You are installing a new pre-constructed fence in front of your house. each fence section measures 4 ½ feet wide, and each end will also have a decorative piece that measures 1 ¾ feet wide. if the space for the fence is 30 feet wide, what is the most number of 4 ½ foot fence sections you could install?

4 sections can be installed.

Step-by-step explanation:

Fence space for the fence in front of the house = 30 feet

Each fence section measures = 4.5 feet wide

let the numbers of sections installed = x

Then measure of fence covered by the sections = 4.5x feet

At each end of the section a piece of decorative piece measure= 1.75 feet wide

If x sections are installed then number of decorative pieces required will be same as x.

Therefore, length of decorative pieces = 1.75x feet

Now the total length of fence = Length of sections installed + Length of decorative pieces

4.5x + 1.75x = 30

6.25x = 30

x =

x = 4.8

Since number of sections can not be in the fraction or decimals so maximum 4 sections can be installed.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)