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Category: Algebra

a-b-c-N-a-b-a-2b-a-3b-105-c-

Question Number 139051 by mathsuji last updated on 21/Apr/21 $${a};{b};{c}\in\mathbb{N} \\ $$$$\left({a}+{b}\right)\left({a}+\mathrm{2}{b}\right)\left({a}+\mathrm{3}{b}\right)=\mathrm{105}^{\boldsymbol{{c}}} \\ $$ Commented by Rasheed.Sindhi last updated on 22/Apr/21 $$\left({a}+{b}\right)\left({a}+\mathrm{2}{b}\right)\left({a}+\mathrm{3}{b}\right)=\mathrm{105}^{\boldsymbol{{c}}} \\ $$$$\left({a}+{b}\right)\left({a}+\mathrm{2}{b}\right)\left({a}+\mathrm{3}{b}\right)=\mathrm{3}^{{c}} .\mathrm{5}^{{c}}…

Let-a-and-b-be-complex-numbers-representing-the-points-A-and-B-respectively-in-the-complex-plane-If-a-b-b-a-1-and-O-is-the-origin-Then-OAB-is-

Question Number 139055 by EnterUsername last updated on 21/Apr/21 $$\mathrm{Let}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{be}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{representing}\:\mathrm{the}\:\mathrm{points} \\ $$$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{respectively}\:\mathrm{in}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{plane}. \\ $$$$\mathrm{If}\:\frac{\mathrm{a}}{\mathrm{b}}+\frac{\mathrm{b}}{\mathrm{a}}=\mathrm{1}\:\mathrm{and}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the}\:\mathrm{origin}.\:\mathrm{Then}\:\Delta\mathrm{OAB}\:\mathrm{is}\:? \\ $$ Answered by MJS_new last updated on 22/Apr/21 $$\frac{{a}}{{b}}+\frac{{b}}{{a}}=\mathrm{1}\:\Rightarrow\:{b}={a}\left(\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i}\right) \\…

During-one-year-in-a-school-5-8-of-the-students-had-measiles-1-2-had-chickenpox-and-1-8-had-Neither-What-fraction-of-the-school-had-both-measiles-and-chickenpox-

Question Number 7969 by tawakalitu last updated on 26/Sep/16 $${During}\:{one}\:{year}\:{in}\:{a}\:{school},\:\frac{\mathrm{5}}{\mathrm{8}}\:{of}\:{the}\:{students} \\ $$$${had}\:{measiles}.\:\frac{\mathrm{1}}{\mathrm{2}}\:{had}\:{chickenpox},\:{and}\:\frac{\mathrm{1}}{\mathrm{8}}\:{had} \\ $$$${Neither}.\:{What}\:{fraction}\:{of}\:{the}\:{school}\:{had}\:{both} \\ $$$${measiles}\:{and}\:{chickenpox}. \\ $$ Answered by Rasheed Soomro last updated on…

soit-le-systeme-suivant-2s-4c-3t-700-3s-2c-2t-500-8s-7c-8t-comment-determiner-le-resultat-de-la-3-e-equation-

Question Number 73468 by mathocean1 last updated on 12/Nov/19 $$\mathrm{soit}\:\mathrm{le}\:\mathrm{systeme}\:\mathrm{suivant} \\ $$$$\begin{cases}{\mathrm{2s}+\mathrm{4c}+\mathrm{3t}=\mathrm{700}}\\{\mathrm{3s}+\mathrm{2c}+\mathrm{2t}=\mathrm{500}}\end{cases} \\ $$$$\:\:\mathrm{8s}+\mathrm{7c}+\mathrm{8t}=…?… \\ $$$$\mathrm{comment}\:\mathrm{determiner}\:\mathrm{le}\:\mathrm{resultat}\:…?…\: \\ $$$$\mathrm{de}\:\mathrm{la}\:\mathrm{3}^{\mathrm{e}} \mathrm{equation}\:? \\ $$ Answered by MJS last…

