1. ## absolute value equations

I just started learning about absolute values so I am still very shaky in the concepts. If there are any sites that can help me learn more pls let me know. Thanks.

The fuel efficiency m(in miles per gallon) of a truck depends on the speed r (in miles per hour) at which it is driven. The relationship between m and r usually takes m = a l r- h l + k. For Sasha's truck, the optimal fuel efficiency is 24 miles per gallon, attained when the truck is driven at 50 miles per hour, When Sasha drives at 60 miles per hour, however, the fuel efficiency drops to only 20 miles per gallon.

a. Find another driving speed r for which the fuel efficiency for Sasha's truck is exactly 20 mpg.

24 = a l 50 - h l + k

20 = a l 60 - h l + k

I plugged in the numbers but I am not sure what to do with these.
were these equations supposed to help me get the answer?

Just guessing I think it will be 40 mph.

b. Fill in the rest of the missine entries in the table

r m

60 20
50 24
40 20
30 16
20 12
10 8

c. find the values of k, a, h

I don't know how to solve the equations to find the values and not sure about the other answers.

I really appreciate the help I get from everyone.

Vicky.

2. $\displaystyle m = a|r - h| + k$
You know that the graph of the absolute-value function is a V (either right side up or upside down). The vertex (point in the V) is given by (h, k), and this represents, in our case, the optimal fuel efficiency. So h = 50 and k = 24. We're given that when r = 60 mph, m = 20 mph, so plug in:
$\displaystyle 20 = a|60 - 50| + 24$

Solve for a:
$\displaystyle -4 = 10a$
$\displaystyle a = -0.4$

So our complete equation is
$\displaystyle m = -0.4|r - 50| + 24$.

01

3. I understand now. Thank you.

Vicky.