Answers

1. Answer:

   At 2 hours, the traveler is 725 miles from home.

   At 3 hours, the distance is constant, at 875 miles.

   The total distance from home after 6 hours is 1,062.5 miles.

   Step-by-step explanation:

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2. The true statements are (b), (d) and (e)

   • At 2 hours, the traveler is 725 miles from home.
   • At 3 hours, the distance is constant, at 875 miles.
   • The total distance from home after 6 hours is 1,062.5 miles.

   How to determine the times and distances are represented by the function?

   From the function, we have the following piecewise function and the domains

   D(t) = 300t + 125, 0 ≤ t < 2.5

   D(t) = 875, 2.5 ≤ t ≤ 3.5

   D(t) = 75t + 612.5, 3.5 < t ≤ 6

   When t = 2, we use the domain 0 ≤ t < 2.5

   So, we have

   D(2) = 300 * 2 + 125

   Evaluate the product

   D(2) = 600 + 125

   Evaluate the sum

   D(2) = 725 — this is true

   When t = 3, we use the domain 2.5 ≤ t ≤ 3.5

   So, we have

   D(t) = 875

   This gives

   D(3) = 875 — this is true

   When t = 6, we use the domain 3.5 < t ≤ 6

   So, we have

   D(t) = 75t + 612.5

   This gives

   D(6) = 75* 6 + 612.5

   Evaluate the product

   D(6) = 450 + 612.5

   Evaluate the sum

   D(6) = 1062.5 — this is true

   Hence, the true statements are (b), (d) and (e)

   Read more about piecewise functions at:

   https://brainly.com/question/19030976

   #SPJ1

   Complete question

   Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.

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