Apark designer wanted to place a fountain so that it was close to both the slide and the swings. refer to the coordinate grid shown. each unit on the grid represents 100 ft.

(a) find the distance from the slide to the foundation show your work.

(b) if each jump = 100ft, how far is it from the slide to the fountain?

show your work : )

200 ft.

2 jumps

Step-by-step explanation:

The slide is placed at coordinates (-2,0) and the fountain is placed at coordinates (-2,-2).

(A) Therefore, using the distance between two known points formula, the distance from the slide to the fountain is given by  

units.

Now, given that each unit on the grid represents 100 ft.

So, the distance from slide to the fountain is (100 × 2) = 200 ft. (Answer)

(B) Now, if each jump = 100 ft, then the slide is 2 jumps apart from the fountain. (Answer)

We know the distance between two known points on the coordinate plane () and () is given by the following formula

Distance =

there is no question content here, but you for the free points! : d

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!