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Terry is trying to place a satellite dish on the roof of his house at the recommended height of 18 feet. His house is 32 feet wide, and the height of the roof can be described by the function below,where x is the distance along the width of the house. Where should Terry place the dish? h(x) = -3/2 | x - 16 | + 24 A: No place is high enough B: Right at top C: 12 or 20 feet from the edge D: 4 or 28 feet from the edge

Respuesta :

Answer:

C: 12 or 20 feet from the edge

Step-by-step explanation:

We are told the recommended height is 18 feet and that the function describing the height is;

h(x) = -(3/2)|x - 16| + 24

This means that;

-(3/2)|x - 16| + 24 = 18

Multiply through by -2/3 to give;

|x - 16| + 24(-2/3) = 18(-2/3)

|x - 16| - 16 = -12

Add 16 to both sides to get;

|x - 16| = 16 - 12

|x - 16| = 4

Add 16 to both sides to get;

Expanding the absolute value problem, we have;

x - 16 = 4 or -(x - 16) = 4

Thus;

x = 16 + 4 or -x + 16 = 4

x = 20 or x = 16 - 4

x = 20 or x = 12

Since x is the distance along the width of the house, then Terry should place the dish 12 or 20 feet from the edge

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