What is wrong with this "proof" ? "theorem: " for every positive integer n, if x and y are positive integers with max(x, y) = n, then x = y. "basis step: " suppose that n=1. if max(x, y) = 1 and x and y are positive integers, we have x = 1 and y=1. "inductive step: " let k be a positive integer. assume that whenever max(x, y) = k and x and y are positive integers, then x = y. now let max(x, y) = k + 1, where x and y are positive integers. then max(x – 1, y – 1) = k, so by inductive hypothesis, x – 1 = y – 1. it follows that x = y, completing the inductive step.

Carmen begins her next painting on a rectangular canvas that is 82.7 cm long and has a area of 8,137.68 cm2. will the painting fit in a frame with an opening that is 82.7 cm long and 95 cm wide? explain

The weight of an object in the water is 7% of its weight out of the water. what is the weight of a 652g object in the water?

Write the equation of a line that is perpendicular to the given line and that passes through the given point. –3x – 6y = 17; (6, 3) y = x – 9 y = 2x – 9 y = –2x – 9 y = x + 0 3. is the relationship shown by the data linear? if so, model the data with an equation. x y 1 5 5 10 9 15 13 20 the relationship is linear; y – 5 = (x – 1). the relationship is not linear. the relationship is linear; y – 5 = (x – 1). the relationship is linear; y – 1 = (x – 5). write an equation in point-slope form for the line through the given point with the given slope. (–10, –1); m = y + 10 = (x + 1) y – 1 = (x – 10) y – 1 = (x + 10) y + 1 = (x + 10) 5. write an equation for each translation of . 6.5 units up y + 6.5 = | x | y = | 6.5 x | y = | x | + 6.5 y = | x | – 6.5 6. write an equation for each translation of . 5.5 units right y = | x | + 5.5 y = | x – 5.5 | y = | x | – 5.5 y = | x + 5.5 | 7. which equation translates y = | x | by 8 units to the left? y = | x | – 8 y = | x | + 8 y = | x – 8| y = | x + 8|