Look at the attached screenshot

The length of the segment is 5 units.

Step-by-step explanation:

Step 1; First we calculate the length of segment AE in the pentagon ABCDE. To do this we use the formula

Distance = √ (x2 - x1)² + (y2 - y1)².

By plotting the points A and E we get their coordinates as A = (11, 3) and E = (11, 5). So distance between A (11, 3) and E (11, 5) where A is (x1, y1) and E is                          (x2, y2) is;

Distance = √ (11 - 11)² + (5 - 3)² = √ 0 + 4 = √4 = 2 units.

Step 2; To calculate the length of the segment , we multiply the scale factor with the length of the original segment length. So

Length of = Length of AE × = 2 × = 5 units.

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!