Simplify: (x + 4)5log5^(x^2 – 10x + 24) – log5(x^2 – 16)

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?

Let r = 3. what is the value of r + 58?

Come up with a new linear function that has a slope that falls in the range 10 m − < < . choose two different initial values. for this new linear function, what happens to the function’s values after many iterations? are the function’s values getting close to a particular number in each case?