The dog-to-cat ratio at the adoption center is 7:3 The total number of dogs and cats is 110. How many dogs are at the adoption center? How many cats?

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?

Explain step-by-step how to simplify -5(2x – 3y + 6z – 10).

The sum of the reciprocal of a positive number and the reciprocal of 2 more than the number is 3/4 equation: the number is