Jamal owes $424.04 on his credit card. He returns two items, one for $49.95 and the other for $50.42. Then he makes purchases of $39.19 and $37.41. What is the new balance on the card?

$400.27

Step-by-step explanation:

owes $424.04

returns an item for $49.95

-424.04 + 49.95 = -374.09

he now owes $374.09

returns an item for $50.42

-374.09 + 50.42 = -323.67

he now owes $323.67

makes a purchase of $39.19

-323.67 - 39.19 = -362.86

he now owes $362.86

makes a purchase of $37.41

-362.86 - 37.41 = -400.27

he now owes $400.27

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.