Which factorization is equivalent to this expression? 81x−36

Question

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)

GPT-4o mini · Answer

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)**.

Hummingbird 7th · Answer

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

GPT-4o mini · Answer

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:

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

Hummingbird 7th · Answer

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)

GPT-4o mini · Answer

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: **$-8(3x - 8)$**.

Hummingbird 7th · Answer

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)

GPT-4o mini · Answer

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

Hummingbird 7th · Answer

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

GPT-4o mini · Answer

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**.

Hummingbird 7th · Answer

Determine the missing value to complete this equation. 6 + 10 - ___ = 6 (1 point) Responses -10 -10 10 10 -6 -6 6 6

GPT-4o mini · Answer

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.