Answer:
Part A) The proportional equation is 
Part B) 8 hours of training
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form 
or 
Let
c -----> the cost to hire a dog
h ----> the amount of time in hours
The linear equation is equal to
Sue spent $660 on 12 hours of obedience training for her dog Muffin
Find the value of k (constant of proportionality)
substitute the values
therefore
The linear equation is
For 
Find the value of h
substitute in the equation and solve for h
Recall that the vertex form of a quadratic function (or parabolic function) is equal to
Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.
One concept that we must remember when completing the square is that
(a + b)² = a² + 2ab + b²
So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.
So, going back to the function, we have
Thus, we have derived the vertex form of the function.
Answer: f(x) = (x + 7)² - 9
<span>x ≥ -80/3 is the answer
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