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Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable [tex]\( t \)[/tex], and the distance she rides is represented by the variable [tex]\( d \)[/tex]. This relationship is modeled with distance [tex]\( d \)[/tex] as a function of time [tex]\( t \)[/tex].

Which statements are true of the scenario? Select two answers.

A. The independent variable, the input, is the variable [tex]\( d \)[/tex], representing distance.
B. The distance traveled depends on the amount of time Marlene rides her bike.
C. The initial value of the scenario is 16 miles per hour.
D. The equation [tex]\( t = d + 16 \)[/tex] represents the scenario.
E. The function [tex]\( f(t) = 16t \)[/tex] represents the scenario.

Sagot :

GinnyAnswer
Let's analyze each statement one by one:

1. The independent variable, the input, is the variable [tex]\( d \)[/tex], representing distance.
- In this scenario, the time [tex]\( t \)[/tex] is the independent variable because it is what Marlene can control or choose. The distance traveled [tex]\( d \)[/tex] depends on the time spent riding. Hence, this statement is false.

2. The distance traveled depends on the amount of time Marlene rides her bike.
- This statement accurately describes the relationship because the distance [tex]\( d \)[/tex] is a function of time [tex]\( t \)[/tex]. The longer Marlene rides, the farther she will travel. Therefore, this statement is true.

3. The initial value of the scenario is 16 miles per hour.
- The phrase "initial value" typically refers to a starting point or value at time [tex]\( t = 0 \)[/tex]. However, 16 miles per hour is the rate at which Marlene rides, not an initial value. Therefore, this statement is false.

4. The equation [tex]\( t = d + 16 \)[/tex] represents the scenario.
- This equation implies an incorrect relationship between time [tex]\( t \)[/tex] and distance [tex]\( d \)[/tex]. The correct relationship is that distance [tex]\( d \)[/tex] is equal to the rate (16 miles per hour) multiplied by the time [tex]\( t \)[/tex]. Hence, this statement is false.

5. The function [tex]\( f(t) = 16t \)[/tex] represents the scenario.
- This function correctly models the scenario where [tex]\( f(t) \)[/tex] represents the distance [tex]\( d \)[/tex] traveled, which is the product of the rate (16 miles per hour) and the time [tex]\( t \)[/tex]. Therefore, this statement is true.

Based on the analysis, the two statements that are true for the scenario are:

- The distance traveled depends on the amount of time Marlene rides her bike.
- The function [tex]\( f(t) = 16t \)[/tex] represents the scenario.

So, the correct answers are:
- The distance traveled depends on the amount of time Marlene rides her bike.
- The function [tex]\( f(t) = 16t \)[/tex] represents the scenario.
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