Find a formula in n, a, m, and d for the sum (a md) (a (m 1)d) (a (m 2)d) · · · (a (m n)d), where m and n are integers, n ≥ 0, and a and d are real numbers. justify your answer.

Handsome jack is buying a pony made of diamonds. the price of the pony is p dollars, and jack also has to pay a 25% diamond pony tax. which of the following expressions could represent how much jack pays in total for the pony?

Given that δabc is similar to δdef, which is a possible trigonometric ratio for ∠d? a) tan d = 24 30 b) tan d = 30 24 c) tan d = 18 24 d) tan d = 24 18

Given: ae ≅ ce ; de ≅ be prove: abcd is a parallelogram. we have that ab || dc. by a similar argument used to prove that △aeb ≅ △ced, we can show that △ ≅ △ceb by. so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.