Carlos is building three gardens, each the same size, in his backyard. each garden is in the shape of a square with a 3 foot by 3 foot section removed from each of the four corners. one garden is shown below.

what is the total area of all three gardens?

220 ft2
256 ft2
660 ft2
768 ft2

 The correct option is (C) 660 ft².

Step-by-step explanation:  Given that Carlos is building three gardens, each the same size, in his backyard. Each garden is in the shape of a square with a 3 foot by 3 foot section removed from each of the four corners.

One of the gardens is shown in the given figure.

We are to find the total area of all three gardens.

The area of the section removed from the four corners of aech garden is given by

Therefore, the total area of  one garden will be

Since there are three gardens, so the total area of the three gardens is given by

Thus, the total area of the three gardens is 660 ft².

Option (C) is CORRECT.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!