What is the average rate of change for f(x)=x^2-3x-10 from x=4 to x=6

The base of a triangle exceeds the height by 9 inches. if the area is 180 square inches, find the length of the base and the height of the triangle.

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?

The sum of two numbers is 0. twice the smaller number subtracted from 3 times the larger number is 10. let x represent the larger number and y represent the smaller number. what is the equation