\(\left(2x+1\right)^3=125\\ \Rightarrow\left(2x+1\right)^3=5^3\\ \Rightarrow2x+1=5\\ \Rightarrow2x=5-1\\ \Rightarrow2x=4\\ \Rightarrow x=4:2\\ \Rightarrow x=2\)

\(\dfrac{35^{10}:7^{10}-75^5:3^5}{1^2+2^2+3^2+...+100^2}\)

\(=\dfrac{\left(35:7\right)^{10}-\left(75:5\right)^5}{1^2+2^2+3^2+...+100^2}\)

\(=\dfrac{5^{10}-25^5}{1^2+2^2+3^2+...+100^2}\)

\(=\dfrac{5^{10}-5^{10}}{1^2+2^2+3^2+...+100^2}\)

\(=0\)

\(C=\dfrac{5}{28}+\dfrac{1}{14}+\dfrac{1}{26}+...+\dfrac{1}{638}\\ =\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{3190}\\ =\dfrac{5}{4\cdot7}+\dfrac{5}{7\cdot10}+\dfrac{5}{10\cdot13}+...+\dfrac{5}{55\cdot58}\\ =\dfrac{5}{3}\cdot\left(\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+...+\dfrac{3}{55\cdot58}\right)\\ =\dfrac{5}{3}.\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-...-\dfrac{1}{55}+\dfrac{1}{55}-\dfrac{1}{58}\right)\\ =\dfrac{5}{3}\cdot\left(\dfrac{1}{4}-\dfrac{1}{58}\right)\\ =\dfrac{5}{3}\cdot\dfrac{27}{116}\\ =\dfrac{45}{116}\)

Ta có:

\(\left(a+6\right):2=56\\ a+6=56\times2\\ a+6=112\\ a=112-6\\ a=106\)

Vậy: \(a=106\)

Vì: \(a>b\) nên nhân a,b với \(4\), ta có:

\(4a>4b\)

Biết: \(7>5\)

\(\rightarrow4a+7>7b+5\left(đpcm\right)\)

Sửa:

\(b,\left(x+2\right)^4=2^4\cdot5^4\\ \left(x+2\right)^4=10^4\\ \left(x+2\right)^4=\pm10\\\left[{}\begin{matrix}x+2=10\\x+2=-10\end{matrix}\right.\\ \left[{}\begin{matrix}x=8\\x=-12\end{matrix}\right.\)

\(a,5^{x+2}=25^x\\ \Rightarrow5^{x+2}=\left(5^2\right)^x\\ \Rightarrow5^{x+2}=5^{2x}\\ \Rightarrow x+2=2x\\ \Rightarrow x=2\\b,\left(x+2\right)^4=2^4\cdot5^4\\ \Rightarrow\left(x+2\right)^4=10^4\\ \Rightarrow x+2=10\\ \Rightarrow x=10-2\\ \Rightarrow x=8\)

\(a,11,5-x=2,67\\ x=11,5-2,67\\ x=8,83\)

\(b,\dfrac{12}{25}:x=\dfrac{3}{5}\\ x=\dfrac{12}{25}:\dfrac{3}{5}\\ x=\dfrac{12}{25}\times\dfrac{5}{3}\\ x=\dfrac{4}{5}\)

\(c,4,8:0,2+26:\left(3\times x-2\right)=12\times5-17:\dfrac{1}{2}\\ 24+26:\left(3x-2\right)=60-34\\ 24+26:\left(3x-2\right)=26\\ 26:\left(3x-2\right)=26-24\\ 26:\left(3x-2\right)=2\\ 3x-2=2:26\\ 3x-2=\dfrac{1}{13}\\ 3x=\dfrac{27}{13}\\ x=\dfrac{27}{13}:3\\ x=\dfrac{27}{39}\)

Diện tích xung quanh bể cá hình hộp chữ nhật là:

\(\left(1,5+1,1\right)\cdot2\cdot0,8=4,16\left(m^2\right)\)

Diện tích làm bể cá là:

\(4,16+1,5\cdot1,1=5,81\left(m^2\right)\)

Thể tích bể cá hình hộp chữ nhật là:

\(1,5\cdot1,1\cdot0,8=1,32\left(m^3\right)=1320l\)

Hiện tại trong bể có là:

\(1320\cdot74\%=976,8\left(l\right)\)

\(2024-2023+2022-2021+...+4-3+2-1\)

\(=\left(2024-2023\right)+\left(2022-2021\right)+...+\left(4-3\right)+\left(2-1\right)\) (có \(2024\) số hạng)

\(=1+1+...+1+1\) (có \(2024:2=1012\) cặp)

\(=1\times1012\)

\(=1012\)