Answer:
x = 14.25
Step-by-step explanation:
Start with a^2 + b^2 = c^2
a = 11
b = x
c = 18
plug in and solve
11^2 + x^2 = 18^2
121 + x^2 = 324 - Simplify
x^2 = 203 - subtract 121 from both sides
x = 14.247 rounds to 14.25 - square root on both sides
Total capacity = sum of the individual production capacities.
Here,
Total capacity = sum of f(m) = (m + 4)^2 + 100 and g(m) = (m + 12)^2 − 50.
Then f(m) + g(m) = (m + 4)^2 + 100 + (m + 12)^2 − 50.
We must expand the binomial squares in order to combine like terms:
m^2 + 8 m + 16 + 100
+m^2 + 24m + 144 - 50
---------------------------------
Then f(m) + g(m) = 2m^2 + 32m + 160 + 50
f(m) + g(m) = 2m^2 + 32m + 210, where m is the number of
minutes during which the two machines operate.
8x + 84 = 500
8x = 416
x = 52
So if he wants to earn more than 500 dollars, he needs to make more than 52 dollars a week.