Manny has two part-time jobs. She earns $21 per hour (a) working as an aerobics instructor, and $12.50 per hour (d) working at the donut shop. Her earnings are represented by the expression 21a+12.50d.

Question

Manny has two part-time jobs. She earns $21 per hour (a) working as an aerobics instructor, and $12.50 per hour (d) working at the donut shop. Her earnings are represented by the expression 21a+12.50d.
. How much money will she earn working 4 hours as an aerobics instructor and 8 hours at the donut shop?(1 point)
Responses

$134
$134

$218
$218

$33.50
$33.50

$184

GPT-4o mini · Answer

To calculate Manny's earnings for the given hours worked, we can substitute the values into the expression $21a + 12.50d$, where $a$ is the number of hours worked as an aerobics instructor and $d$ is the number of hours worked at the donut shop.

Given:

$a = 4$ (hours as an aerobics instructor)
$d = 8$ (hours at the donut shop)

Now, substitute the values into the expression:

\[ Earnings = 21(4) + 12.50(8) \]

Calculating each term:

\[ 21(4) = 84 \] \[ 12.50(8) = 100 \]

Now, add the two amounts:

\[ Earnings = 84 + 100 = 184 \]

Therefore, Manny will earn $184 working 4 hours as an aerobics instructor and 8 hours at the donut shop.

The correct response is: $184

Hummingbird 7th · Answer

Simplify. 11−9(−2x−3) (1 point) Responses −4x−6 negative 4 x minus 6 18x−38 18 x minus 38 −4x+6 negative 4 x plus 6 18x+38

GPT-4o mini · Answer

To simplify the expression $11 - 9(-2x - 3)$, follow these steps: 1. Distribute $ -9 $ to both terms inside the parentheses: $$ -9(-2x) - 9(-3) = 18x + 27 $$ 2. Substitute back into the expression: $$ 11 + 18x + 27 $$ 3. Combine the constant terms $11$ and $27$: $$ 11 + 27 = 38 $$ So, the expression becomes: $$ 18x + 38 $$ Thus, the simplified expression is **$18x + 38$**. The correct response is: **18x + 38**

Hummingbird 7th · Answer

Factor this expression completely.

35x−40

(1 point)
Responses

7(5x+8)
7 times open paren 5 x plus 8 close paren

7(5x−8)
7 times open paren 5 x minus 8 close paren

5(7x+8)
5 times open paren 7 x plus 8 close paren

5(7x−8)

GPT-4o mini · Answer

To factor the expression $35x - 40$ completely, we first look for the greatest common factor (GCF) of the two terms. The terms are: - $35x$ - $-40$ The GCF of $35$ and $40$ is $5$. Now, we can factor out $5$ from the expression: $$ 35x - 40 = 5(7x - 8) $$ Thus, the completely factored form of the expression is: **$5(7x - 8)$** The correct response is: **5(7x−8)**

Hummingbird 7th · Answer

Factor the expression completely. 45x−18y+36 (1 point)

GPT-4o mini · Answer

To factor the expression $45x - 18y + 36$ completely, we can start by finding the greatest common factor (GCF) of the coefficients of the terms. The terms are: - $45x$ - $-18y$ - $36$ The coefficients are $45$, $-18$, and $36$. The GCF of these numbers is $9$. Now, we will factor out $9$ from the entire expression: $$ 45x - 18y + 36 = 9(5x - 2y + 4) $$ Next, we need to check if the expression inside the parentheses $5x - 2y + 4$ can be factored further. In this case, there are no common factors or specific factorable forms in $5x - 2y + 4$. Thus, the completely factored expression is: $$ \boxed{9(5x - 2y + 4)} $$

Hummingbird 7th · Answer

Factor this expression completely.

−21x+28

(1 point)
Responses

−7(3x−4)
negative 7 times open paren 3 x minus 4 close paren

−7(3x+4)
negative 7 times open paren 3 x plus 4 close paren

7(3x−4)
7 times open paren 3 x minus 4 close paren

−(21x−4)

GPT-4o mini · Answer

To factor the expression $-21x + 28$ completely, we first look for the greatest common factor (GCF) of the coefficients of the terms. The terms are: - $-21x$ - $28$ The GCF of $-21$ and $28$ is $7$. Since the first term is negative, we'll factor out $-7$. Now we can factor the expression: $$ -21x + 28 = -7(3x - 4) $$ Thus, the completely factored form of the expression is: **$-7(3x - 4)$** The correct response is: **−7(3x−4)**

Hummingbird 7th · Answer

Which factorization is equivalent to this expression?

−42k−54

(1 point)
Responses

−6(7k−9)
negative 6 times open paren 7 k minus 9 close paren

6(−7k+9)
6 times open paren negative 7 k plus 9 close paren

−6(7k+9)
negative 6 times open paren 7 k plus 9 close paren

6(7k+9)

GPT-4o mini · Answer

To find an equivalent factorization for the expression $-42k - 54$, we start by determining the greatest common factor (GCF) of the coefficients in the terms.

The coefficients are:

$-42$
$-54$

The GCF of $-42$ and $-54$ is $6$.

Since the expression is negative, we will factor out $-6$:

Factor out $-6$:

\[ -42k - 54 = -6(7k + 9) \]

Thus, the equivalent factorization is:

\[ -6(7k + 9) \]

None of the provided options match $-6(7k + 9)$ directly, but if we consider the structure of the expressions provided:

The option $-6(7k + 9)$ can also be rewritten as $-6(7k + 9)$ indicating that there might be a small error in the presentation of other options.

Therefore, the expression that corresponds correctly to our factorized expression is:

−6(7k+9)