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robert went to the grocery store and purchased cans of soup and frozen dinners. each can of soup has 300 mg of sodium and each frozen dinner has 500 mg of sodium. robert purchased a total of 14 cans of soup and frozen dinners which collectively contain 5200 mg of sodium. write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. define the variables that you use to write the system.

Let s stand for soup, and f stand for frozen dinners.

s + f = 14

s(300mg) + f(500mg) = 5200mg

Step-by-step explanation:

He bought 14 frozen dinners and soups all together, so whatever number you plug in for soups and frozen dinners has to equal 14. Then, you have to make the equations also equal 5200mg. So whatever you plug in for the first equation needs to also work for the second.

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