\(A=\frac{5^{2021}+1}{5^{2022}+1}\Leftrightarrow10A=\frac{5^{2022}+10}{5^{2022}+1}=1+\frac{9}{5^{2022}+1}\)

\(B=\frac{5^{2020}+1}{5^{2021}+1}\Leftrightarrow10B=\frac{5^{2021}+10}{5^{2021}+1}=1+\frac{9}{5^{2021}+1}\)

Vì\(\frac{9}{5^{2022}+1}< \frac{9}{5^{2021}+1}\left(10A< 10B\right)\Leftrightarrow A< B\)Vậy\(A< B\)

A=52022+152021+1​⇔10A=52022+152022+10​=1+52022+19​

�=52020+152021+1⇔10�=52021+1052021+1=1+952021+1B=52021+152020+1​⇔10B=52021+152021+10​=1+52021+19​

Vì952022+1<952021+1(10�<10�)⇔�<�52022+19​<52021+19​(10A<10B)⇔A<BVậy$A<B$

\(20-\left[30-\left(1-5\right)^2\right]\)

\(=20-\left[30-\left(-4^2\right)\right]\)

\(=20-4\)

\(=16\)

\(20-\left[30-\left(1-5\right)^2\right]\)

\(\Rightarrow20-\left[30-\left(-4\right)^2\right]\)

\(\Rightarrow20-\left(30-16\right)\)

\(\Rightarrow20-14\)

\(\Rightarrow6\)

 \(\frac{7}{x}\) = \(\frac{y}{27}\)= \(\frac{-7}{9}\)

Ta có:

+ \(\frac{7}{x}\)= \(\frac{-7}{9}\)

     =>  7 . 9 = -7 . x =>  x = \(\frac{7.9}{-7}\)= -9

+ \(\frac{y}{27}\)= \(\frac{-7}{9}\) 

     =>  y . 9 = -7. 27 => y = \(\frac{-7.27}{9}\) = -21

Ta có:

Vì\(\frac{4}{x}=\frac{y}{21}=\frac{z}{49}=\frac{52}{91}\)nên\(\frac{52}{91}=\frac{4}{x};\frac{y}{21};\frac{z}{49}\)

*Xét trường hợp z:\(\frac{z}{49}=\frac{52}{91}\Leftrightarrow\frac{z}{637}=\frac{364}{637}\)

\(\Rightarrow z=364\)

*Xét trường hợp y:\(\frac{y}{21}=\frac{52}{91}\Leftrightarrow\frac{y}{273}=\frac{156}{273}\)

\(\Rightarrow y=156\)

*Xét trường hợp x:\(\frac{4}{x}=\frac{52}{91}\Leftrightarrow\frac{52}{13x}=\frac{52}{91}\)

\(\Rightarrow x=91\)

Vậy:\(\hept{\begin{cases}x=91\\y=156\\z=364\end{cases}}\)

số học sinh giỏi lớp 6a là:

\(40\cdot\frac{1}{4}=10\left(hs\right)\)

Đáp số: \(10hs\)

Đ/S là 10h/s nha

HT

0.5x-4/5=40/100

1/2x-4/5=2/5

1/2x=2/5+4/5

1/2x=6/5

x=6/5:1/2

x=6/5*2/1

x=12/5

2 nha bạn đó là số 31 và 37

2 ban nhe

x+2 chia hết cho x-3
=x-3+5 chia hết cho x-3
=(x-3)+5 chia hết cho x-3
vì (x-3) chia hết cho (x-3) nên 5 chia hết cho (x-3)hay (x-3) thuộc Ư(5)={1;-1;5;-5)

Vậy n thuộc {4;2;8;-2}

\(a)\)\(x+2\)\(⋮\)\(x-3\)

\(\Rightarrow(x-3)+5⋮x-3\)

Mà \(x-3\)\(⋮\)\(x-3\)

\(\Rightarrow\)\(5\)\(⋮\)\(x-3\)

\(\Rightarrow x-3\in\left\{1;5;-1;-5\right\}\)

\(\Rightarrow x\in\left\{4;8;2;-2\right\}\)

Vậy \(x\in\left\{4;8;2;-2\right\}\)

\(\frac{11}{8}+\frac{13}{6}=\frac{85}{x}\)

\(\frac{33}{24}+\frac{52}{24}=\frac{85}{24}=\frac{85}{x}\)

\(\Leftrightarrow85x=85.24\)

\(\Leftrightarrow85x=2040\)

\(\Leftrightarrow x=2040:85=24\)

Vậy x = 24