What does the triangle in front of a variable mean and how is it used?

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 15.

If sin θ=24/25 and 0 less than or equal to θ less than or equal to π/2, find the exact value of tan 2θ. answers; a) -527/336 b) -336/527 c)7/24 d) 24/7

Damon makes 20 cups of lemonade by mixing lemon juice and water. the ratio of lemon juice to water is shown in the tape diagram. lemon juice\text{lemon juice} lemon juice water\text{water} water how much lemon juice did damon use in the lemonade? cups