Graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function. f(x) = 4^x g(x) = 4x^2 x = -1 x = 0 x = 1 x = 2

Teams of 4 are competing in a 1/4 mile relay race. each runner must run the same exact distance. what is the distance each teammate runs?

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?

1. find the area of the unshaded square 2. find the area of the large square 3. what is the area of the frame represented by the shaded region show