The cost to fill a car's tank with gas and get a car wash is a linear function of the capacity of the tank. the costs of a fill-up and a car wash for three different customers are shown in the table. write an equation for the function in slope-intercept form. then, find the cost of a fill-up and a car wash for a customer with a truck whose tank size is 25 gallons.

Step-by-step explanation:

To right the linear equation in slope-intercept form, we first need to find the slop, which is defined

Now, we choose to points from the table and . Using this points, we calculate the slope.

Now, using one point and the slope, we find the point-slope form, which is gonna give us the slope-intercept form:

Therefore, the right choice is the first one, because it's the only one that has this linear equation.

In addition, to find the cost for a car with 25 gallons of gas size, we just have to replace this number in the x-variable:

Therefore, the cost for a truck with a tank size of 25 gallons, is $55.75.

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step-by-step explanation:

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: