the legend on the map states that 1 cm is 15 km. if you measure 11 cm on the map, how many kilometers would the actual distance be?

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?

Aline passes through (1,-5) and(-3,7) write an equation for the line in point slope form rewrite the equation in slope intercept form

The graph of a hyperbola is shown. what are the coordinates of a vertex of the hyperbola? (0, −4) (−3, 0) (0, 0) (0, 5)