"The employees from maintenance go for coffee together every day at 9 AM. On Monday, Hector paid $5.45 for three cartons of milk, four cups of coffee and seven doughnuts. On Tuesday, Guillermo paid $5.30 for four milks, two coffees, and eight doughnuts. On Wednesday, Anna paid $5.15 for two milks, five coffees, and six doughnuts. On Thursday, Alphonse had to pay for five milks, two coffees, and nine doughnuts. How much change did he get back from his $10 bill?

The change will be $4.75

Step-by-step explanation:

Given data:

Monday

Total paid = 5.45

milk bought =3

coffee bought = 4

doughnuhts = 7

Tuesday

Total paid = 5.30

milk bought =4

coffee bought = 2

doughnuhts = 8

Wednesday

Total paid = 5.15

milk bought =2

coffee bought = 5

doughnuhts = 6

Thursday

Total paid = X

milk bought =5

coffee bought = 2

doughnuhts = 9

Let milk be m, Let coffee be c and Let doughnuts be d

3m + 4c + 7d = 5.45 (eqaution 1)

4m + 2c + 8d = 5.30 (equation 2)

2m + 5c + 6d = 5.15 (equation 3)

Using equation 1 and equation 2 ( to eliminate m)

3m + 4c + 7d = 5.45 (Multiply the whole equation by 4)

4m + 2c + 8d = 5.30 (Multiply the whole equation by 3)

12m + 16c +28d = 21.8

12m + 6c +24d = 15.9   (Subtracting the two equations)

0m +10c + 4d = 5.9

therefore 10c +4d = 5.9 (equation 4)

Using equation 2 and equation 3 (to eliminate m)

4m + 2c + 8d = 5.30 (Multiply the whole equation by 2)

2m + 5c + 6d = 5.15 (Multiply the whole equation by 4)

8m + 4c + 16d = 10.6

8m +20c +24d = 20.6  (Subtracting the two equations)

0m -16c -8d = -10

-16c -8d = -10 (equation 5)

Solving equation 4 and equation 5( to eliminate d)

10c +4d = 5.9 (Multiply whole equation by 8)

-16c -8d = -10 (Multiply whole equation by 4)

80c + 32d = 47.2

-64c  -32d = -40 (Adding the equations)

16c              =7.2

therefore c = 0.45

Substituting into equation 4

10(0.45) + 4d = 5.9

4.5 + 4d = 5.9

4d = 5.9-4.5

4d = 1.4

therefore d = 0.35

Substituting c and d into equation 1

3m + 4c + 7d = 5.45

3m + 4(0.45) + 7(0.35) = 5.45

3m + 1.8 + 2.45 = 5.45

3m = 5.45-2.45-1.8

3m = 1.2 therefore m = 0.4

Alphonse has to pay 3m + 2c + 9d

Alphonse change will be 10 - (3m + 2c + 9d) (Substituting m, c and d)

10- (3(0.4) + 2(0.45) + 9(0.35) = 10 -(1.2+0.9+3.15)

which simplifies to 10- 5.25=4.75

The change will be $4.75

1; 35 is the ratio

step-by-step explanation:

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