A municipal electrical utility charges customers a $15 per month fee plus 12 cents per kilowatt- hour of energy used.

Write an equation for a customer's monthly costs, C (in dollars) for electric service as a function of r, the kilowatt-hours used.

a. C(x) 12 + 0.15x

b. C(z) = 15e0.12z

c. C(x) = 15 + 12z

d. C(z) = 15 + 0.12c

e. C(z)= 15(1.12)"

No option is correct.

Step-by-step explanation:

Modeling With Functions

The customer's monthly costs C expressed in dollars has two parts: one fixed cost regardless of the energy used ($15) and a variable cost (12 cents per kilowatt-hours). This can be expressed as 12/100*r = 0.12 r, being r the kilowatt-hours used. Joining both parts, we get the total cost expression as

From the options presented, none of them can be called as correct, only the option d. is close enough to the real answer, but the variables z and c used are not accurate.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .