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13 tháng 11 2023

a: \(A=1+3+3^2+...+3^{11}\)

\(=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{10}+3^{11}\right)\)

\(=\left(1+3\right)+3^2\left(1+3\right)+...+3^{10}\left(1+3\right)\)

\(=4\left(1+3^2+...+3^{10}\right)⋮4\)

b: \(B=16^5+2^{15}\)

\(=\left(2^4\right)^5+2^{15}\)

\(=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{15}\cdot33⋮33\)

c: \(C=5+5^2+5^3+...+5^8\)

\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^7+5^8\right)\)

\(=30+5^2\left(5+5^2\right)+...+5^6\left(5+5^2\right)\)

\(=30\left(1+5^2+...+5^6\right)⋮30\)

d: \(45⋮9;99⋮9;180⋮9\)

=>\(45+99+180⋮9\)

=>D chia hết cho 9

17 tháng 12 2021

has watched

do-do

went-stayed

listens

doesn't play

is often

have been-wee

had walked

had finished

had moved

9 tháng 11 2021

B A B' A' O

Vẽ 1 tia sáng qua điểm A và đến điểm I

Vẽ tia phản từ ảnh của A là A' đi qua điểm I 

19 tháng 8 2023

Bài 1:

câu a: 4\(\dfrac{4}{9}\) : 2\(\dfrac{2}{3}\) + 3\(\dfrac{1}{6}\)

        = \(\dfrac{40}{9}\) : \(\dfrac{8}{3}\) + \(\dfrac{19}{6}\)

        = \(\dfrac{5}{3}\) + \(\dfrac{19}{6}\)

         = \(\dfrac{10}{6}\) + \(\dfrac{19}{6}\)

          = \(\dfrac{29}{6}\)

b, (15,25 + 3,75) \(\times\) 4 + ( 20,71 + 5,29)\(\times\) 5

     = 19 \(\times\) 4 + 26 \(\times\) 5

     = 76 + 130

     = 206

19 tháng 8 2023

c, \(\dfrac{4}{5}\) \(\times\) \(\dfrac{1}{2}\) + \(\dfrac{4}{5}\) \(\times\) \(\dfrac{1}{3}\) - \(\dfrac{4}{5}\) \(\times\) \(\dfrac{1}{4}\)

\(\dfrac{2}{5}\)    + \(\dfrac{4}{15}\) - \(\dfrac{1}{5}\)

\(\dfrac{6}{15}\) + \(\dfrac{4}{15}\) - \(\dfrac{3}{15}\)

\(\dfrac{7}{15}\) 

d, 1\(\dfrac{5}{7}\) + 7\(\dfrac{3}{6}\) + 2\(\dfrac{2}{7}\) - 4\(\dfrac{3}{6}\)

= (1 + 2 + \(\dfrac{5}{7}\) + \(\dfrac{2}{7}\)) + ( 7 + \(\dfrac{3}{6}\) - 4 - \(\dfrac{3}{6}\))

=  3 + 1 + 3 

= 7

16 tháng 4 2023

a)  5/17 * 8/-7+8/17*-7/3+-7/3*4/17

-40/119 + 12/17 × -7/3

-40/119 + -28/17 =-236/119

b) -10/13 + 5/17 - 3/13 + 12/17 - 11/20

(5/17+12/17)-(10/13+3/13)-11/20

-11/20

17 tháng 4 2023

a)  5/17 * 8/-7+8/17*-7/3+-7/3*4/17

-40/119 + 12/17 × -7/3

-40/119 + -28/17 =-236/119

b) -10/13 + 5/17 - 3/13 + 12/17 - 11/20

(5/17+12/17)-(10/13+3/13)-11/20

-11/20

19 tháng 7 2023

\(l,\\ 2^x=1=2^0\\ Vậy:x=0\\ m,\\ 3^x=81=3^4\\ Vậy:x=4\\ n,\\ 3^x=37=3^3\\ Vậy:x=3\\ o,\\ 9^x=3^4=\left(3^2\right)^2=9^2\\ Vậy:x=2\)

19 tháng 7 2023

l) x = 0

m) x = 4

n) x = 3

o) x = 2

26 tháng 8 2023

\(A=\dfrac{2}{1x3}+\dfrac{2}{3x5}+\dfrac{2}{5x7}+...+\dfrac{2}{21x23}\)

\(A=2x\left(\dfrac{1}{1x3}+\dfrac{1}{3x5}+\dfrac{1}{5x7}+...+\dfrac{1}{21x23}\right)\)

\(A=2x\dfrac{1}{2}x\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{21}-\dfrac{1}{23}\right)\)

\(A=1-\dfrac{1}{23}\)

\(A=\dfrac{22}{23}\)

26 tháng 8 2023

\(B=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)

\(B=\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+\dfrac{1}{5x6}+\dfrac{1}{6x7}+\dfrac{1}{7x8}+\dfrac{1}{8x9}+\dfrac{1}{9x10}\)

\(B=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)

\(B=\dfrac{1}{2}-\dfrac{1}{10}\)

\(B=\dfrac{5}{10}-\dfrac{1}{10}\)

\(B=\dfrac{4}{10}\)

\(B=\dfrac{2}{5}\)

20 tháng 7 2018

\(\frac{x-3}{5}+\frac{x-3}{6}+\frac{x-3}{7}=0\)

\(\left(x-3\right).\left(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}\right)=0\)

mà \(\frac{1}{5}>0;\frac{1}{6}>0;\frac{1}{7}>0\Rightarrow\frac{1}{5}+\frac{1}{6}+\frac{1}{7}\ne0\)

=> x - 3= 0

x = 3

26 tháng 8 2023

Chiều rộng:

\(\dfrac{3}{4}-\dfrac{1}{3}=\dfrac{5}{12}\left(km\right)\)

Chu vi:

\(2\cdot\left(\dfrac{3}{4}+\dfrac{5}{12}\right)=\dfrac{7}{3}\left(km\right)\)

Diện tích:

\(\dfrac{3}{4}\cdot\dfrac{5}{12}=\dfrac{5}{16}\left(km^2\right)\)

`#040911`

`b)`

\(A=\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+...+\dfrac{1}{19\times21}\)

`=`\(\dfrac{1}{2}\times\left(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+...+\dfrac{2}{19\times21}\right)\)

`=`\(\dfrac{1}{2}\times\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{21}\right)\)

`=`\(\dfrac{1}{2}\times\left(1-\dfrac{1}{21}\right)\)

\(=\dfrac{1}{2}\times\dfrac{20}{21}\\ =\dfrac{10}{21}\\ \text{ Vậy, A = }\dfrac{10}{21}\)