Four freinds went to see a movie. each ticket cost $x. the table shows the prices of several items at the theater. they bought four large pretzels and four bottles of water. write and simplify an expression that represents the total cost of tickets and snack or beverages. large popcorn $4. large pretzel$3. small soda$2 bottle of water $2

Y= 4x+20

combine the cost of water and pretzels into 1

T=4x+20
t stands for the total.
x is the cost of each ticket. 
We have 4 friends and therefore four tickets so x is multiplied by 4. 
Four large pretzels are purchased at 3 dollars each which multiplies to equal 12 dollars.
Four bottles of water are purchased at 2 dollars each which multiplies to 8 dollars.
These two numbers add to 20 dollars. 
Therefore, the total is equal to four times the ticket cost (x) plus 20, or
t=4x+20

Answer

1 number

explanation

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.

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