The cost C ( x ) , where x is the number of miles driven, of renting a car for a day is $37 plus $0.95 per mile. What is the slope of the linear function and its units?

Slope is 0.95 and its unit is dollar per mile

Step-by-step explanation:

To write the slope and its units, what we first need to do is to write the given words in form of an equation.

Given that the cost is the dependent variable and the cost per mile the independent variable, we have;

C(x) = $0.95(x) + 37

Comparing to the general equation of a straight line;

y = mx + c

we can see that the slope is 0.95 and its unit is $/mile (dollars per mile)

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

my dear correct answer is option number 3