For all real numbers, if vr is irrational then r isirrational.
if true, give a rigorous proof, and if false give adisproof by
counterexample
prove that for all integers n, if n is not divisible by 2 or3,
then n^2 +23 is divisible by 12.

Rose and andrew are financing $128,000 to purchase a condominium. they obtained a 15-year, fixed-rate loan with a rate of 5.05%. they have been given the option of purchasing up to four points to lower their rate to 4.81%. how much will the four points cost them?