For f (x), evaluate the following: a, f(0) b. f(6) Show all of your work

Mathematics

1 answer:

Anestetic [448]3 years ago

5 0

Answer:

a). f(0) = 4

b). f(6) = 8

Step-by-step explanation:

a). When x < 5, piecewise function to be considered,

f(x) = x + 4

Since, x = 0 is less than x = 5

f(0) = 0 + 4

f(0) = 4

b). When 5 ≤ x < 7,

Piecewise function to be considered,

f(x) = 8

Therefore, for x = 6,

f(6) = 8

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Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) an

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The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.

Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165

Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters

Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012

Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters

Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.