parentheses.

First, distribute -3 to the term m:

-3 * m = -3m

Next, distribute -3 to the term 6:

-3 * 6 = -18

Combine the terms to get the simplified expression:

-3m - 18

So, the simplified form of -3(m + 6) is -3m - 18.

Answer 22

Select the TWO expressions below that are equivalent to 5(x + 3) - 4(2 points)
Responses

5x - 1
5x - 1

5x + 15 - 4
5x + 15 - 4

5x - 5
5x - 5

5x + 11
5x + 11

5x + 3 - 4

Answer 23

The two equivalent expressions to 5(x + 3) - 4 are:

5x + 15 - 4

and

5x - 5

Answer 24

How can the whole number 378 be expressed as a product of prime numbers with exponents?(1 point)
Responses

14⋅27
14 times 27

2⋅27⋅7
2 times 27 times 7

2⋅33⋅7
2 times 3 cubed times 7

2⋅3⋅3⋅3⋅7

Answer 25

To express the whole number 378 as a product of prime numbers with exponents, you need to factorize it.

The correct expression is:

2 * 3 * 3 * 3 * 7

This means that 378 can be expressed as the product of the prime numbers 2, 3, and 7, with the exponents 1, 3, and 1, respectively.

Answer 26

Find the GCF of 18j+27 .(1 point)
Responses

18
18

54
54

9
9

3

Answer 27

To find the greatest common factor (GCF) of 18j + 27, we can first factor out any common factors between the terms.

The GCF between 18 and 27 is 9, so we can factor out 9:

18j + 27 = 9(2j + 3)

Therefore, the GCF of 18j + 27 is 9.

Answer 28

Find the GCF of 42m−28n .(1 point)
Responses

84
84

7
7

2
2

14

Answer 29

To find the greatest common factor (GCF) of 42m - 28n, we can first factor out any common factors between the terms.

The GCF between 42 and 28 is 14, and there are no common variables.

Therefore, the GCF of 42m - 28n is 14.

Answer 30

Use properties of operations to factor 8w + 16 using the GCF. (1 point)
Responses

2(4w + 8)
2 Left Parenthesis 4 w plus 8 Right Parenthesis

4(2w + 4)
4 Left Parenthesis 2 w plus 4 Right Parenthesis

6(2w + 10)
6 Left Parenthesis 2 w plus 10 Right Parenthesis

8(w + 2)

Answer 31

To factor 8w + 16 using the greatest common factor (GCF), we first determine the GCF of 8 and 16, which is 8.

Next, we divide each term by the GCF, 8:

8w ÷ 8 = w
16 ÷ 8 = 2

Finally, we rewrite the expression using the GCF and the divided terms:

8w + 16 = 8(w + 2)

So, using the GCF, 8w + 16 can be factored as 8(w + 2).

Answer 32

Factor −27h + 6 using the GCF. (1 point)
Responses

​​​​​​​3(9h + 2)
3 Left Parenthesis 9 h plus 2 Right Parenthesis

​​​​​​​3(−9h + 2)
3 Left Parenthesis negative 9 h plus 2 Right Parenthesis

​​​​​​​3(−9h − 2)
3 Left Parenthesis negative 9 h minus 2 Right Parenthesis

​​​​​​​3(9h − 2)

Answer 33

To factor -27h + 6 using the greatest common factor (GCF), we first determine the GCF of -27 and 6, which is 3.

Next, we divide each term by the GCF, 3:

-27h ÷ 3 = -9h
6 ÷ 3 = 2

Finally, we rewrite the expression using the GCF and the divided terms:

-27h + 6 = 3(-9h + 2)

So, using the GCF, -27h + 6 can be factored as 3(-9h + 2).

Answer 34

How can the whole number 125 be expressed as a product of prime numbers with exponents?(1 point)

Answer 35

To express the whole number 125 as a product of prime numbers with exponents, you need to factorize it.

The correct expression is:

5^3

This means that 125 can be expressed as 5 raised to the power of 3.

Answer 36

Find the GCF of 15q+6 .

Answer 37

To find the greatest common factor (GCF) of 15q + 6, we can first look for any common factors between the terms.

The GCF between 15 and 6 is 3, and there are no common variables in this case.

Therefore, the GCF of 15q + 6 is 3.

Answer 38

Find the GCF of 8d−20 .

Answer 39

To find the greatest common factor (GCF) of 8d - 20, we can first look for any common factors between the terms.

Both 8d and 20 are divisible by 4, so we can factor out 4:

8d - 20 = 4(2d - 5)

Therefore, the GCF of 8d - 20 is 4.

Answer 40

Factor 9z + 18 using the GCF.

Answer 41

To factor 9z + 18 using the greatest common factor (GCF), we first determine the GCF of 9 and 18, which is 9.

