Ababysitter is trying to determine the ages of three children: jerome, keenan, and leitha. she knows the following facts about their ages: the sum of jerome’s and keenan’s ages is 18 years; the sum of jerome’s and leitha’s ages is 19 years; and the sum of keenan’s and leitha’s ages is 21 years. how old is keenan?

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?

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

He graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. which statement about the domain and range of each function is correct? the range of the transformed function and the parent function are both all real numbers greater than or equal to 4. the domain of the transformed function is all real numbers and is, therefore, different from that of the parent function. the range of the transformed function is all real numbers greater than or equal to 0 and is, therefore, different from that of the parent function. the domain of the transformed function and the parent function are both all real numbers.