Jill is experimenting with three different strawberry smoothie recipes. She makes all three smoothies for each of her x friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6. Pick all the expressions that represent how many strawberries Jill needs for all the smoothies.

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Which graph represents the function g(x) = |x + 4| + 2?

Which of the following contains a variable?