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Category: Algebra

Let-30-furniture-sets-arrive-at-two-city-stations-A-and-B-15-sets-for-each-station-All-funiture-sets-need-to-be-delivered-to-two-furniture-stores-C-and-D-and-10-sets-must-be-delivered-to-store-C-and-

Question Number 118346 by 1549442205PVT last updated on 17/Oct/20 $$\mathrm{Let}\:\mathrm{30}\:\mathrm{furniture}\:\mathrm{sets}\:\mathrm{arrive}\:\mathrm{at}\:\mathrm{two}\:\mathrm{city} \\ $$$$\mathrm{stations}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:,\mathrm{15}\:\mathrm{sets}\:\mathrm{for}\:\mathrm{each}\:\mathrm{station} \\ $$$$\mathrm{All}\:\mathrm{funiture}\:\mathrm{sets}\:\mathrm{need}\:\mathrm{to}\:\mathrm{be}\:\mathrm{delivered} \\ $$$$\mathrm{to}\:\mathrm{two}\:\mathrm{furniture}\:\mathrm{stores}\:\mathrm{C}\:\mathrm{and}\:\mathrm{D},\mathrm{and}\:\mathrm{10} \\ $$$$\mathrm{sets}\:\mathrm{must}\:\mathrm{be}\:\mathrm{delivered}\:\mathrm{to}\:\mathrm{store}\:\mathrm{C},\mathrm{and} \\ $$$$\mathrm{to}\:\mathrm{store}\:\mathrm{D}−\mathrm{20}.\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{delivery} \\ $$$$\mathrm{one}\:\mathrm{furniture}\:\mathrm{set}\:\mathrm{from}\:\mathrm{the}\:\mathrm{station}\:\mathrm{A}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{stores}\:\mathrm{C}\:\mathrm{and}\:\mathrm{D}\:\mathrm{costs}\:\mathrm{1}\:\mathrm{and}\:\mathrm{3}\:\mathrm{monetary} \\…

solve-1-x-1-y-1-z-3-4-with-x-y-z-N-

Question Number 118322 by mr W last updated on 16/Oct/20 $${solve} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${with}\:{x},{y},{z}\in\mathbb{N} \\ $$ Commented by malwaan last updated on 17/Oct/20 $$\frac{{yz}+{xz}+{xy}}{{xyz}}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\:\left({x}\neq\mathrm{0};{y}\neq\mathrm{0};{z}\neq\mathrm{0}\right)…

Question-183848

Question Number 183848 by Michaelfaraday last updated on 30/Dec/22 Commented by MJS_new last updated on 31/Dec/22 $${y}=−{a}\vee{y}=−{b} \\ $$$$\mathrm{look}\:\mathrm{at}\:\mathrm{it},\:\mathrm{it}'\mathrm{s}\:\mathrm{plain}\:\mathrm{to}\:\mathrm{see} \\ $$ Answered by a.lgnaoui last…

Question-183847

Question Number 183847 by Michaelfaraday last updated on 30/Dec/22 Answered by MJS_new last updated on 31/Dec/22 $$\mathrm{5}{x}^{\mathrm{2}} −\mathrm{7}{x}={t} \\ $$$$\sqrt{{t}+\mathrm{10}}−\sqrt{{t}−\mathrm{9}}=\mathrm{1} \\ $$$$\sqrt{\mathrm{100}}−\sqrt{\mathrm{81}}=\mathrm{1} \\ $$$${t}=\mathrm{90} \\…

Question-183846

Question Number 183846 by Michaelfaraday last updated on 30/Dec/22 Answered by MJS_new last updated on 31/Dec/22 $$\mathrm{1}.\:{x}=\mathrm{0}\:\Rightarrow\:\sqrt{{x}−\sqrt{{x}}}=\mathrm{0} \\ $$$$\mathrm{2}.\:{x}>\mathrm{0} \\ $$$${t}=\sqrt{{x}−\sqrt{{x}}}\geqslant\mathrm{0}\:\Rightarrow\:{x}=\frac{\left(\mathrm{1}\pm\sqrt{\mathrm{4}{t}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} }{\mathrm{4}} \\ $$$$\mathrm{insert}\:\mathrm{in}\:\mathrm{the}\:\mathrm{given}\:\mathrm{equation}\:\mathrm{to}\:\mathrm{get}…

Question-183843

Question Number 183843 by Michaelfaraday last updated on 30/Dec/22 Answered by mr W last updated on 31/Dec/22 $$\left(\underset{{a}=\mathrm{0}} {\overset{\mathrm{4}} {\sum}}{C}_{{a}} ^{\mathrm{4}} {x}^{\mathrm{2}{a}} \right)\left(\underset{{b}=\mathrm{0}} {\overset{\mathrm{7}} {\sum}}{C}_{{b}}…

b-x-y-c-are-consecutive-terms-of-a-G-P-x-br-y-br-2-c-br-3-A-M-between-b-and-c-is-a-b-c-2-a-2a-b-c-2abc-

Question Number 118298 by hmh2k20 last updated on 16/Oct/20 $$\:\:\:\:\:\mathrm{b},\:\mathrm{x},\:\mathrm{y},\:\mathrm{c}\:\mathrm{are}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\therefore\:\:\:\:\:\boldsymbol{\mathrm{x}}\:=\:\boldsymbol{\mathrm{br}},\:\boldsymbol{\mathrm{y}}\:=\:\boldsymbol{\mathrm{br}}^{\mathrm{2}} ,\:\boldsymbol{\mathrm{c}}\:=\:\boldsymbol{\mathrm{br}}^{\mathrm{3}} \: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\mathrm{A}.\mathrm{M}.\:\mathrm{between}\:\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{is}\:\mathrm{a} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\:\:\frac{\mathrm{b}+\mathrm{c}}{\mathrm{2}}\:\:=\:\mathrm{a}\:\:\:\:\Rightarrow\:\:\mathrm{2}\boldsymbol{\mathrm{a}}\:=\:\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\boldsymbol{\mathrm{a}}\mathrm{bc}\:=\:\left(\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\right)\mathrm{bc} \\…