How many, and what type of solutions does 2x^2 + 11x +15 =0 have? a.) 2 irrational solutions b.) 2 nonreal solutions c.) 1 rational solutions d.) 2 rational solutions

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?

Which point lies on a circle with a radius of 5 units and center at p(6, 1)?

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.