9. start from 110 feet away, a person on a bicycle rides towards a checkpoint and then it passes it. the rider is traveling at a constant rate of 30 feet per second. the distance between the bicycle and the checkpoint is given by the equation d=|110-3t|. at what times is the bike 40 feet away from the checkpoint?
a. 2.3 sec and 5 sec
b. 1.6 sec and 5 sec
c. 2.3 sec and 4.6 sec
d. 1.6 sec and 4.6 sec

A. 2.3 sec and 5 sec

Step-by-step explanation:

We are given that start from 110 feet away, a person on a bicycle rides towards a checkpoint and then it passes it. the rider is traveling at a constant rate of 30 feet per second.

The distance between the bicycle and the checkpoint is given by the equation :

Now we are required to calculate at what times is the bike 40 feet away from the checkpoint. So, substitute d = 40 in the equation

    and    

    and  

              and  

                  and  

                 and  

Hence at 2.3 sec and 5 sec  the bike is 40 feet away from the checkpoint.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

the one below it is a function