Andrew owns a company that makes two different kinds of hot sauce and sells them to restaurants and stores. Both sauces are made from the same ingredients, but they vary in the number of green peppers and hot chili peppers used. Sauce I : yeilds 1 pint 6 green peppers 4 hot chili peppers Sauce II: yields 1 pint 3 green peppers 10 hot chilli peppers Andrew buys 975 green peppers and 1,250 hot chili peppers. He uses all of those peppers to make the two types of sauce. Andrew buys 975 green peppers and 1,250 hot chili peppers. He uses all of those peppers to make the two types of sauce. Write a system of equations that shows how Andrew can use the peppers to make x pints of Sauce I and y pints of Sauce II. Then graph (on the next slide) and solve the system. Explain what information is given by the solution of the system.

x^6

step-by-step explanation:

this is correct because:

x-6=0

0*x=0

so

x^6

9 x 8 divided by (5-3)=36

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

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