A small triangular lot has three sides of different length. The second side is 11 feet longer than the first side. The third side is 8 feet less than twice the first side. The perimeter of the lot is 71 feet. How long is the third side? A) 28 ft
B) 38 ft
C) 17ft
D) 26ft

first side = 17 ft

second side = 28 ft

third side = 26 ft

Step-by-step explanation:

a + b + c  = 71

b = a + 11

c = 2a - 8

a = first side lenght

b = second side lenght

c = third side lenght

a + (a+11) + (2a-8) = 71

4a + 11 - 8 = 71

4a + 3 = 71

4a = 71 - 3

4a = 68

a = 68/4

a = 17

b = a + 11

b = 17 + 11

b = 28

c = 2a - 8

c = 2*17  -  8

c = 34 - 8

c = 26

Check:

17 + 28 + 26 = 71

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42

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!