Which story problem could be solved using the given equation? 1/3×7/8=m julia has a bucket that contains 7/8 gallon of water. she wants to pour the water to fill some dog bowls. each bowl holds 1/3 gallon of liquid. how many dog bowls can julia fill with water? the city park has an area of 7/8 square kilometer. the width of the park is 1/3 kilometer. what is the length of the park? bo is carrying a bag of topsoil that is 7/8 full. he drops the bag and 1/3 of the soil pours out onto the ground. how much of the bag of soil poured onto the ground? kai has a rope that is 7/8 meter long. kai cuts off a piece that is 1/3 meters long. how long, in meters, is the piece of rope after he cuts it?

the city one, if the dog bowl is an option, then that one two

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.