Two consecutive positive integers form part of a pythagorean triple. always, never, or sometimes?

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?

Using only the digits 5, 6, 7, 8, how many different three digit numbers can be formed if no digit is repeated in a number?

In the diagram below,abc is congruent to dec what is the value of x