Adoll maker puts a small bag
with 5 hair ribbons inside each
box with a doll. how many bags
of 5 hair ribbons can be made
from 45 hair ribbons?

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?

Simplify.7x + 3y - 2 + 6x + 1 + y squared 2 you! ; )

Select the lengths in centimeters that would form a right triangle