For this problem, we are given a quadratic equation that models the total amount spent on clothing and footwear in the years 2000-2009. We need to use the model to determine the maximum amount spent during the period.
The equation is shown below:
Since the leading term is negative, the vertex of this function will represent an absolute maximum value. Therefore we can determine the vertex to answer the problem, the vertex's coordinates are given below:
Then we have:
In the year 2008, 384 billion was spent on clothing and footwear.
Since our line is perpendicular to this line, the slope of
our line is the negative reciprocal of 1/4, which is -4/1.
Remember, negative reciprocal is just a fancy way
of saying flip the fraction and change the sign.
So the slope of our line is -4/1 and we use this slope along
with our given point to write the equation of our line.
Start with the point-slope formula.
Y - y1 = m(x - x1).
~Substitute
Y - -2 = -4/1(x - 5).
Minus a negative is plus a positive.
Y + 2 = -4/1x + 20.
Subtract 2 from both sides.
Y = -4/1x + 18
So, our answer is C.
Combine the numbers with the same variable
18a + 9a = 27a
24b + 14b = 38b
your answer is 27a +38b
