A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 120 gallons of a mixture that contains 85% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

The graph shows the charges for a health club in a month. make a function table for the input-output values. writes an equation that can be used to find the total charge y for the number of x classes

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?