Ineed to learn how to solve this problem

x = 7/2, so every side equals 15.

Step-by-step explanation:

The first thing you want to notice about this problem is that keyword "equilateral." That means every one of the sides are equal, and that means you can play around with the algebra to get your answer.

In an equilateral triangle, if you have two sides 4x + 1 and 6x - 6, these sides must be equal. To solve for x, simply set these two equations equal to each other. Note that you can pick any pairing of the three sides and get the same answer; I only chose these because they look easier.

4x + 1 = 6x - 6 ... subtract 4x from both sides

1 = 2x - 6 ... add 6 to both sides

7 = 2x ... solve for x

x = 7/2

You get the same answer if you try 8x - 13 = 4x + 1, and if you do 8x - 13 = 6x - 6. Now that you have the value of x, take that and plug it into ANY of the sides to get the length. (It would be good to plug 7/2 into all of them to check your work!)

4(7/2) + 1 = 15

So the lengths are all 15 feet each.

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!