Use mathematical induction to prove that the statement is true for every positive integer n. show your work.

2 is a factor of n2 - n + 2

Find two consexutive odd integers such that the sum of their square is 650

Alice is paying her bill at a restaurant. but tax on the cost of a male is 5%. she decides to leave a tip 20% of the cost of the meal plus the tax

Tyler went to the supermarket to buy food for a food pantry. he has $36, and can carry up to 20 pounds of food in his backpack. pasta costs $1 for a 1-pound package. pasta sauce costs $3 for a 1.5 pound jar. let x = the number of packages of pasta and y = the number of jars of pasta sauce. one package of pasta is the right amount to go with one jar of pasta sauce. what is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry? how many packages of pasta? how many jars of pasta sauce? explain your reasoning.