On a coordinate plane, a parabola opens up. It goes through (negative 7, 5), has a vertex at (negative 4, negative 4), and goes through (negative 1, 5). The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = –4. The domain is all real numbers. The range is all real numbers. The function is increasing over (–∞, –4). The x-intercepts are at (–6, 0) and (–2, 0)

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

What is the area of the trapezoid shown ?