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Category: Arithmetic

The-diagonals-of-a-trapezoid-ABCD-intersect-at-point-Q-lies-between-the-parallel-line-BC-and-AD-such-that-AQD-CQB-line-CD-separates-points-P-and-Q-Prove-that-BQP-DAQ-

Question Number 104221 by bemath last updated on 20/Jul/20 $${The}\:{diagonals}\:{of}\:{a} \\ $$$${trapezoid}\:{ABCD}\:{intersect} \\ $$$${at}\:{point}\:{Q}\:{lies}\:{between}\:{the} \\ $$$${parallel}\:{line}\:{BC}\:{and}\:{AD} \\ $$$${such}\:{that}\:\angle{AQD}\:=\:\angle{CQB}\:, \\ $$$${line}\:{CD}\:{separates}\:{points}\:{P} \\ $$$${and}\:{Q}\:.\:{Prove}\:{that} \\ $$$$\angle{BQP}\:=\:\angle{DAQ}\: \\…

Question-169538

Question Number 169538 by BRR last updated on 02/May/22 Commented by Tinku Tara last updated on 02/May/22 $$\mathrm{fare}\:\mathrm{increase}\:\mathrm{5}{x} \\ $$$$\mathrm{total}\:\mathrm{earning}\:=\left(\mathrm{400}−\mathrm{10}{x}\right)×\left(\mathrm{50}+\mathrm{5}{x}\right) \\ $$$${f}\left({x}\right)=\mathrm{20000}+\mathrm{1500}{x}−\mathrm{50}{x}^{\mathrm{2}} \\ $$$${f}\:'\left({x}\right)=\mathrm{1500}−\mathrm{100}{x} \\…

220-30-35-

Question Number 169429 by Fridunatjan08 last updated on 30/Apr/22 $$\sqrt{\mathrm{220}+\mathrm{30}\sqrt{\mathrm{35}}}= \\ $$ Answered by cortano1 last updated on 30/Apr/22 $$\sqrt{\mathrm{220}+\mathrm{2}\sqrt{\mathrm{225}×\mathrm{35}}}\:=\sqrt{\left(\mathrm{45}+\mathrm{175}\right)+\mathrm{2}\sqrt{\mathrm{45}×\mathrm{175}}} \\ $$$$=\:\sqrt{\mathrm{45}}\:+\sqrt{\mathrm{175}} \\ $$$$=\mathrm{3}\sqrt{\mathrm{5}}\:+\mathrm{5}\sqrt{\mathrm{7}} \\…