Asmall shelf sits on two braces that are in the shape of a right triangle. the leg (brace) attached to the wall is 4.5 inches and the hypotenuse is 7.5 inches. the leg holding the shelf is the same length as the width of the shelf. what is the width of the shelf?

The width of the shelf is 6 inches.

Step-by-step explanation:

The leg (brace) attached to the wall is 4.5 inches.

The length of the  hypotenuse =  7.5 inches.

Also, the Length of leg holding the shelf =  Width of the shelf

Now, as the brace is in the shape of right triangle.

In a Right Triangle, by PYTHAGORAS THEOREM:

Putting here the values of hypotenuse and base, we get:

So, the length of the leg = 6 inches

Hence, the width of the shelf is 6 inches.

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!