You are buying ribbon to make costumes for a school play. Organza ribbon costs $.07 per yard. Satin ribbon costs $.04 per yard. Write an equation to model the possible combinations of yards of organza ribbon and yards of satin ribbon you can buy for $5. List several possible combinations.

Let's define the variables:

x = yards of Organza ribbon that you buy.

y = yards of Satin ribbon that you buy.

We know that the price per yard of Organza ribbon is $0.07, this means tat if you buy x yards, the cost will be:

C = x*$0.07

And the cost of the Satin ribbon is $0.04, so if you buy y yards of that ribbon, the cost will be:

C = y*$0.04

Adding that together, the total cost is:

C = x*$0.07 + y*$0.04

Now we know that you pay $5, this means that the total cost is exactly $5, then we have the equation:

$5 = x*$0.07 + y*$0.04

Now we can isolate the variable y to get:

y = ($5/$0.04) - x*($0.07/$0.04)

y = 125 - x*1.75

Now we can just input different values of x to find the correspondent value of y.

This means that:

if x = 0 (0 yards of the Organza ribbon)

then:

y = 125 - 0*1.75 = 0

This combination is:

0 yards of organza, and 125 yards of satin.

Now, if x = 20, then:

y = 125 - 20*1.75  = 90

This combination is:

20 yards of organza, and 90 yards of satin.

if x = 40, then:

y = 125 - 40*1.75 = 55

This combination is:

40 yards of organza, and 55 yards of satin.

The 3 combinations that we found cost exactly $5.

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