Question

Jacqueline has two part-time jobs. She earns $15 per hour, l , working as a lab assistant, and $12 per hour, s , working as a cashier. This is modeled by 15l+12s . Evaluate for l=5 and s=7 to find how much money Jacqueline will earn at her two jobs this week.

Answer 1

Simplify  5a−8c+b+3c−9a+6b .

Answer 2

Simplify  −3/4r + 3 − 5/6r − 6 .

Answer 3

But how is 3-6= -3

Answer 4

Expand 8(3p+2).

Answer 5

Expand −4(6a−5)

Answer 6

To find out how much money Jacqueline will earn at her two jobs this week, we can use the expression \( 15l + 12s \).

Given:
- \( l = 5 \) (hours worked as a lab assistant)
- \( s = 7 \) (hours worked as a cashier)

Now we can substitute the values into the expression:

\[
15l + 12s = 15(5) + 12(7)
\]

Calculating each part:

1. \( 15(5) = 75 \)
2. \( 12(7) = 84 \)

Now combine the results:

\[
75 + 84 = 159
\]

Thus, Jacqueline will earn **$159** this week at her two jobs.

Answer 7

To simplify the expression \(5a - 8c + b + 3c - 9a + 6b\), we can combine like terms.

Let's group the terms by their variables:

- **Terms with \(a\)**: \(5a - 9a\)
- **Terms with \(b\)**: \(b + 6b\)
- **Terms with \(c\)**: \(-8c + 3c\)

Now, simplify each group:

1. \(5a - 9a = -4a\)
2. \(b + 6b = 7b\)
3. \(-8c + 3c = -5c\)

Now combine these results:

\[
-4a + 7b - 5c
\]

So, the simplified expression is:

\[
\boxed{-4a + 7b - 5c}
\]

Answer 8

To simplify the expression \(-\frac{3}{4}r + 3 - \frac{5}{6}r - 6\), we will first combine like terms.

1. **Combine the constant terms**:
\[
3 - 6 = -3
\]

2. **Combine the \(r\) terms**:
\[
-\frac{3}{4}r - \frac{5}{6}r
\]
To combine these, we need a common denominator. The least common multiple of 4 and 6 is 12.

- Convert \(-\frac{3}{4}r\) to a fraction with a denominator of 12:
\[
-\frac{3}{4}r = -\frac{3 \times 3}{4 \times 3}r = -\frac{9}{12}r
\]

- Convert \(-\frac{5}{6}r\) to a fraction with a denominator of 12:
\[
-\frac{5}{6}r = -\frac{5 \times 2}{6 \times 2}r = -\frac{10}{12}r
\]

Now combine the two \(r\) terms:
\[
-\frac{9}{12}r - \frac{10}{12}r = -\frac{19}{12}r
\]

3. **Putting it all together**:
\[
-\frac{19}{12}r - 3
\]

Thus, the simplified expression is:

\[
\boxed{-\frac{19}{12}r - 3}
\]

Answer 9

I apologize for any confusion; let’s clarify that step.

When we subtract \(6\) from \(3\):

\[
3 - 6 = -3
\]

This means that if you have \(3\) and then take away \(6\), you are left with \(-3\), which indicates a debt or being below zero.

To recap the entire simplification of \(-\frac{3}{4}r + 3 - \frac{5}{6}r - 6\):

1. **Combine the constant terms**:
\[
3 - 6 = -3
\]

2. **Combine the \(r\) terms**:
\[
-\frac{3}{4}r - \frac{5}{6}r
\]
To combine these, we convert them to a common denominator:
- \(-\frac{3}{4}r = -\frac{9}{12}r\)
- \(-\frac{5}{6}r = -\frac{10}{12}r\)

Thus,
\[
-\frac{9}{12}r - \frac{10}{12}r = -\frac{19}{12}r
\]

3. **Combining everything** gives:
\[
-\frac{19}{12}r - 3
\]

So the final simplified expression is:

\[
\boxed{-\frac{19}{12}r - 3}
\]

Thank you for your understanding! If you have any more questions or need further clarification, feel free to ask!

Answer 10

To expand the expression \(8(3p + 2)\), you distribute the \(8\) to both terms inside the parentheses:

\[
8(3p) + 8(2)
\]

Now, calculate each term:

1. \(8 \cdot 3p = 24p\)
2. \(8 \cdot 2 = 16\)

Now combine the results:

\[
24p + 16
\]

So, the expanded expression is:

\[
\boxed{24p + 16}
\]

Answer 11

To expand the expression \(-4(6a - 5)\), you distribute the \(-4\) to both terms inside the parentheses:

\[
-4(6a) + (-4)(-5)
\]

Now, calculate each term:

1. \(-4 \times 6a = -24a\)
2. \(-4 \times -5 = 20\)

Now combine the results:

\[
-24a + 20
\]

So, the expanded expression is:

\[
\boxed{-24a + 20}
\]