The required simplified value of B - A = -6.
<h3>What is simplification?</h3>
The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.
Since, line Ax + By = 3 and x + 3y = -5 are parallel than slope of both the line will be same,
m = -1/3 = -A/B
From above
A = B/3 - - - - -(1)
Now line Ax + By = 3 passed through the point (-7, 2). So,
-7A + 2B = 3
from equation 1
-7B/3 + 2B = 3
-B/3 = 3
B = -9
Now put B in equation 1
A = -9 / 3
A = -3
Here,
B - A = -9 + 3 = -6
Thus, the required simplified value of B - A = -6.
Learn more about simplification here: brainly.com/question/12501526
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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 
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