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

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 break down each part of the question step-by-step:

### Denominator of Practice Ride 2

For Gilbert's second practice ride, the function modeling his time is given by [tex]\( b(x) = \frac{9}{x+2} \)[/tex], where [tex]\( x \)[/tex] represents his speed during the first ride. The denominator here is [tex]\( x+2 \)[/tex], which represents Gilbert's speed on the second ride increased by 2 miles/hour. This means that his speed during his second ride is 2 miles/hour more than his speed during the first ride.

### Total Time Function

To determine the total time Gilbert spent on his practice rides, we need to sum the times for each ride. The functions for each ride are:
- Practice Ride 1: [tex]\( a(x) = \frac{5}{x} \)[/tex]
- Practice Ride 2: [tex]\( b(x) = \frac{9}{x+2} \)[/tex]

Thus, the total time function [tex]\( T(x) \)[/tex] is the sum of these two functions:
[tex]\[ T(x) = a(x) + b(x) = \frac{5}{x} + \frac{9}{x+2} \][/tex]

### Filling in the Blanks

1. The denominator of the function that models practice ride 2 represents __the speed increased by 2 miles/hour__.
2. To find a function that models the total amount of time Gilbert spent doing practice rides on the race course, __sum__ the functions.

Therefore, the correct selections are:

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

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