There are 4, 6, and 7 points on three lines. How many triangles is it possible to create with given points as vertices?

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?

Need to increase the numbers of customers i talk to daily by 20% how many customers do i need to talk to if i talk to a average of 8 customers per hour during an 8 hour shift

Identify a1 and r for the geometric sequence an= -256(-1/4) n-1