Atriangle has vertices at (1, 3), (2, -3), and (-1, -1). what is the approximate perimeter of the triangle?

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?

4. find the geometric mean of 4 and 12. 24 8

Asalesperson earns $320 per week plus 8% of her weekly sales. the expression representing her earnings is 320 + 0.08x. which of the following describes the sales necessary for the salesperson to earn at least $1000 in the one week?