Prove that given any 17 integers, there exist nine of them whose sum is divisible by 9.

(it might to use the fact that given any five integer you can find three whose sum is divisible by 3)

Restrictions on f(x) = 1/x+5 and g(x) = x-2

Beth makes batches of bluberry muffins and banna muffins. each batchis 6 muffins. she makes 2.5 batches of bluberry muffins. how many batches of bananna muffins should beth make if she wants to have a total of 60 muffins?

Mary beth used the mapping rule to find the coordinates of a point that had been rotated 90° counterclockwise around the origin. examine the steps to determine whether she made an error. m (3, –6) is rotated 90° counterclockwise. (x, y) → (–y, x) 1. switch the x- and y-coordinates: (6, –3) 2. multiply the new x-coordinate by –1: (6(–1), –3) 3. simplify: (–6, –3) .