A helium balloon on a string is tethered to a fence outside of a house. The altitude of the balloon can
be represented by the rational number 12 1/4 feet.
The string breaks and the balloon ascends 20 feet
per minute for 5 minutes. The helium then begins
to leak out of the balloon, causing it to descend at
3 1/2 feet per minute for 4 minutes. What is the
elevation of the balloon after it descends for 4
minutes?

Compare the cost of the bike trips from the two companies shown.for both the cost in a linear function of the number of days which statements is true

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?

Rewrite the following quadratic functions in intercept or factored form. show your work. y = 4x^2 - 19x- 5