Need help please, i don’t get it

This is the same as saying x = 3 and x = 7.

========================================

Work Shown:

Plug x = 3 into f(x)

f(x) = (1/2)*|x-3| + 3

f(3) = (1/2)*|3-3| + 3

f(3) = 0.5*|0| + 3

f(3) = 0.5*0 + 3

f(3) = 0 + 3

f(3) = 3

-----------------------

Plug x = 5 into f(x)

f(x) = (1/2)*|x-3| + 3

f(5) = (1/2)*|5-3| + 3

f(5) = 0.5*|2| + 3

f(5) = 0.5*2 + 3

f(5) = 1 + 3

f(5) = 4

-----------------------

Plug x = 7 into f(x)

f(x) = (1/2)*|x-3| + 3

f(7) = (1/2)*|7-3| + 3

f(7) = 0.5*|4| + 3

f(7) = 0.5*4 + 3

f(7) = 2 + 3

f(7) = 5

-----------------------

Plug x = 3 into g(x)

g(x) = sqrt(x-3) + 3

g(3) = sqrt(3-3) + 3

g(3) = sqrt(0) + 3

g(3) = 0 + 3

g(3) = 3

-----------------------

Plug x = 5 into g(x)

g(x) = sqrt(x-3) + 3

g(5) = sqrt(5-3) + 3

g(5) = sqrt(2) + 3

g(5) = 1.414214 + 3

g(5) = 4.414214 ..... which is approximate

-----------------------

Plug x = 7 into g(x)

g(x) = sqrt(x-3) + 3

g(7) = sqrt(7-3) + 3

g(7) = sqrt(4) + 3

g(7) = 2 + 3

g(7) = 5

-----------------------

To summarize everything, refer to the table below.

The rows highlighted in yellow refer to when f(x) = g(x)

This happens twice when x = 3 and x = 7

If x = 3, then f(x) = g(x) = 3

If x = 7, then f(x) = g(x) = 5

Therefore, x = 3 and x = 7 are two solutions to f(x) = g(x)

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation: