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
. 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
Answers
GPT-4o mini
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**
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**
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
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
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**
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**
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)
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
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)**
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)**
Factor the expression completely.
45x−18y+36
(1 point)
45x−18y+36
(1 point)
GPT-4o mini
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:
\[
\boxed{9(5x - 2y + 4)}
\]
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:
\[
\boxed{9(5x - 2y + 4)}
\]
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)
−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
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)**
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)**
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)
−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
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 \(-6\):
1. 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)**
The coefficients are:
- \(-42\)
- \(-54\)
The GCF of \(-42\) and \(-54\) is \(6\).
Since the expression is negative, we will factor out \(-6\):
1. 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)**
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