Leo, Angie, and Scott are making frosting to decorate cookies. A recipe for one serving of frosting calls for 1 3/4 cups of sugar and 2 tablespoons of vanilla. They each brought the ingredients they had at home.

Leo brought 2 cups of sugar and 2/3 tablespoon of vanilla.
Angie brought 1 2/3 cups of sugar and 1 1/2 tablespoons of vanilla.
Scott brought 1 4/5 cups of sugar and 2 1/4 tablespoons of vanilla.
What is the maximum number of whole servings of frosting they can make with the ingredients they brought?

they can only make 2 servings.

Step-by-step explanation:

after all the vanila they get 4 5/12 and after all the sugar they get 5 7/15 which mean they can only make 2 serving becuase they only have 4 5/12 tablespoons of vanila. To have 3 servings they would need 6 table spoons of vanila

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.