Karen is buying pens and pencils for the new school year. she wants to have no more than 25 writing utensils in all. she also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

An appliance store sells a washer-dryer combination for $1800. if the washer costs $300 more than the dryer, find the cost for each appliance.

Let f(x) = 3 − x . find the average rate of change of f(x) from x = a to x = a + h and simplify your answer so that no single factor of h is left in the denominator.

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?