The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs three times as much (per unit area) as glass, use Lagrange multipliers to find the dimensions of the aquarium that minimize the cost of the materials. (Enter the dimensions as a comma separated list.)

Consider the table below. x y -1 -5 0 5 1 11 2 13 3 11 complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.

Ben is three times as old as samantha, who is two years older than half of michel's age. if michel is 12. how old is ben?

Mrs. morton has a special reward system for her class. when all her students behave well, she rewards them by putting 3 marbles into a marble jar. when the jar has 100 or more marbles, the students have a party. right now, the the jar has 24 marbles. how could mrs. morton reward the class in order for the students to have a party?