Guys, I need help for questions #10 and #11 of 4.5 Modelling With Algebra from Hung Vuong Learning Centre like immediately: Take a look at 2 of the images below and answer it as soon as possible!

I will give anyone a Brainliest to see if whoever got the best answers with the best effort and step-by-step explanations, well good luck guys and I check anyone’s answers to see if it’s appropriate for me! :)

X2 + y 2 = 36 x + y = 6 solve the system of equations.

1- 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.2- 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 the first question?

"which statement is necessarily true if bd is an altitude to the hypotenuse of right ? abc? a.) ? adb? ? bdc b.) ? adb~? bdc c.) abbc=acbd d.) ? bac? ? bdc"