Select the correct answer from each drop-down menu. Polygon PQRS, shown in the figure, is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in polygon P'Q'R'S'. The slope of P'Q' is -0.75 . The length of P'Q' is approximately 7.21 .

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?

What is the solution set of the quadratic inequality x^2-5< or equal to 0

How many real-number solutions does the equation have? -4x^2 + 10x + 6 = 0 a. no solutions b. two solutions c. infinitely many solutions d. one solution