Question

URGENT!!! am tema pe vacanta ce trebuie predata cel tarziu duminica seara dar nu prea ma descurc la acest exercitiu!

Answer 1

Răspuns:

Explicație pas cu pas:

Succes!

Answer 2

$\displaystyle a)~\frac{5}{4} =\frac{x}{5,6} \Rightarrow \frac{5}{4} =\frac{x}{\cfrac{56}{10} } \Rightarrow \frac{5}{4} =x \cdot \frac{10}{56}\Rightarrow \frac{5}{4} =\frac{10x}{56} \Rightarrow 5 \cdot 56=10x \cdot 4 \Rightarrow \\\\ \Rightarrow 280=40x \Rightarrow x=\frac{280}{40}\Rightarrow x= 7$

$\displaystyle b)~\frac{x}{0,5} =\frac{5}{1,25} \Rightarrow \frac{x}{\cfrac{5}{10} } =\frac{5}{\cfrac{125}{100} } \Rightarrow x \cdot \frac{10}{5} =5 \cdot \frac{100}{125}\Rightarrow 2x= 4\Rightarrow x=\frac{4}{2}\Rightarrow x=2$

$\displaystyle c)~\frac{0,2}{x} =\frac{0,(6)}{1,(3)} \Rightarrow \frac{\cfrac{2}{10} }{x} =\frac{\cfrac{6}{9} }{\cfrac{12}{9} } \Rightarrow \frac{2}{10} \cdot \frac{1}{x} =\frac{6}{9} \cdot \frac{9}{12} \Rightarrow \frac{1}{5x} =\frac{1}{2} \Rightarrow \\\\ \Rightarrow 1 \cdot 2=1 \cdot 5x\Rightarrow 2=5x \Rightarrow x=\frac{2}{5}$

$\displaystyle d)~\frac{1,(6)}{0,2(5)} =\frac{15}{2,3x} \Rightarrow \frac{\cfrac{15}{9} }{\cfrac{23}{90} } =\frac{15}{\cfrac{23}{10}x } \Rightarrow \frac{15}{9} \cdot \frac{90}{23} =15 \cdot \frac{10}{23} x \Rightarrow \frac{150}{23}=\frac{150x}{23}\Rightarrow \\\\\Rightarrow 150 \cdot 23=150x \cdot 23 \Rightarrow 3450=3450x \Rightarrow x=\frac{3450}{3450} \Rightarrow x=1$

$\displaystyle e)~\frac{1,2(6)}{2x}=\frac{1,9}{4,5} \Rightarrow \frac{\cfrac{114}{90} }{2x} =\frac{\cfrac{19}{10} }{\cfrac{45}{10} } \Rightarrow \frac{114}{90} \cdot \frac{1}{2x}=\frac{19}{10} \cdot \frac{10}{45}\Rightarrow \frac{114}{180x} =\frac{19}{45}\Rightarrow \\\\ \Rightarrow 114 \cdot 45=19 \cdot 180x \Rightarrow 5130=3420x \Rightarrow x=\frac{5130}{3420} \Rightarrow x=\frac{3}{2}$

$\displaystyle f)~\frac{x}{\cfrac{5}{2} } =\frac{\cfrac{16}{12} }{\cfrac{10}{6} }\Rightarrow x \cdot \frac{2}{5} =\frac{16}{12} \cdot \frac{6}{10} \Rightarrow \frac{2x}{5} =\frac{4}{5} \Rightarrow 2x \cdot 5=4 \cdot 5 \Rightarrow 10x=20 \Rightarrow \\\\ \Rightarrow x=\frac{20}{10}\Rightarrow x=2$

$\displaystyle g)~\frac{3,5}{[1+0,1(6)]^2} =\frac{x}{0,7} \Rightarrow \frac{\cfrac{35}{10} }{\Bigg(1+\cfrac{15}{90} \Bigg)^2} =\frac{x}{\cfrac{7}{10} } \Rightarrow \frac{\cfrac{35}{10} }{\Bigg(\cfrac{90+15}{90}\Bigg)^2 } =x \cdot \frac{10}{7} \Rightarrow$

$\displaystyle \Rightarrow \frac{\cfrac{35}{10} }{\Bigg(\cfrac{105}{90}\Bigg)^2 } =\frac{10x}{7}\Rightarrow \frac{\cfrac{35}{10} }{\Bigg(\cfrac{7}{6} \Bigg)^2}=\frac{10x}{7} \Rightarrow \frac{\cfrac{35}{10} }{\cfrac{49}{36} } =\frac{10x}{7} \Rightarrow \frac{35}{10} \cdot \frac{36}{49} =\frac{10x}{7} \Rightarrow \\\\ \Rightarrow \frac{18}{7} =\frac{10x}{7}\Rightarrow 18 \cdot 7=10x \cdot 7 \Rightarrow 126=70x \Rightarrow x=\frac{126}{70} \Rightarrow x=\frac{9}{5}$

$\displaystyle h)~\frac{3^{100}-3^{99}-3^{98}}{x} =\frac{27^{32}}{0,(3)} \Rightarrow \frac{3^{100}-3^{99}-3^{98}}{x} =\frac{3^{3 \cdot 32}}{\cfrac{3}{9} }\Rightarrow \\\\ \Rightarrow \frac{3^{100}-3^{99}-3^{98}}{x} = 3^{96}\cdot \frac{9}{3}\Rightarrow \frac{3^{100}-3^{99}-3^{98}}{x} =\frac{3^{96}\cdot 3^2}{3} \Rightarrow \\\\ \Rightarrow \frac{3^{100}-3^{99}-3^{98}}{x} =3^{97}\Rightarrow 3^{97}x=3^{100}-3^{99}-3^{98}\Rightarrow$

$\Rightarrow 3^{97}x=3^{98}\Big(3^2-3^1-1\Big)\Rightarrow x=\frac{3^{98}\Big(9-3-1\Big)}{3^{97}} \Rightarrow x=3 \cdot 5 \Rightarrow x=15$

$\displaystyle i)~\frac{51}{1+2+3+...+101}=\frac{2}{5x-3} \Rightarrow \frac{51}{\cfrac{101(101+1)}{2} } =\frac{2}{5x-3}\Rightarrow \\\\ \Rightarrow \frac{51}{\cfrac{101 \cdot 102}{2} }=\frac{2}{5x-3}\Rightarrow \frac{51}{101 \cdot 51} =\frac{2}{5x-3} \Rightarrow \frac{1}{101} =\frac{2}{5x-3}\Rightarrow \\\\ \Rightarrow 1 \cdot (5x-3)=2 \cdot 101 \Rightarrow 5x-3= 202 \Rightarrow 5x=202+3 \Rightarrow 5x=205 \Rightarrow \\\\ \Rightarrow x=\frac{205}{5} \Rightarrow x=41$