Question

1. U earn $9 per hr babysittng and 4$ hr washing cars Modled by 9b + 4c Evaluate if u babysit for b = 10 hrs and wash c + 10 cars to find total earnings

2. *a - 5c + b - 7a - 4c + 2b

3. Expand using the distributive property -2(3n +3 )

4. factor using yeh GCF 12a - 30 ( give BOTH factors )

5. Simplify -5(.2k + 1 ) -2 (.4k -2 )

Answer 1

Let's solve each of your questions one by one.

### 1. Total Earnings from Babysitting and Washing Cars
You earn $9 per hour for babysitting and $4 per hour for washing cars.

Given:
- \( b = 10 \) hours babysitting
- \( c = 10 \) cars washed

The total earnings can be calculated as follows:

\[
\text{Total Earnings} = 9b + 4c
\]

Substituting the values:

\[
\text{Total Earnings} = 9(10) + 4(10)
\]

Calculating:

\[
= 90 + 40 = 130
\]

So, your total earnings are **$130**.

---

### 2. Simplifying the Expression
The expression to simplify is:

\[
a - 5c + b - 7a - 4c + 2b
\]

Combine like terms:

\[
= (a - 7a) + (b + 2b) + (-5c - 4c)
\]

Calculating:

\[
= -6a + 3b - 9c
\]

So, the simplified expression is **\(-6a + 3b - 9c\)**.

---

### 3. Expanding Using the Distributive Property
To expand \(-2(3n + 3)\):

Using the distributive property:

\[
-2 \cdot 3n - 2 \cdot 3
\]

Calculating:

\[
= -6n - 6
\]

So, the expanded form is **\(-6n - 6\)**.

---

### 4. Factoring Using the GCF
To factor \(12a - 30\):

First, find the greatest common factor (GCF). The GCF of 12 and 30 is 6.

Now, factor out the GCF:

\[
12a - 30 = 6(2a - 5)
\]

Thus, the factors are **6** and **(2a - 5)**.

---

### 5. Simplifying the Expression
Now to simplify the expression:

\[
-5(0.2k + 1) - 2(0.4k - 2)
\]

Distributing:

\[
= -5 \cdot 0.2k - 5 \cdot 1 - 2 \cdot 0.4k + 2 \cdot 2
\]

Calculating each term:

\[
= -1k - 5 - 0.8k + 4
\]

Combining like terms:

\[
= (-1k - 0.8k) + (-5 + 4)
\]

Calculating further:

\[
= -1.8k - 1
\]

So, the simplified expression is **\(-1.8k - 1\)**.

---

If you have any more questions or need further assistance, feel free to ask!