Amusement Park Buildings Part 1
There are two buildings that you want to have in the amusement park, but the size hasn’t been determined yet. Although you don’t know the specific dimensions, you do know the relationships between the sides.
The first is the rectangular gift shop. You know that the length will be 20x+24 feet and the width will be 36x-20 feet.
1.Write the expression that represents the area of the gift shop, in terms of x.
2.Write the expression that represents the perimeter of the gift shop, in terms of x.
3.If the perimeter is going to be 176 feet, what are the dimensions of the building?

Part 2
The next building is the gazebo that will be in the shape of a regular hexagon. (What does regular mean?) Each side will be 5x + 21
4.Write the expression that represents the perimeter of the gazebo, in terms of x.
5.If the perimeter is going to be 36 feet, what are the dimensions of the building?

d

step-by-step explanation:

d

step-by-step explanation:

i think the answer is b.

step-by-step explanation:

not 100% sure though.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.