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 )

1 answer

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!