An oil company fills 1 over 12 of a tank in 1 over 3 hour. At this rate, which expression can be used to determine how long will it take for the tank to fill completely?

4

Step-by-step explanation:

Don't let fractions fool you.

of a tank in  an hour is equal to:

1/12 of a tank in 20 minutes.

Thus we know in an hour, an oil company can fill 3/12 of a tank (60 minutes in an hour).

3 x 4 = 12, and 12/12 = 1(a whole tank), so we multiply 1 (hour) by 4.

Our answer is that it takes 4 hours to fill a tank.

it's  1/3 ⋅ 12 hours

or

3 ⋅ 12 hours

Step-by-step explanation:

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.

ok

step-by-step explanation: