5. Liz's resting heart rate is 64 beats per minute. During a recent workout, she measured her heart rate to be 112 beats per minute. By what percentage did her heart rate increase during her workout?

In simplified exponential notation, the expression a^2•a^-3•a 1/a 0

Aline on the wall and a line on the floor are skew. always, sometimes, or never?

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?