8. find a simple closed formula for -1)4k. prove your answer using induction. hint: try computing the first several partial sums, to guess at what the closed formula might be

What expression is equivalent to 42x-56y

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

The measures of the legs of a right triangle are 15m and 20m . what is the length of the hypotenuse