Question

va rog sa ma ajutati cu exercitiile incercuite. Dau coroana Multumesc

Answer 1

$\displaystyle\\ 1)\\ x=0,6=\frac{6}{10}\\\\ y=0,(6)=\frac{6}{9}\\\\ a)~~\frac{x}{y} =\frac{\dfrac{6}{10}}{\dfrac{6}{9}}= \frac{6}{10}\cdot \frac{9}{6}=\boxed{\frac{9}{10}}\\\\ b)~~\frac{x^2}{y^2} =\frac{\left(\dfrac{6}{10}\right)^2}{\left(\dfrac{6}{9}\right)^2}= \frac{\dfrac{6^2}{10^2}}{\dfrac{6^2}{9^2}}= \frac{6^2}{10^2}\cdot \frac{9^2}{6^2}= \frac{9^2}{10^2}= \boxed{\frac{81}{100}}$

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$\displaystyle\\ 2)\\ \text{Avem proportia:}\\\\ \frac{x}{3}=\frac{15}{y}\\\\ a)~~xy=3\cdot 15=45~\Longrightarrow~30-\frac{45}{xy}=30-\frac{45}{45}=30-1=\boxed{29}\\\\ b)~~y = \frac{3\cdot 15}{x}= \frac{45}{10}= \boxed{\frac{9}{2}}=\boxed{4,5}$

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$\displaystyle\\ 3)\\ \text{Se da:}\\\\ \frac{x}{y}=4\\\\ x-y=18\\\\ a)\\ x=4y~~~\text{Din prima ecuatie}\\\\ 4y-y=18\\\\ 3y=18\\\\ y=\frac{18}{3}=\boxed{6}\\\\ x=4y=4\cdot6=\boxed{24}\\\\ b)\\\\ m_a = \frac{6+24}{2}= \frac{30}{2}=\boxed{15}$