The slope of a hill next to a highway decreases 2 vertical feet for every 3 horizontal feet away from the highway.
which function represents the vertical distance as a function of the horizontal distance, and what is the vertical distance, v(h), from the highway when the horizontal distance, h, is 12 feet?

a. v(h)=-3h+2, and the vertical distance is -34 feet.

b. v(h)=-3h-2, and the vertical distance is -38 feet.

c. v(h)=-3/2h, and the vertical distance is -18feet.

d. v(h)=-2/3h, and the vertical distance is -8 feet

Slope is the change in Y ( vertical) over the change in X( horizontal).

The slope would be -2 /3

You would multiply the horizontal distance by the slope:

-2/3 x 12 = -8

The answer would be D. v(h)=-2/3h, and the vertical distance is -8 feet.

answer: it is d

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4