An amusement park collected $15,513 in revenue from ticket sales one day. They charge $30 for adults and $9 for children. If there were 865 people in attendance that day, how many were adults?

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?

Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 4 p plus 4 x plus 2 pxequals56. suppose also that p and x are both functions of time, measured in days. find the rate at which x is changing when xequals2, pequals6, and startfraction dp over dt endfraction equals1.5.

Which function is represented by the graph? a. f(x)=|x-1|+3 b. f(x)=|x+1|-3 c. f(x)=|x-1|-3 d. f(x)=|x+1|+3