Vicki has 210 baseball cards and buys an additional 15 cards every week. jeb has 275 baseball cards and buys an additional 10 cards every week. after how many weeks will vicki and jeb have the same number of baseball cards?

13 weeks

Step-by-step explanation:

X = number of weeks

Vicki = 210 + 15(x)

Jet = 275 + 10(x)

210 + 15(x) = 275 + 10(x)

Find like terms

5x=65

Isolate the variable

5x = 65

5      5          65 divide by 5= 13

*If you need to check substitute 13 for x in the equation and see if it is correct*

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.