2. The total cost of fixtures and luminaries for an office lighting installation is found by an electrician. The following fixtures and
luminaries are specified: 12 incandescent fixtures at $18 each, 22
semidirect fluorescent luminaries at $37 each, and 33 direct
fluorescent luminaries at $28 each. Find the total cost.

Asequence of numbers begins with 12 and progresses geometrically. each number is the previous number divided by 2. which value can be used as the common ratio in an explicit formula that represents the sequence? 1/2 2 6 12

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?

If you prove that ∆wxz is congruent to ∆yzx, which general statement best describes what you have proved?