Question

A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by the function f(m) = (m + 4)2 + 100, and the capacity of machine 2 is defined by the function g(m) = (m + 12)2 − 50, where m is the number of minutes the packaging machine operates. Create the function C(m) that represents the combined capacity of the two machines.

Answer 1

I assume that there is an operato ^ missing in each function and that the right functions are:

f(m) = (m+40)^2 + 10 and
g(m) = (m+12)^2 - 50

C(m) = f(m) + g(m)

To perform that sum you need to expand the two square parentheses, this way:

f(m) = (m+40)^2 + 10 = m^2 + 80m + 1600 + 10 = m^2 + 80m + 1610

g(m) = (m+12)^2 - 50 = m^2 + 24m + 144 - 50 = m^2 +24m + 94

Now you can add f(m) + g(m) = 2m^2 + 104m + 1704

Answer: c(m) = 2m^2 + 104m + 1704

Answer 2

The answer is a combination of the two functions. (Its a lot of work to write out so if you're on plato I'll just explain then give the answer)

Disrepute the exponent attached to the parentheses
(m+4)^2+100 and (m+12)^2-50

You end up with
m^2+16+100+m^2+144-50

Simplify and you get the answer of
2m^2+32m+210