Suppose in exercise 7.1, the test for starch and for reducing sugars was positive after 1-hour incubation, but after the tubes incubated for 2-hours the test for starch was negative. how could you explain these results?

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?

Donald has x twenty-dollar bills and 11 ten-dollar bill. how much money does donald have? write your answer as an expression.

What is the inverse of the function f(x) = 2x + 1?