The school cafeteria is offering a choice of two side dishes at lunch today either watermelon or french fries the ratio of the number of orders of french fries to the total number of side dishes ordered is 9:14 A: there are 9 orders of french fries for every 14 orders of watermelon

B:there are 5 orders of watermelon for every 9 orders of french fries

C: there are 14 orders of french fries for every 9 orders of watermelon

D: there are 5 orders of french fries for every 9 orders of watermelon

B

Step-by-step explanation:

Here, we are to select the best option that defines the ratio given in the question;

From the question, we are told that the ratio of french fries to the number of side dishes ordered is 9:14

Since 9 represents the french fries, then the ratio representing water melon orders will be 14-9 = 5

Hence, the ratio of french fries orders to water melon orders will be 9:5

The correct option is thus;

There are 9 orders of french fries for every 5 orders of watermelon

Or

There are 5 orders of watermelon for every 9 orders of french fries

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.

b

step-by-step explanation:

calculate the scale factor as the ratio of corresponding sides, image to original, that is

scale factor = = = = 1