The scale drawing of a rectangular room has a length of 18 inches and a width of 12 inches. If the scale for the drawing is 1 inch = 2 1/2 feet, what is the perimeter of the actual room?

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?

Abbey purchased a house using a fixed rate mortgage. the annual interest rate is 4.2% compounded monthly for 20 years. the mortgage amount is $235,000. what is the monthly payment on the mortgage? this isn't a multiple choice question have to show my work

Aball is dropped from a height of 10m above the ground. it bounce to 90% of its previous height on each bounce. what is the approximate height that the ball bounce to the fourth bounce?