The number $ 2013 $ is expressed in the form$$ 2013=\frac{a_1!a_2!\cdots a_m!}{b_1!b_2!\cdots b_n!}, $$where $ a_1\ge a_2\ge\ldots\ge a_m $ and $ b_1\ge b_2\ge\ldots\ge b_n $ are positive integers. What is the smallest possible value for $a_1+b_1$?

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?

Plz determine whether the polynomial is a difference of squares and if it is, factor it. y2 – 196 is a difference of squares: (y + 14)2 is a difference of squares: (y – 14)2 is a difference of squares: (y + 14)(y – 14) is not a difference of squares

Suppose you are going to graph the data in the table. minutes temperature (°c) 0 -2 1 1 2 3 3 4 4 5 5 -4 6 2 7 -3 what data should be represented on each axis, and what should the axis increments be? x-axis: minutes in increments of 1; y-axis: temperature in increments of 5 x-axis: temperature in increments of 5; y-axis: minutes in increments of 1 x-axis: minutes in increments of 1; y-axis: temperature in increments of 1 x-axis: temperature in increments of 1; y-axis: minutes in increments of 5