Enrique drank 2 3/16 cups of coffee in 2 1/2 hours. how much coffee did he drink each hour? a. 4⁄5 of a cup b. 1 1⁄8 cups c. 5 15⁄32 cups d. 7⁄8 of a cup

Remark

This is sort of like a problem using d=r*t. The formula would be somewhat the same.

Givens

t  = 2 1/2 hours

C = Cups of coffee = 2 3/16

R = ??

Formula

C = R * T

Solution

2 3/16 = R * 2 1/2  Change to decimals

2.1875 = R * 2.5    Divide both sides by 2.5

R = 2.1875 / 2.5

R = 0.875 cups / hour

That's the same thing as 7/8 cup (just run through the answers with a calculator if you are not sure where that comes from).

third option: 6x+8

step-by-step explanation:

we can see that the given question is a sum of series and the values of n vary from 0 to 3

the first term will be:

when n=0, [(0)*x+2] => (0+2) => 2

when n=1, [(1)*x+2] => (x+2) => x+2

when n=2, [(2)*x+2] => 2x+2

when n=4, [(3)*x+2] => 3x+2

so adding up all the terms will give us:

=2+x+2+2x+2+3x+2

=x+2x+3x+2+2+2+2

=6x+8

so,

third option is the correct answer ..

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.