Answered

Select the correct answer from each drop-down menu.

Gilbert is training for a bike race. As part of his training, he does practice rides on portions of the actual race course. Gilbert's first practice ride covers 5 miles of the course, and his second practice ride covers 9 miles of the course. Between these practice rides, he increases his average speed by 2 miles/hour.

These functions model the time it took Gilbert to do each practice ride, where [tex]\(x\)[/tex] is his speed during the first practice ride.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Practice Ride 1 & Practice Ride 2 \\
\hline
$a(x)=\frac{5}{x}$ & $b(x)=\frac{9}{x+2}$ \\
\hline
\end{tabular}
\][/tex]

The denominator of the function that models practice ride 2 represents the [tex]\(\square\)[/tex].

To find a function that models the total amount of time Gilbert spent doing practice rides on the race course, [tex]\(\square\)[/tex] the functions.



Answer :

GinnyAnswer
Let's analyze the given functions and the information provided in the problem to select the correct answers from each drop-down menu.

The functions given are:
- For Practice Ride 1: [tex]\( a(x) = \frac{5}{x} \)[/tex]
- For Practice Ride 2: [tex]\( b(x) = \frac{9}{x+2} \)[/tex]

### Denominator of the Practice Ride 2 Function:
The function [tex]\( b(x) = \frac{9}{x+2} \)[/tex] represents the time for the second practice ride, where [tex]\( x \)[/tex] is Gilbert's speed during the first ride. The denominator [tex]\( x+2 \)[/tex] is the speed during the second practice ride, as he increased his speed by 2 miles per hour between the first and second rides.

Thus, the denominator of the function that models practice ride 2 represents the speed during the second practice ride.

### Function for the Total Time:
To find a function that models the total amount of time Gilbert spent doing practice rides on the race course, we need to combine the time taken for the first practice ride and the time taken for the second practice ride. This involves summing the two functions [tex]\( a(x) \)[/tex] and [tex]\( b(x) \)[/tex].

Thus, to find a function that models the total amount of time, sum the functions.

Putting it all together:

- The denominator of the function that models practice ride 2 represents the speed during the second practice ride.
- To find a function that models the total amount of time Gilbert spent doing practice rides on the race course, sum the functions.