A rental car company offers a rental package for a midsize car. The cost comprises a fixed $30 administrative fee for the cleaning and maintenance of the car plus a rental cost of $35 per day. Using for the number of days and for the total cost in dollars, construct a function to model the relationship between the number of days and the total cost of renting a midsize car

y = 30 + 35(x)

Step-by-step explanation:

The complete question is as follows;

A rental car company offers a rental package for a midsize car. The cost comprises a fixed $30 administrative fee for the cleaning and maintenance of the car plus a rental cost of $35 per day. Using x for the number of days and y for the total cost in dollars, construct a function to model the relationship between the number of days and the total cost of renting a midsize car

Solution;

In this question, we are tasked with formulating a function to show the relationship between the total cost of the car rent-age and the number of days in which the car was rented

To construct a correct model, we have ti identify two things. Firstly, we need to identify the dependent variable and the independent variable. From the question, we can see that out of the two variables listed, it is the total cost of the car that is the dependent variable while the number of days is the independent variable.

This is because it is the total cost that depends on the number of days.

Hence, mathematically, by taking the other dependent factor which is constant into consideration, the equation we have formulated is below;

y = Administrative fee + rental cost(x)

Plugging the values from the question, we have;

y = 30 + 35(x)

x = 30 + 35y

Step-by-step explanation: Let the total cost be represented by letter x and let the number of days be represented by letter y.

The total cost function is such that, for every rental, a fixed amount of $30 is paid and is rightly called fixed which implies its a constant regardless of the number of days the car was rented out. Also the cost includes a daily rental fee of $35 per day. In other words, everyday means 35 dollars in addition to the 30 dollars already charged. Hence, for one day's rent, the charge would be a total of 30 dollars plus one times 35 dollars. For two day's rent, it would become, 30 dollars  plus two times 35 dollars, and so on.

Therefore, for y number of days, the cost of rental in total becomes;

x = 30 + 35y

Where x represents the total amount charged for the rental and y represents the number of days the car has been rented.

i think c. but don't trust it.

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!