Next, we divide each term by the GCF, 9:

9z ÷ 9 = z
18 ÷ 9 = 2

Finally, we rewrite the expression using the GCF and the divided terms:

9z + 18 = 9(z + 2)

So, using the GCF, 9z + 18 can be factored as 9(z + 2).

Answer 42

Factor 16d − 12 using the GCF

Answer 43

To factor 16d - 12 using the greatest common factor (GCF), we first determine the GCF of 16 and 12, which is 4.

Next, we divide each term by the GCF, 4:

16d ÷ 4 = 4d
12 ÷ 4 = 3

Finally, we rewrite the expression using the GCF and the divided terms:

16d - 12 = 4(4d - 3)

So, using the GCF, 16d - 12 can be factored as 4(4d - 3).

Answer 44

Add: 12(x+4)+14(4x−2) . Answer should be in mixed number form.

Answer 45

To add 12(x + 4) + 14(4x - 2), we can simplify each term before combining them.
First, distribute 12 and 14 to each term within the parentheses:

12(x + 4) = 12x + 48
14(4x - 2) = 56x - 28

Now, combine like terms:

12x + 48 + 56x - 28

Adding the x terms and the constant terms separately:

12x + 56x + 48 - 28

68x + 20

Therefore, the sum of 12(x + 4) + 14(4x - 2) is 68x + 20.

Answer 46

Add: 1/2(x+4)+14(4x−2) . Answer should be in mixed number form.(1 point

Answer 47

To add 1/2(x + 4) + 14(4x - 2), we can simplify each term before combining them.

First, distribute 1/2 and 14 to each term within the parentheses:

1/2(x + 4) = 1/2x + 2
14(4x - 2) = 56x - 28

Now, combine like terms:

1/2x + 2 + 56x - 28

Adding the x terms and the constant terms separately:

1/2x + 56x + 2 - 28

56 1/2x - 26

Therefore, the sum of 1/2(x + 4) + 14(4x - 2) is 56 1/2x - 26.

Answer 48

Add: (4d−3)+(12d+4)

Answer 49

To add (4d - 3) + (12d + 4), we can combine like terms:

4d - 3 + 12d + 4

Combining the d terms and the constant terms separately:
(4d + 12d) + (-3 + 4)

16d + 1

Therefore, the sum of (4d - 3) + (12d + 4) is 16d + 1.

Answer 50

Add: (2m−3)+(3n−1)+(3m+1)

Answer 51

To add (2m - 3) + (3n - 1) + (3m + 1), we can group like terms together and then combine them:

(2m + 3m) + (-3 + 1 + 1) + (3n)

This simplifies to:

5m - 1 + 3n

Therefore, the sum of (2m - 3) + (3n - 1) + (3m + 1) is 5m - 1 + 3n.

Answer 52

Subtract: 2(10b+4)−(b−2) .

Answer 53

To subtract 2(10b + 4) - (b - 2), we can simplify the expression by distributing the 2 to the terms within the parentheses:

2(10b + 4) - (b - 2)

= 20b + 8 - (b - 2)

= 20b + 8 - b + 2

Next, combine like terms:

= (20b - b) + (8 + 2)

= 19b + 10

Therefore, the subtraction of 2(10b + 4) - (b - 2) is 19b + 10.

Answer 54

Subtract: (3g−4)−2(3g+4) .

Answer 55

To subtract (3g - 4) - 2(3g + 4), we can first distribute the -2 to the terms within the second parentheses:

(3g - 4) - 2(3g + 4)

= 3g - 4 - 2(3g) - 2(4)

= 3g - 4 - 6g - 8

Next, combine like terms:

= (3g - 6g) + (-4 - 8)

= -3g - 12

Therefore, the subtraction of (3g - 4) - 2(3g + 4) is -3g - 12.

Answer 56

Use the properties of operations to add 9(k+13)+10(12k−1) .(1 point)
Responses

1912k−23
19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction

14k−7
14 k minus 7

14k−23
14 k minus Start Fraction 2 over 3 End Fraction

14k+13

Answer 57

Use the properties of operations to add 4(g−2)+(g+2) .(1 point)
Responses

5g+10
5 g plus 10

5g−6
5 g minus 6

5g−10
5 g minus 10

5g

Answer 58

Use the properties of operations to subtract (h+k)−(2k−h) .(1 point)
Responses

2h−k
2 h minus k

2h+k
2 h plus k

−2h−k
negative 2 h minus k

−k

Answer 59

Use the properties of operations to subtract (p−3)−(2.4+2p) .(1 point)
Responses

p−5.4
p minus 5.4

−p−5.4
negative p minus 5.4

3p−5.4
3 p minus 5.4

−p+5.4

Answer 60

Subtract: 2(k−4)−3(2k−1) .(1 point)
Responses

−4k−5
negative 4 k minus 5

−6k−18
negative 6 k minus 18

8k−11
8 k minus 11

−4k−11

Answer 61

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