The formula for finding the surface area of a cube is 6s2 , where s is the length of each side of the square. Evaluate for s=10 to find the number of square centimeters ( cm2 ) for the surface area of a cube with a side length of 10 cm.

Answer 1

To find the surface area of a cube with a side length of \( s = 10 \) cm, we can use the formula:

\[ \text{Surface Area} = 6s^2 \]

Substituting \( s = 10 \) cm into the formula:

\[ \text{Surface Area} = 6(10)^2 \]

Calculating \( (10)^2 \):

\[ (10)^2 = 100 \]

Now substituting that back into the equation:

\[ \text{Surface Area} = 6 \times 100 = 600 \]

Therefore, the surface area of the cube is:

\[ \text{Surface Area} = 600 \text{ cm}^2 \]

Answer 2

Alicia works for Thomas Edison Electrical Company. She earns $100 for going to a customer’s house and $65 per hour, h , for the job. This is modeled by 65h+100 . Evaluate for h=3 to find how much Alicia will earn for a job that takes 3 hours.

Answer 3

To find out how much Alicia will earn for a job that takes 3 hours, we can use the formula for her earnings:

\[ \text{Earnings} = 65h + 100 \]

Substituting \( h = 3 \) into the formula:

\[ \text{Earnings} = 65(3) + 100 \]

Calculating \( 65(3) \):

\[ 65 \times 3 = 195 \]

Now substituting that back into the equation:

\[ \text{Earnings} = 195 + 100 = 295 \]

Therefore, Alicia will earn:

\[ \text{Earnings} = 295 \text{ dollars} \]

Answer 4

A competitive cliff-diver jumps from a height of 75 feet. Find the number of feet the diver is above the ocean in 2 seconds. Evaluate for t=2 by using the formula 75−16t2 , where t is time in seconds.

Answer 5

To find the height of the diver above the ocean after 2 seconds, we can use the formula:

\[ \text{Height} = 75 - 16t^2 \]

We will evaluate this formula for \( t = 2 \) seconds:

\[ \text{Height} = 75 - 16(2)^2 \]

Calculating \( (2)^2 \):

\[ (2)^2 = 4 \]

Now substituting that back into the equation:

\[ \text{Height} = 75 - 16 \times 4 \]

Calculating \( 16 \times 4 \):

\[ 16 \times 4 = 64 \]

Now substituting that value back into the equation:

\[ \text{Height} = 75 - 64 = 11 \]

Therefore, after 2 seconds, the diver is:

\[ \text{Height} = 11 \text{ feet} \]

above the ocean.

Answer 6

Gabrielle wants to put a border around her garden. It costs $1.50 per yard for the materials. Use 1.50(2l+2w) , where l is the length and w is the width of her garden, to find the cost for a garden that has a length of 4 yards and a width of 3 yards.

Answer 7

To find the cost of putting a border around Gabrielle's garden, we can use the formula:

\[ \text{Cost} = 1.50(2l + 2w) \]

Given that the length \( l = 4 \) yards and the width \( w = 3 \) yards, we can substitute these values into the formula.

First, we calculate \( 2l + 2w \):

\[ 2l + 2w = 2(4) + 2(3) \]

Calculating each term:

\[ 2(4) = 8 \] \[ 2(3) = 6 \]

Now, adding these together:

\[ 2l + 2w = 8 + 6 = 14 \]

Now we can substitute this value back into the cost formula:

\[ \text{Cost} = 1.50(14) \]

Calculating the cost:

\[ 1.50 \times 14 = 21.00 \]

Therefore, the total cost for the border around the garden is:

\[ \text{Cost} = 21.00 \text{ dollars} \]