36-x-2-4-y-1-4-x-2-y-1-28-find-x-amp-y-

Question Number 138984 by bramlexs22 last updated on 20/Apr/21 $$\frac{\mathrm{36}}{\:\sqrt{\mathrm{x}−\mathrm{2}}}\:+\frac{\mathrm{4}}{\:\sqrt{\mathrm{y}−\mathrm{1}}}\:+\mathrm{4}\sqrt{\mathrm{x}−\mathrm{2}}\:+\sqrt{\mathrm{y}−\mathrm{1}}\:=\:\mathrm{28} \\ $$$$\mathrm{find}\:\mathrm{x}\:\&\:\mathrm{y} \\ $$ Answered by mitica last updated on 21/Apr/21 $$\frac{\mathrm{36}}{\:\sqrt{{x}−\mathrm{2}}}+\mathrm{4}\sqrt{{x}−\mathrm{2}}+\frac{\mathrm{4}}{\:\sqrt{{y}−\mathrm{1}}}+\sqrt{{y}−\mathrm{1}}\geqslant \\ $$$$\mathrm{2}\sqrt{\frac{\mathrm{36}}{\:\sqrt{{x}−\mathrm{2}}}\centerdot\mathrm{4}\sqrt{{x}−\mathrm{2}}}+\mathrm{2}\sqrt{\frac{\mathrm{4}}{\:\sqrt{{y}−\mathrm{1}}}\centerdot\sqrt{{y}−\mathrm{1}}}=\mathrm{24}+\mathrm{4}=\mathrm{28}\Rightarrow \\…

a-3-b-3-

Question Number 7912 by anshumansingh585@gmail.com last updated on 24/Sep/16 $${a}^{\mathrm{3}} +{b}^{\mathrm{3}} =? \\ $$ Commented by prakash jain last updated on 24/Sep/16 $$\left({a}+{b}\right)\left({a}^{\mathrm{2}} −{ab}+{b}^{\mathrm{2}} \right)…

Question-138979

Question Number 138979 by byaw last updated on 20/Apr/21 Answered by greg_ed last updated on 20/Apr/21 $$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{granddaughter}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{years}}\:\boldsymbol{\mathrm{old}}.\: \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{get}}\:: \\ $$$$\mathrm{10}{x}\:=\:{x}\:+\:\mathrm{54}\:\Rightarrow \\ $$$$\mathrm{9}{x}\:=\:\mathrm{54}\:\Rightarrow \\ $$$${x}\:=\:\mathrm{6}…

Question-7903

Question Number 7903 by tawakalitu last updated on 24/Sep/16 Commented by sou1618 last updated on 24/Sep/16 $${S}\:=\:\frac{\:\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}+\sqrt{{k}}}\:}{\:\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}−\sqrt{{k}}}\:} \\ $$$${S}\fallingdotseq{S}\:'=\frac{\:\:\int_{\mathrm{0}} ^{\mathrm{100}} \sqrt{\mathrm{10}+\sqrt{{x}}\:}\:{dx}\:}{\:\:\int_{\mathrm{0}}…

A-dealer-sold-a-car-to-a-man-and-made-a-profit-of-15-the-man-then-sold-it-to-a-woman-for-120-175-00-at-a-loss-of-5-How-much-did-the-dealer-buy-the-car-

Question Number 7901 by tawakalitu last updated on 24/Sep/16 $${A}\:{dealer}\:{sold}\:{a}\:{car}\:{to}\:{a}\:{man}\:{and}\:{made}\:{a}\:{profit}\:{of}\:\mathrm{15\%} \\ $$$${the}\:{man}\:{then}\:{sold}\:{it}\:{to}\:{a}\:{woman}\:{for}\:#\mathrm{120},\mathrm{175}.\mathrm{00} \\ $$$${at}\:{a}\:{loss}\:{of}\:\mathrm{5\%}.\:{How}\:{much}\:{did}\:{the}\:{dealer}\:{buy}\:{the}\:{car}. \\ $$ Answered by sandy_suhendra last updated on 24/Sep/16 $${the}\:{man}\:{buys}\:{the}\:{car}\:=\:\frac{\mathrm{100}}{\mathrm{95}}×\mathrm{120},\mathrm{175}=\:\mathrm{126},\mathrm{500}\:={the}\:{dealer}\:{sold} \\…