\(\dfrac{5}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)+\dfrac{7}{4}.\left(\dfrac{1}{14}-\dfrac{2}{7}\right)\)

\(\dfrac{5}{9}:\dfrac{-3}{22}+\dfrac{7}{4}.\dfrac{-3}{14}\)

\(=\dfrac{-5.22}{9.3}-\dfrac{7.3}{4.14}\)

\(=-\dfrac{110}{27}-\dfrac{3}{8}=-\dfrac{961}{216}\)

\(\dfrac{5}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)+\dfrac{7}{4}.\left(\dfrac{1}{14}-\dfrac{2}{7}\right)\)

\(=\dfrac{5}{9}:\left(-\dfrac{3}{22}\right)+\dfrac{7}{4}.\left(-\dfrac{3}{22}\right)\)

\(=\dfrac{5}{9}.\left(-\dfrac{22}{3}\right)+\dfrac{7}{4}.\left(-\dfrac{3}{22}\right)\)

\(=-\dfrac{110}{27}+\left(-\dfrac{21}{88}\right)\)

\(=-\dfrac{9113}{2376}\)

\(\left(1+\dfrac{1}{2}\right).\left(1+\dfrac{1}{3}\right).....\left(1+\dfrac{1}{2012}\right)\)

\(=\dfrac{3}{2}.\dfrac{4}{3}.....\dfrac{2013}{2012}\)

\(=\dfrac{2013}{2}\)

(1+1/2).(1+1/3) ... (1+1/2012)

=> 3/2 . 4/3 ... 2013/2012

=>2013/2

– Diện tích trần nhà là:
4,5 x 3,7 = 16,65 (m2)
– Diện tích 4 bức tường (hay còn gọi là diện tích xung quanh) là:
2.4,5.3 + 2.3.3,7 = 2.(4,5 + 3,7).3 = 49,2 (m2)
– Diện tích cần được quét vôi là:
16,65 + 49,2 – 5,8 = 60,05 (m2)

bạn ơi bạn lạc đề rồi 

Vì p là số nguyên tố lớn hơn 3 nên p=3k+1 hoặc p=3k+2 ( k là stn khác 0).

Th1: p=3k+1

=> 14p+1= 14(3k+1)+1=42k+15 chia hết cho 3

Mà 14p+1> 3=> 14p+1 là hợp số ( Loại)

=>p=3k+2.Vì p là số nguyên tố lớn hơn 3 nên p lẻ

=> 7p+1 là số chẵn=> 7p+1 chia hết cho 2 (1)

Ta có: 7p+1= 7(3k+2)+1= 21k+15 chia hết cho 3=> 7p+1 chia hết cho 3 (2)

   Từ (1) và (2)=> 7p+1 chia hết cho 6 ( do (2,3)=1)

\(\left(x+3\right).\left(x-2\right)>0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+3>0\\x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+3< 0\\x-2< 0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-3\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x< -3\\x< 2\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x>2\\x< -3\end{matrix}\right.\)

\(\left(x+3\right)\left(x-2\right)>0\)

+) \(\left\{{}\begin{matrix}x+3>0\\x-2>0\end{matrix}\right.\Rightarrow x>2}\)

+) \(\left\{{}\begin{matrix}x+3< 0\\x-2< 0\end{matrix}\right.\Rightarrow x< -3}\)

\(4< 2^x< 8.16\)

\(\Leftrightarrow2^2< 2^x< 2^3.2^4\)

\(\Leftrightarrow2^2< 2^x< 2^7\)

\(\Leftrightarrow x\in\left\{3;4;5;6\right\}\)

8.16>2^x>4

=> x = { 3;4;5;6 }

\(3^1.3^x+5.3^x-1=162\)

\(\Leftrightarrow3^x\left(3+5\right)=163\)

\(\Leftrightarrow3^x=\dfrac{163}{8}\)

\(\Leftrightarrow x\approx2,7\)

31.3x+5.3x−1=162

\Leftrightarrow3^x\left(3+5\right)=163⇔3x(3+5)=163

\Leftrightarrow3^x=\dfrac{163}{8}⇔3x=8163​

$\iff x\approx 2,7$