Answer:
x = 12
Step-by-step explanation:
Vertical angles are congruent, so ...
4x = 48°
x = 12° . . . . . . divide by 4
A function that gives the amount that the plant earns per man-hour t years after it opens is 
<h3><u>Solution:</u></h3>
Given that
A manufacturing plant earned $80 per man-hour of labor when it opened.
Each year, the plant earns an additional 5% per man-hour.
Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.
Amount earned by plant when it is opened = $80 per man-hour
As it is given that each year, the plants earns an additional of 5% per man hour
So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)
Amount earned by plant after two years is given as:

Similarly Amount earned by plant after three years 

Hence a function that gives the amount that the plant earns per man-hour t years after it opens is 
You'll want to use the quadratic formula:
-b (+/-) sqrt(b^2 - 4ac), all divided by 2a.
Under the square root you'll get:
-11
remember that the square root of -1 is i.
sqrt(-11) can be factored to sqrt(11*-1) and then sqrt(-1) * sqrt(11)
which becomes i*sqrt(11)
so your complex solution is:
-3 (+/-) (i*sqrt(11)), all over 4