The school cafeteria ordered macaroni and cheese for their monthly supplies. in the past 2 months they ordered 178 and 224 boxes for $105.02 and $132.16 respectively. both times they had too much left over so this month they decided to buy 103 boxes. how much did they spend on macaroni and cheese this month?

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?

How do the definitions, properties, and postulates you've learned about line segments, parallel lines, and angles to define the shapes of polygons

Consider the following equation. 1/2x^3+x-7=-3sqrtx-1 approximate the solution to the equation using three iterations of successive approximation. use the graph below as a starting point. a. b. c. d.