Determine the GCF (greatest common factor) for the expression 18j+27

Question

.(1 point).
The GCF of 18j+27
is
.

Answer 1

To find the greatest common factor (GCF) of the expression \( 18j + 27 \), we need to determine the GCF of the numerical coefficients of the terms.

1. Identify the coefficients:

   • For \( 18j \), the coefficient is \( 18 \).
   • For \( 27 \), the coefficient is \( 27 \).

2. Find the GCF of \( 18 \) and \( 27 \):

   • The factors of \( 18 \) are \( 1, 2, 3, 6, 9, 18 \).
   • The factors of \( 27 \) are \( 1, 3, 9, 27 \).
   • The common factors of \( 18 \) and \( 27 \) are \( 1, 3, 9 \).

3. The greatest of these common factors is \( 9 \).

Thus, the GCF of \( 18j + 27 \) is \( 9 \).

Answer 2

Determine the GCF (greatest common factor) of the expression 42m−28n
.(1 point)
The GCF for 42m−28n
is
.

Answer 3

To find the greatest common factor (GCF) of the expression \( 42m - 28n \), we need to determine the GCF of the numerical coefficients of the terms.

1. Identify the coefficients:

   • For \( 42m \), the coefficient is \( 42 \).
   • For \( -28n \), the coefficient is \( -28 \) (we can use \( 28 \) since GCF is generally considered with positive values).

2. Find the GCF of \( 42 \) and \( 28 \):

   • The factors of \( 42 \) are \( 1, 2, 3, 6, 7, 14, 21, 42 \).
   • The factors of \( 28 \) are \( 1, 2, 4, 7, 14, 28 \).
   • The common factors of \( 42 \) and \( 28 \) are \( 1, 2, 7, 14 \).

3. The greatest of these common factors is \( 14 \).

Thus, the GCF of \( 42m - 28n \) is \( 14 \).

Answer 4

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

8(w+2)
8 times open paren w plus 2 close paren

2(4w+8)
2 times open paren 4 w plus 8 close paren

4(2w+4)
4 times open paren 2 w plus 4 close paren

6(2w+10)

Answer 5

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

1. The GCF of \( 8 \) and \( 16 \) is \( 8 \).

Now, we can factor out \( 8 \) from the expression:

\[ 8w + 16 = 8(w + 2) \]

So, the correct factorization is:

8(w + 2)

Therefore, the correct response is:

8 times open parenthesis w plus 2 close parenthesis.

Answer 6

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

3(−9h−2)
3 times open paren negative 9 h minus 2 close paren

3(9h+2)
3 times open paren 9 h plus 2 close paren

3(−9h+2)
3 times open paren negative 9 h plus 2 close paren

3(−9h−2)

Answer 7

To factor the expression \( -27h + 6 \) using the greatest common factor (GCF), we first need to determine the GCF of the coefficients \( -27 \) and \( 6 \).

1. The GCF of \( 27 \) and \( 6 \) is \( 3 \) (considering both coefficients as positive since GCF is typically expressed as a positive value).

Now we can factor out \( 3 \) from the expression \( -27h + 6 \).

2. When factoring out \( 3 \), we will be left with: \[ -27h + 6 = 3(-9h + 2) \]

Thus, the correct form of the expression is: \[ 3(-9h + 2) \]

Therefore, the correct response is:

3 times open parenthesis negative 9 h plus 2 close parenthesis.

Answer 8

Use the distributive property to expand the following expression:

−5(−3−11g)
(1 point)
Responses

55g+15
55 g plus 15

−55g+15
negative 55 g plus 15

55g−15
55 g minus 15

−55g−15

Answer 9

To expand the expression \( -5(-3 - 11g) \) using the distributive property, we will multiply \( -5 \) by each term inside the parentheses.

1. Distribute \( -5 \): \[ -5(-3) + (-5)(-11g) \]

2. Calculate each term:

   • \( -5(-3) = 15 \)
   • \( -5(-11g) = 55g \)

So combining these gives: \[ 15 + 55g \]

This can be written as: \[ 55g + 15 \]

Therefore, the correct response is:

55g + 15.

Answer 10

Simplify the expression by combining like terms.

2/8x+3/10y−5/8x+4/10y
(1 point)
Responses

4/18xy
4 over 18 x y

−3/8x+7/10y
negative 3 eighths x plus 7 tenths y

14/18xy
14 over 18 x y

7/10x+7/8y
7 tenths x plus 7 eighths y

Answer 11

To simplify the expression \( \frac{2}{8}x + \frac{3}{10}y - \frac{5}{8}x + \frac{4}{10}y \), we will combine like terms.

1. Combine the x-terms: \[ \frac{2}{8}x - \frac{5}{8}x = \left( \frac{2}{8} - \frac{5}{8} \right)x = \frac{2 - 5}{8}x = \frac{-3}{8}x \]

2. Combine the y-terms: \[ \frac{3}{10}y + \frac{4}{10}y = \left( \frac{3}{10} + \frac{4}{10} \right)y = \frac{3 + 4}{10}y = \frac{7}{10}y \]

Now, we can combine the results: \[ \frac{-3}{8}x + \frac{7}{10}y \]

Thus, the simplified expression is: \[ -\frac{3}{8}x + \frac{7}{10}y \]

Therefore, the correct response is:

−3/8x + 7/10y.