gọi số học sinh giỏi, khá , tb lần lượt là x,y,z

ta có \(y=20\)

* \(x=\dfrac{1}{5}\left(x+y+z\right)=\dfrac{1}{5}\left(x+z+20\right)\)

* \(5x=x+z+20\Leftrightarrow z=4x-20\)

* \(z=\dfrac{3}{7}\left(x+y\right)\Leftrightarrow7z=3\left(x+20\right)\)

\(7\left(4x-20\right)=3\left(x+20\right)\)

\(\Leftrightarrow28x-140=3x+60\)

\(\Leftrightarrow x=8\)

mà \(z=4x-20\)

\(z=4.8-20=12\)

vậy có 8 hsg , có 20 hsk , có 12 hstb

thanks you ! Happy new year

ta có: S=1-3+3^2-3^3+...+3^98-3^99

=>S=(1-3+3^2-3^3)+....+(3^96-3^97+3^98-3^99)

=>S=-20+....+(3^96.1-3^96.3+3^96.3^2-3^96.3^3)

=>S=-20+...+3^96(1-3+3^2-3^3)

=>A=-20+...+3^96.(-20)

=>S=-20(1+...+3^96)

vì -20 chia hết cho -20 nên S chia hết cho -20

vậy S là bội của -20

b) ta có: S=....

=>3S=3-3^2+3^3-3^4+....+3^99-3^100

=>3S+S=1-3^100

=>4S=1-3^100

=>S=1-3^100/4

vậy....

Cạnh hình vuông là:160:4=40

Diện tích là:40.40=1600

D/S1600

bài 1

\(A=\left(\dfrac{3}{8}+\dfrac{1}{4}+\dfrac{5}{12}\right):\dfrac{7}{8}\)

\(A=\dfrac{9+6+10}{24}:\dfrac{7}{8}=\dfrac{25}{24}.\dfrac{8}{7}=\dfrac{25.1}{3.7}=\dfrac{25}{21}\)

\(B=\dfrac{1}{4}:\left(10,3-9,8\right)-\dfrac{3}{4}\)

\(B=\dfrac{1}{4}:\dfrac{1}{2}-\dfrac{3}{4}\)

\(B=\dfrac{1}{4}.2-\dfrac{3}{4}\)

\(B=\dfrac{1}{2}-\dfrac{3}{4}=-\dfrac{1}{4}\)

\(M=-\dfrac{5}{7}.\dfrac{2}{11}+\dfrac{5}{7}.\dfrac{9}{11}+1\dfrac{5}{7}\)

\(M=-\dfrac{5}{7}\left(-\dfrac{2}{11}+\dfrac{9}{11}\right)+1\dfrac{5}{7}\)

\(M=-\dfrac{5}{7}.\dfrac{7}{11}+\dfrac{12}{7}\)

\(M=-\dfrac{5}{11}+\dfrac{12}{7}=\dfrac{97}{77}\)

\(N=\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.\left(-2\right)^2\)

\(N=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3.4}{16}\)

\(N=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}=\dfrac{6}{7}-\dfrac{5}{8}=\dfrac{13}{56}\)

b) \(\left(x-\dfrac{3}{5}\right)^2=4\)

\(\Leftrightarrow\sqrt{\left(x-\dfrac{5}{3}\right)^2}=\sqrt{4}\)

\(\Leftrightarrow\left|x-\dfrac{3}{5}\right|=2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{5}=2\\x-\dfrac{3}{5}=-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{13}{5}\\x=-\dfrac{7}{5}\end{matrix}\right.\)

vậy

a) \(5^{61}+\left(5^2\right)^{31}+\left(5^3\right)^{21}\)

\(5^{61}+5^{61}+5^{63}\)

\(5^{61}\left(1+5+5^2\right)\)

\(5^{61}.31⋮31\)

vậy....

\(\dfrac{1}{5}x-\dfrac{2}{3}x-\dfrac{2}{3}-\dfrac{1}{3}=0\)

\(\Leftrightarrow\dfrac{-7}{15}x-1=0\)

\(\Leftrightarrow\dfrac{-7x}{15}=1\)

\(\Leftrightarrow x=\dfrac{-15}{7}\)

\(\dfrac{x+3}{-15}=\dfrac{1}{3}\)

\(\Leftrightarrow\dfrac{x+3}{-15}=\dfrac{-5}{-15}\)

\(\Leftrightarrow x+3=-5\)

\(\Leftrightarrow x=-8\)

so do la 615 ban nhe