You want to prove a theorem in a two-column proof. you start with your given statement and list deductions in the left-hand column. what are the three main types of reasoning you will use for reasons in the right-hand column? (ps this is not multiple choice it is open answer)

In a young single person's monthly budget, $150 is spent on food, $175 is spent on housing, and $175 is spend on other items. suppose you drew a circle graph to represent this information, what percent of the graph represents housing?

Frank is lending $1,000 to sarah for two years. frank and sarah agree that frank should earn a real return of 4 percent per year. instructions: a. the cpi (times 100) is 100 at the time that frank makes the loan. it is expected to be 113 in one year and 127.7 in two years. what nominal rate of interest should frank charge sarah?

Which of the following constants can be added to x2 - 3x to form a perfect square trinomial?