Question Number 216607 by Tawa11 last updated on 12/Feb/25 Answered by Rasheed.Sindhi last updated on 12/Feb/25 $$\mathrm{4}{x}^{\mathrm{2}} +{bx}−\mathrm{45}=\left({hx}+{k}\right)\left({x}+{j}\right);{h},{k},{j}\in\mathbb{Z} \\ $$$$\:\:\:\:\:\:\:\:={hx}^{\mathrm{2}} +\left({hj}+{k}\right){x}+{kj} \\ $$$${kj}=−\mathrm{45}\Rightarrow{j}=−\frac{\mathrm{45}}{{k}} \\ $$$$\frac{\mathrm{45}}{{k}}=−{j}\:\in\:\mathbb{Z}\:\rightarrow\left({D}\right)…
Question Number 216630 by Tawa11 last updated on 12/Feb/25 the circles x² + y² -4x -2y +3 =0 and x² +y² + 2x +4y -3…
Question Number 216387 by Tawa11 last updated on 06/Feb/25 Answered by mr W last updated on 06/Feb/25 $$\left(\mathrm{6},\:\mathrm{0}\right)\: \\ $$$$\left(\mathrm{6}−\mathrm{6}\right)^{\mathrm{2}} +\left(\mathrm{0}−\mathrm{3}+{a}\right)^{\mathrm{2}} =\mathrm{5}^{\mathrm{2}} \\ $$$$\Rightarrow−\mathrm{3}+{a}=\mathrm{5}\:\Rightarrow{a}=\mathrm{8} \\…
Question Number 216060 by mr W last updated on 26/Jan/25 Commented by mr W last updated on 26/Jan/25 $${find}\:{radius}\:{of}\:{inscribed}\:{circle}\:{r}=? \\ $$ Answered by mr W…
Question Number 215230 by Mingma last updated on 01/Jan/25 Answered by A5T last updated on 01/Jan/25 Commented by A5T last updated on 01/Jan/25 $$\mathrm{AC}=\mathrm{BC}=\mathrm{a};\:\mathrm{AB}=\mathrm{c};\:\:\angle\mathrm{CAB}=\theta;\:\mathrm{IE}\parallel\mathrm{AB} \\…
Question Number 215004 by efronzo1 last updated on 25/Dec/24 Commented by mr W last updated on 26/Dec/24 $$\left({xy}+\frac{\lambda^{\mathrm{2}} }{{xy}}\right)_{{min}} =\frac{\mathrm{1}}{\mathrm{4}}+\mathrm{4}\lambda^{\mathrm{2}} \\ $$ Commented by efronzo1…
Question Number 214784 by efronzo1 last updated on 19/Dec/24 $$\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by A5T last updated on 19/Dec/24 $$\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }+\sqrt{{c}^{\mathrm{2}} +{d}^{\mathrm{2}} }\geqslant\sqrt{\left({a}+{c}\right)^{\mathrm{2}} +\left({b}+{d}\right)^{\mathrm{2}}…
Question Number 214020 by ajfour last updated on 24/Nov/24 Commented by ajfour last updated on 24/Nov/24 $${Red}\:{area}\:=\:{Blue}\:{area}.\:{Find}\:{r}\:{in} \\ $$$${terms}\:{of}\:{k},\:\phi. \\ $$ Answered by dionigi last…
Question Number 213745 by efronzo1 last updated on 15/Nov/24 Answered by mnjuly1970 last updated on 16/Nov/24 $$\:\left(\mathrm{M}{edian}\:{theorem}\:\right):\:\:\:\:\:\:\mathrm{7}^{\mathrm{2}} \:+\:{R}^{\mathrm{2}} =\:\mathrm{2}\left(\sqrt{\mathrm{14}}\:\right)^{\mathrm{2}} \:+\:\frac{\left(\mathrm{2}{R}\right)^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\mathrm{49}\:+\:{R}^{\mathrm{2}} \:=\:\mathrm{28}\:+\:\mathrm{2}{R}^{\mathrm{2}} \\…
Question Number 213203 by golsendro last updated on 01/Nov/24 $$\:\:\:\:\:\:\cancel{\underline{\underbrace{\mathscr{G}}}} \\ $$ Answered by lepuissantcedricjunior last updated on 01/Nov/24 $$\boldsymbol{{f}}\left(\boldsymbol{{xy}}\right)=\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{f}}\left(\boldsymbol{{y}}\right) \\ $$$$\boldsymbol{{f}}\left(\mathrm{10}\right)=\mathrm{14};\boldsymbol{{f}}\left(\mathrm{20}\right)=\mathrm{40} \\ $$$$\boldsymbol{{calculons}}\:\boldsymbol{{f}}\left(\mathrm{500}\right) \\…