The total cost of renting the car can be represented by the expression that includes both the fixed fee and the variable cost based on the miles driven.
Eloise pays a fixed fee of $35 and an additional $0.10 for every mile she drives, which can be denoted as \(m\) (the number of miles driven).
The correct expression for the total cost \(C\) of renting the car would be:
\[ C = 35 + 0.10m \]
So, the correct choice from the options you provided is:
.10m + 35 (which can also be written as \(35 + 0.10m\)).