At a given time, the length, L, of the shadow of an object varies directly as the height of the object, H. If the shadow is 27 ft when the height of
the object is 12 ft, what is the height of the object if the shadow is 18 ft?

8 ft

Step-by-step explanation:

Use the direct variation equation, y = kx, where k is a constant.

Change the equation to fit the variables: L = kH

Plug in the given length of the shadow and the height of the object, then solve for k:

L = kH

27 = k(12)

2.25 = k

So, the equation is L = 2.25H

Then, plug in 18 as L, and solve for H:

L = 2.25H

18 = 2.25H

8 = H

So, when the shadow is 18 feet, the height of the object is 8 ft

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is