What is -3(4x+3)+4(6x+1)? what is x when the answer is 41?

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?

Arestaurant chef made 1 1/2 jars of pasta sauce. each serving of pasta requires 1/2 of a jar of sauce. how many servings of pasta will the chef be able to prepare using the sauce?

Which of these side lengths could form a triangle a) 2 cm , 2 cm , 4 cm b) 3 cm , 5 cm , 10 cm c) 3 cm , 4 cm , 5 cm d) 4 cm , 8 cm , 15 cm