The sum of two positive integers, a and b, is at least 30. the difference of the two integers is at least 10. if b is the greater integer, which system of inequalities could represent the values of a and b?

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.

what i would say the best answer is a. 40.5