Question

Am si eu nevoie de toate rezolvarile inafara de cele de geometrie​

Answer 1

1)

       48 = 2⁴ · 3

       64 = 2⁶

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[48,  64] =  2⁶· 3 = 192

(48,  64) = 2⁴ = 16

2)

$\it a)\ \dfrac{20}{x}=\dfrac{180}{63} \Rightarrow x = \dfrac{20\cdot63}{180} =7\\ \\ \\ b)\ \\ \\ 10m ---------- 12z\\ 15m ----------\ xz$

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Avem proporționalitate inversă, deci:

$\it \dfrac{10}{15} = \dfrac{x}{12} \Rightarrow x=\dfrac{10\cdot12}{15} = 8\ zile$

3)

$\it 36\%\ din\ 150=\dfrac{36}{100}\cdot150=54$

4)

$\it a)\ =\dfrac{4}{9}\cdot\Big(\dfrac{3}{9}+\dfrac{1}{2}\cdot\dfrac{4}{3}\Big)\cdot\dfrac{9}{8}=\dfrac{4}{9}\cdot\dfrac{9}{8}\Big(\dfrac{1}{3}+\dfrac{2}{3}\Big)=\dfrac{1}{2}\cdot\dfrac{3}{3}=\dfrac{1}{2}\cdot1=\dfrac{1}{2}$

$\it b)\ =-169:(-8-12+7) =-169:(-13)=13$

5)

$\it \dfrac{6}{2x+1}\in\mathbb{Z} \Rightarrow 2x+1\in D_6\ \ \ \ (1)\\ \\ \\ x\in\mathbb{Z} \Rightarrow 2x+1=impar\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow 2x+1\in\{-3,\ -1,\ 1,\ 3\}|_{-1} \Rightarrow 2x\in\{-4,\ -2,\ 0,\ 2\}|_{:2}\Rightarrow\\ \\ \Rightarrow x\in\{-2,\ -1,\ 0,\ 1\}$