`-5(x+4) -3(x-2)=-114`

`=>-5x-20 - (3x-6)=-114`

`=> -5x-20 - 3x+6=-114`

`=> -8x -14=-114`

`=>-8x= -100`

`=>x=-100 : (-8)`

`=>x= 12,5`

giúp mik nha mik cần gấp

Ta có 2^{4n + 1} + 3 = 2⁴ⁿ . 2 + 3 = 16ⁿ . 2 + 3 = ( ...6 ) . 2 + 3 = ( ...2 ) + 3 = ( ...5 )

Vì số có chữ số tận cùng là 5 thì chia hết cho 5 nên ( 2^{4n + 1} + 3 ) ⋮ 5 

dư 11

,dư 11

helppppppppppppppppppppppppppppppppppppppppppppppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

độ dài đoạn CI là

CI=CE+EI=2+5=7(cm)`

Ta có : \(A\text{=}\dfrac{2023^{2023}}{2023^{2024}}\text{=}\dfrac{1}{2023}\)

và \(B\text{=}\dfrac{2023^{2022}}{2023^{2023}}\text{=}\dfrac{1}{2023}\)

\(\Rightarrow A\text{=}B\)

Ta có :

A=\(\dfrac{2023^{2023}}{2023^{2024}}\)=\(\dfrac{2023^{2022}.2023}{2023^{2023}.2023}\)=\(\dfrac{2023^{2022}}{2023^{2023}}\)

Mà B=\(\dfrac{2023^{2023}}{2023^{2024}}\)

Vậy A=B

\(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{117\cdot120}\)

\(=\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{117}-\dfrac{1}{120}\\ =\dfrac{1}{2}-\dfrac{1}{120}\\ =\dfrac{59}{120}\)

Gọi ƯCLN của 6n+7 và 2n+1 là : a

\(\Rightarrow6n+7⋮a\) và \(2n+1⋮a\)

\(\Rightarrow3\left(2n+1\right)⋮a\)

\(\Rightarrow(6n+7-6n-3)⋮a\)

\(\Rightarrow4⋮a\)

\(\Rightarrow a\inƯ\left(4\right)\in\left(1;-1;2;-2;4;-4\right)\)

mà \(2n+1\) là số lẻ nên không có ước là : (2;-2;4;-4)

\(\Rightarrow a\in\left(1;-1\right)\)

\(\Rightarrow A\) tối giản

\(1.\dfrac{-7}{18}+\dfrac{-5}{12}-\dfrac{-13}{18}\text{=}\left(\dfrac{-7}{18}-\dfrac{-13}{18}\right)+\dfrac{-5}{12}\text{=}\dfrac{1}{3}+\dfrac{-5}{12}\text{=}\dfrac{-1}{12}\)

\(2.\dfrac{-13}{17}+\dfrac{-13}{21}+\dfrac{-4}{17}\text{=}\left(\dfrac{-13}{17}+\dfrac{-4}{17}\right)+\dfrac{-13}{21}\text{=}-1+\dfrac{-13}{21}\text{=}\dfrac{-34}{21}\)

\(3.\dfrac{-13}{10}-\dfrac{-4}{13}+\dfrac{-11}{10}\text{=}\dfrac{-12}{5}-\dfrac{-4}{13}\text{=}\dfrac{-136}{65}\)

\(4.\dfrac{13}{17}\times\left(\dfrac{-4}{5}+\dfrac{-3}{4}\right)\text{=}\dfrac{13}{17}\times\dfrac{-31}{20}\text{=}\dfrac{-403}{340}\)

\(5.\left(\dfrac{-5}{12}\times\dfrac{-9}{20}\right)\times\dfrac{-7}{17}\text{=}\dfrac{3}{16}\times\dfrac{-7}{17}\text{=}\dfrac{-21}{272}\)

\(6.\dfrac{11}{23}\times\left(\dfrac{5}{9}+\dfrac{17}{9}-\dfrac{13}{9}\right)\text{=}\dfrac{11}{23}\times1\text{=}\dfrac{11}{23}\)