Let L be the line given by the span of ⎡⎣⎢−6−5−9⎤⎦⎥ in R3. Find a basis for the orthogonal complement L⊥ of L.

Orly uses 2 cups of raisins for every 12 cups of trail mix she makes. how many cups of trail mix will she make if she uses 8 cups of raisins?

Twice the sum of a number and 4 is equal to three times the difference of the number and 7. find the number.

Suppose that sahil knows that 45 people with ages of 18 to 29 voted. without using a calculator, he quickly says then 135 people with ages of 30to 49 voted. is he correct? how might sohil have come up with his answer so quickly?