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Category: Algebra

x-2-x-6y-y-2-y-6x-x-y-

Question Number 207092 by hardmath last updated on 06/May/24 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{x}\:−\:\mathrm{6y}}\\{\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{y}\:−\:\mathrm{6x}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:=\:? \\ $$ Answered by A5T last updated on 06/May/24 $${x}^{\mathrm{2}} −{y}^{\mathrm{2}} ={x}−{y}−\mathrm{6}{y}+\mathrm{6}{x}=\mathrm{7}{x}−\mathrm{7}{y} \\…

120-x-1-x-3-x-5-max-

Question Number 206987 by hardmath last updated on 02/May/24 $$\frac{\mathrm{120}}{\mid\mathrm{x}−\mathrm{1}\mid\:+\:\mid\mathrm{x}−\mathrm{3}\mid\:+\:\mid\mathrm{x}−\mathrm{5}\mid}\:\:\:\Rightarrow\:\:\:\mathrm{max}\:=\:? \\ $$ Answered by Frix last updated on 02/May/24 $$\frac{\mathrm{120}}{{f}\left({x}\right)}\:\mathrm{is}\:\mathrm{max}\:\Rightarrow\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{min} \\ $$$$\mathrm{4}\leqslant\mid{x}−\mathrm{1}\mid+\mid{x}−\mathrm{3}\mid+\mid{x}−\mathrm{5}\mid \\ $$$$\Rightarrow\:\mathrm{Answer}\:\mathrm{is}\:\frac{\mathrm{120}}{\mathrm{4}}=\mathrm{30} \\…

If-1-3-x-5-find-9-x-1-

Question Number 206958 by hardmath last updated on 01/May/24 $$\mathrm{If}\:\:\:\frac{\mathrm{1}}{\mathrm{3}^{−\boldsymbol{\mathrm{x}}} }\:=\:\mathrm{5}\:\:\:\mathrm{find}:\:\:\mathrm{9}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:=\:? \\ $$ Answered by Frix last updated on 01/May/24 $$\mathrm{3}^{{x}} =\mathrm{5} \\ $$$$\left(\mathrm{3}^{{x}}…

x-

Question Number 206881 by efronzo1 last updated on 29/Apr/24 $$\:\:\cancel{\underline{\underbrace{\boldsymbol{{x}}}}} \\ $$ Answered by Skabetix last updated on 29/Apr/24 $$\sum_{{n}=\mathrm{0}} ^{\infty} \frac{{x}^{{n}} }{{n}!}={e}^{{x}} \rightarrow{here}\:{x}\:=\:\mathrm{1}\:{so}\:\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{2}!}+…={e} \\…