Solve x^2=28 where x is a real number

the Johnsons want to cover their backyard with new grass their backyard is rectangular with a length of 3x - 2 feet and a width

Andre45 [30]

<h2>Hello!</h2>

The answer is:

The area that the want to cover with new grass will be:

$Area_{grass}=8x^{2} -12x-22$

If we want to calculate what is the ara of the region of the backyard that they want to cover with new grass, we need to calculate the area of the backyard, calculate the area of the swimming pool and its patio, and the last step is to subtract the area of the swimming pool and its patio to the total area of the backyard.

So, to calculate the areas, we need to use the following formula:

$Area=Length*Width$

Also, we need to remember how the distributive property works, since we are going to need it.

We have that:

$(a+b)(c+d)=ac+ad+bc+bd$

We are given the following information:

For the backyard we have:

$Length=3x-2\\Width=3x+1$

For the swimming pool and its patio:

Since there it's not mentioned, let be the first expression the length, and the second one, the width.

$Length=x+4\\Width=x+5$

Then, calculating we have:

Backyard:

$Area_{backyard}=(3x-2)*(3x+1)=9x^{2}+3x-6x-2=9x^{2}-3x-2$

Swimming pool and patio:

$Area_{swimmingpool}=(x+4)*(x+5)=x^{2}+5x+4x+20=x^{2}+9x+20$

Now, calculating the area that they want to cover with new grass, we have:

$Area_{grass}=Area_{backyard}-Area_{swimmingPool}\\\\Area_{grass}=(9x^{2}-3x-2)-(x^{2}+9x+20)\\\\Area_{grass}=9x^{2} -x^{2} -3x-9x-2-20\\\\Area_{grass}=8x^{2} -12x-22$

Hence, we have that the area that the want to cover with new grass will be:

$Area_{grass}=8x^{2} -12x-22$

Have a nice day!

3 0

3 years ago

How far will a cyclist travel in 1/4 hour if he cycles at 18 kilometres per hour

Zinaida [17]

In one hour he would cycle 18Km, therefore in a 1/4 hour the cyclist would ride a 1/4 of 18 = 4.5Km.

3 0

3 years ago

What is the value of the 1 in 3.619? Any idea

Kazeer [188]

C. one hundrenth. It's in the hundrenths place.

5 0

3 years ago

A prism has a square base with a side length of 4 1 2 4 1 2 feet. The height of the prism is 6 feet. What is the volume of the p

dusya [7]

We have been given that a prism has a square base with a side length of 4 1/2 feet. The height of the prism is 6 feet. We are asked to find the volume of the prism.

We know that volume of prism is base area times height.

$\text{Area of base}=\text{Area of square}=\text{Side length}^2$