Question

Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and the distance she rides is represented by the variable d. Which statements are true of the scenario? Check all that apply.

*The independent variable, the input, is the variable d, representing distance.
*The distance traveled depends on the amount of time Marlene rides her bike.
*The initial value of the scenario is 16 miles per hour.
*The equation t = d + 16 represents the scenario.
*The function f(t) = 16t represents the scenario.

Answer 1

The distance traveled depends on the amount of time Marlene rides her bike. The initial value of the scenario is 16 miles per hour. The function f(t) = 16t represents the scenario.

Step-by-step explanation:

The statements that are true of the scenario are:

The distance traveled depends on the amount of time Marlene rides her bike. This is because the distance Marlene travels is determined by the time she spends riding her bike. The longer she rides, the farther she will go.

The initial value of the scenario is 16 miles per hour. This means that when Marlene starts riding her bike, she is going at a speed of 16 miles per hour.

The function f(t) = 16t represents the scenario. This function shows the relationship between the time Marlene rides her bike (t) and the distance she travels. The distance is directly proportional to the time, with a rate of 16 miles per hour.

Answer 2

Let

t--------> the time in hours

d-------> the distance in miles

we know that

`d=16t`

this is a linear equation that represent the scenario

in this equation the independent variable is the time t and the dependent variable is the distance d

The distance's equation in function notation is equal to

`f(t)=16t`

Using a graph tool

see the attached figure

The domain of the function is the interval----------> [0,∞)

`t\geq0`

The range of the function is the interval-------> [0,∞)

`f(t)\geq0`

Statements

a) The independent variable, the input, is the variable d, representing distance

The statement is false

Because the independent variable is the variable t

b) The distance traveled depends on the amount of time Marlene rides her bike

The statement is true

Because the distance's equation in function notation is equal to

`f(t)=16t`

c) The initial value of the scenario is 16 miles per hour

The statement is false

Because
`16` represent the rate or the slope of the linear equation

d) The equation t = d + 16 represents the scenario

The statement is false

Because, the scenario is represented by the function
`f(t)=16t`

e) The function f(t) = 16t represents the scenario

The statement is true