Asked by Hummingbird 7th

Which factorization is equivalent to this expression? 81x−36
(1 point)
Responses

9(9x−8)
9 times open paren 9 x minus 8 close paren

−9(9x−4)
negative 9 times open paren 9 x minus 4 close paren

9x−4
9 x minus 4

9(9x−4)
Answered by Hummingbird 7th
Sarah wants to buy balloons (b) that cost $0.75 each and cupcakes (c) that cost $2.00 each. The expression that represents her purchase is 0.75b+2c
. How much will she spend if she buys 6 balloons and 5 cupcakes?(1 point)
Responses

$2.75
$2.75

$30.25
$30.25

$14.50
$14.50

$15.75
Answered by Hummingbird 7th
Question
Which is the complete factorization of this expression? −24x+64
(1 point)
Responses

−8(3x−8)
negative 8 times open paren 3 x minus 8 close paren

8(2x−8)
8 times open paren 2 x minus 8 close paren

−8(3x+8)
negative 8 times open paren 3 x plus 8 close paren

−8(x+8)
Answered by Hummingbird 7th
Which is the complete factorization of this expression? −20x−5y
(1 point)
Responses

5(4x+y)
5 times open paren 4 x plus y close paren

−5(4x+y)
negative 5 times open paren 4 x plus y close paren

4(5x−y)
4 times open paren 5 x minus y close paren

−5(4x−y)
Answered by Hummingbird 7th
Simplify

−(16−5x)


(1 point)
Responses

−5x−16
negative 5 x minus 16

−5x+16
negative 5 x plus 16

5x+16
5 x plus 16

5x−16
5 x minus 16
Answered by Hummingbird 7th
Determine the missing value to complete this equation.

6 + 10 - ___ = 6

(1 point)
Responses

-10
-10

10
10

-6
-6

6
6
Answered by GPT-4o mini
To factor the expression \(81x - 36\), we first notice that both terms have a common factor.

The greatest common factor (GCF) of \(81\) and \(36\) is \(9\).

So we can factor out \(9\):

\[
81x - 36 = 9(9x - 4)
\]

Thus, the correct factorization of the expression \(81x - 36\) is:

**9(9x - 4)**

This corresponds with the option:

**9(9x−4)**.
Answered by GPT-4o mini
To find out how much Sarah will spend if she buys 6 balloons and 5 cupcakes, we can use the expression \(0.75b + 2c\), where \(b\) is the number of balloons and \(c\) is the number of cupcakes.

Substituting \(b = 6\) and \(c = 5\) into the expression:

\[
0.75(6) + 2(5)
\]

Calculating each term:

1. For the balloons:
\[
0.75 \times 6 = 4.50
\]

2. For the cupcakes:
\[
2 \times 5 = 10.00
\]

Now, add the two amounts together:

\[
4.50 + 10.00 = 14.50
\]

Thus, Sarah will spend **$14.50**. The correct response is:

**$14.50**.
Answered by GPT-4o mini
To factor the expression \(-24x + 64\), we start by identifying the greatest common factor (GCF) of the terms.

The GCF of \(-24\) and \(64\) is \(8\). However, since we are factoring out a negative from the expression for simplicity, we can take out \(-8\):

\(-24x\) divided by \(-8\) gives \(3x\), and \(64\) divided by \(-8\) gives \(-8\). Therefore, we can factor as follows:

\[
-24x + 64 = -8(3x - 8)
\]

Thus, the complete factorization of the expression \(-24x + 64\) is:

**\(-8(3x - 8)\)**.
Answered by GPT-4o mini
To factor the expression \(-20x - 5y\), we start by identifying the greatest common factor (GCF) of the terms.

The GCF of \(-20\) and \(-5\) is \(5\). Therefore, we can factor out \(-5\) for simplicity:

\[
-20x - 5y = -5(4x + y)
\]

So the complete factorization of the expression \(-20x - 5y\) is:

**\(-5(4x + y)\)**.

However, since this option is not listed among your responses, the correct response is **\(-5(4x+y)\)**.
Answered by GPT-4o mini
To simplify the expression \(- (16 - 5x)\), we distribute the negative sign inside the parentheses:

\[
- (16 - 5x) = -16 + 5x
\]

This can be rearranged as:

\[
5x - 16
\]

Thus, the simplified form of \(- (16 - 5x)\) is:

**5x - 16**.

The correct response is:

**5x - 16**.
Answered by GPT-4o mini
To find the missing value in the equation:

\[
6 + 10 - \_\_ = 6
\]

First, we can simplify the left side:

\[
6 + 10 = 16
\]

So the equation becomes:

\[
16 - \_\_ = 6
\]

Now, to isolate the missing value, we can subtract \(6\) from \(16\):

\[
16 - 6 = 10
\]

This means:

\[
\_\_ = 10
\]

Thus, the missing value is **10**.

The correct response is:

**10**.