Kara has 21 collectible buttons to sell. she sells the small buttons for $3 and the large buttons for $4, and earns a total of $68. if the small buttons are represented by x and the large buttons are represented by y, which of the following systems of equations can be used to calculate the number of large and small buttons sold?
a.) x + y = 21, 3x + 4y = 68
b.) x + y = 68, 3x + 4y = 21
c.) x + y = 21, 4x + 3y = 68
d.) x + y = 68, 4x + 3y = 21

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

answer: c.  

step-by-step explanation:

mixtures containing substances that get attracted to magnet can be separated using a magnet. we can separate iron from a mixture of sand and iron, as only iron attracts to the magnet.