Hansen and kirk went to an arcade where the machine took tokens hansen played 3 games of skee ball and 6 games of pinball using a total of 15 tokens at the same time kirk played 2 games of skee ball and 6 games of pinball using up 14 tokens how many tokens does each game require

skee ball = 1

pinball = 2

Step-by-step explanation:

Let's say skee ball game is S and pinball games is P. Hansen paid 15 tokens to play 3 games of skee ball and 6 games of pinball. Then the equation will be:

3S + 6P = 15

We can change the equation to solve for S

3S= 15- 6P

S= 5-2P

Kirk paid 14 tokens to play 2 games of skeel ball and 6 games of pinball. The equation is:

2S + 6P = 14

We can substitute the first equation that solves for S to this

2(5-2P) + 6P = 14

10-4P + 6P= 14

2P= 14-10

2P=4

P=2

Then we can put P to the first equation to find S value

S= 5-2P

S= 5-2(2)

S=1

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.