Marry is making pillows for her life skills class. she bought 2 1/2 yards of fabric. her total cost was $15. what was the cost per yard?

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?

The sketch shows two parallel lines cut by a transversal. angle 2 2 is 36° 36 ° . what is the measure of angle 8 8 ?

G(x) = 2 sin(2x - π) + 4. using complete sentences, explain how to find the minimum value for the function.