Consider m = y2 - y1/ x2 - x1 . which x1 and x2-values would determine that the line is vertical? justify your answer

Given the points a(-2, 1) and b(8, 6), find the coordinates of the point c on directed line segment ab, that partitions ab in the ration 2: 3.

The revenue each season from tickets at the theme park is represented by t(c)=5x. the cost to pay the employees each season is represented by r(x)=(1.5)^x. examine the graph of the combined function for total profit and estimate the profit after four seasons

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.