How many quarts of peanut oil worth 19 cents a quart must be mixed with 100 quarts worth 25 cents a quart to produce a mixture which will be worth 24 cents a quart?

20 quarts of peanut oil worth 19 cents a quart must be mixed.

Step-by-step explanation:

Let x represent the number of quarts of peanut oil worth 19 cents a quart that would be in the mixture.

The total number of quarts in the mixture would be x + 100

The cost of the x quarts would be x × 19 = 19x cents

The cost of 100 quarts of the other peanut oil would be 25 × 100 = 2500 cents

The cost of the mixture would be

24(x + 100) = 24x + 2400

Therefore, the equation would be

19x + 2500 = 24x + 2400

24x - 19x = 2500 - 2400

5x = 100

x = 100/5

x = 20

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1