Answer :
We are given that the truck rental company charges a flat rate of \[tex]$35 plus \$[/tex]0.20 per mile. This means the cost function is
[tex]$$
f(x)=0.20x+35,
$$[/tex]
where [tex]$x$[/tex] is the number of miles driven.
Step 1. Write the function.
The cost for driving [tex]$x$[/tex] miles is
[tex]$$
f(x)=0.20x+35.
$$[/tex]
This matches option D.
Step 2. Calculate the cost for 20 miles.
Substitute [tex]$x=20$[/tex] into the function:
[tex]$$
f(20)=0.20(20)+35=4+35=39.
$$[/tex]
This matches option A.
Step 3. Check other options.
- For option B: [tex]$f(30)$[/tex] should be calculated as
[tex]$$
f(30)=0.20(30)+35=6+35=41,
$$[/tex]
which does not match the given [tex]$f(30)=42$[/tex].
- For option C: [tex]$f(40)$[/tex] should be calculated as
[tex]$$
f(40)=0.20(40)+35=8+35=43,
$$[/tex]
which does not match the given [tex]$f(40)=45$[/tex].
- Option E represents another cost function, but it is written as
[tex]$$
f(x)=0.20x+35x=(0.20+35)x=35.20x.
$$[/tex]
This is incorrect because it does not include the flat fee of \[tex]$35 properly; instead, it suggests an additional mileage cost, which is not the case.
Final Answer:
The two correct responses are option A ($[/tex]f(20)=39[tex]$) and option D ($[/tex]f(x)=0.20x+35$).
[tex]$$
f(x)=0.20x+35,
$$[/tex]
where [tex]$x$[/tex] is the number of miles driven.
Step 1. Write the function.
The cost for driving [tex]$x$[/tex] miles is
[tex]$$
f(x)=0.20x+35.
$$[/tex]
This matches option D.
Step 2. Calculate the cost for 20 miles.
Substitute [tex]$x=20$[/tex] into the function:
[tex]$$
f(20)=0.20(20)+35=4+35=39.
$$[/tex]
This matches option A.
Step 3. Check other options.
- For option B: [tex]$f(30)$[/tex] should be calculated as
[tex]$$
f(30)=0.20(30)+35=6+35=41,
$$[/tex]
which does not match the given [tex]$f(30)=42$[/tex].
- For option C: [tex]$f(40)$[/tex] should be calculated as
[tex]$$
f(40)=0.20(40)+35=8+35=43,
$$[/tex]
which does not match the given [tex]$f(40)=45$[/tex].
- Option E represents another cost function, but it is written as
[tex]$$
f(x)=0.20x+35x=(0.20+35)x=35.20x.
$$[/tex]
This is incorrect because it does not include the flat fee of \[tex]$35 properly; instead, it suggests an additional mileage cost, which is not the case.
Final Answer:
The two correct responses are option A ($[/tex]f(20)=39[tex]$) and option D ($[/tex]f(x)=0.20x+35$).
