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Question-138513

Question Number 138513 by mathlove last updated on 14/Apr/21 Answered by MJS_new last updated on 14/Apr/21 $${AB}+\mathrm{9}=\mathrm{3}\left({BA}\right) \\ $$$$\mathrm{10}{A}+{B}+\mathrm{9}=\mathrm{30}{B}+\mathrm{3}{A} \\ $$$${A}=\frac{\mathrm{29}{B}−\mathrm{9}}{\mathrm{7}}\:\Rightarrow\:{B}=\mathrm{2}\wedge{A}=\mathrm{7} \\ $$$$\mathrm{72}+\mathrm{9}=\mathrm{3}×\mathrm{27} \\ $$$${A}+{B}=\mathrm{9}…

Prove-that-If-A-B-and-C-are-subset-of-the-same-universal-set-then-A-B-A-C-A-B-C-

Question Number 7440 by Tawakalitu. last updated on 29/Aug/16 $${Prove}\:{that} \\ $$$${If}\:\:{A},\:{B}\:{and}\:{C}\:{are}\:{subset}\:{of}\:{the}\:{same}\:{universal}\:{set} \\ $$$${then}\:\left({A}\:−\:{B}\right)\:\cap\:\left({A}\:−\:{C}\right)\:=\:{A}\:−\:\left({B}\:−\:{C}\right) \\ $$ Commented by Yozzia last updated on 29/Aug/16 $${Let}\:{A}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\right\},\:{B}=\left\{\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\},\:{C}=\left\{\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right\}. \\…

Question-138511

Question Number 138511 by mathlove last updated on 14/Apr/21 Commented by MJS_new last updated on 14/Apr/21 $$\mathrm{005}\:\:\:\:\:\mathrm{014}\:\:\:\:\:\mathrm{023}\:\:\:\:\:\mathrm{113}\:\:\:\:\:\mathrm{122}\:\:\:\:\:… \\ $$$$\mathrm{050}\:\:\:\:\:\mathrm{140}\:\:\:\:\:\mathrm{230}\:\:\:\:\:\mathrm{131}\:\:\:\:\:\mathrm{221} \\ $$$$\mathrm{500}\:\:\:\:\:\mathrm{401}\:\:\:\:\:\mathrm{302}\:\:\:\:\:\mathrm{311}\:\:\:\:\:\mathrm{212} \\ $$$$==\:\:\:\:\:==\:\:\:\:\:==\:\:\:\:\:==\:\:\:\:\:== \\ $$$$\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}…

Question-7433

Question Number 7433 by Tawakalitu. last updated on 28/Aug/16 Commented by Yozzia last updated on 28/Aug/16 $$ \\ $$$${u}=\frac{\underset{{i}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}+\sqrt{{i}}}}{\underset{{i}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}−\sqrt{{i}}}} \\ $$$$\Rightarrow{u}\underset{{i}=\mathrm{1}}…

Prove-that-this-equation-is-true-x-1-n-1-2x-1-2x-1-2-x-1-x-1-

Question Number 72965 by Raxreedoroid last updated on 05/Nov/19 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{this}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{true}: \\ $$$$\underset{{x}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\left(\mathrm{2}{x}+\mathrm{1}\right)=\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)!}{\left(\mathrm{2}\right)^{{x}−\mathrm{1}} \left({x}−\mathrm{1}\right)!} \\ $$ Commented by mathmax by abdo last updated on…

Produce-a-3-3-array-of-different-numbers-whose-all-the-rows-and-all-the-columns-make-AP-s-of-different-common-digfernces-

Question Number 7423 by Rasheed Soomro last updated on 28/Aug/16 $${Produce}\:{a}\:\mathrm{3}×\mathrm{3}\:\boldsymbol{{array}}\:{of}\:\boldsymbol{{different}}\:{numbers} \\ $$$${whose}\:{all}\:{the}\:\boldsymbol{{rows}}\:{and}\:{all}\:{the}\:\boldsymbol{{columns}}\:{make} \\ $$$$\boldsymbol{{AP}}'\boldsymbol{{s}}\:{of}\:\boldsymbol{{different}}\:\boldsymbol{{common}}-\boldsymbol{{digfernces}}. \\ $$ Commented by Yozzia last updated on 28/Aug/16 $$\begin{pmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}\\{\mathrm{5}}&{\mathrm{7}}&{\mathrm{9}}\\{\mathrm{9}}&{\mathrm{12}}&{\mathrm{15}}\end{pmatrix}\:…