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Bài 5:
a: Diện tích mảnh vườn là:
\(60\cdot60\cdot\dfrac{2}{3}=2400\left(m^2\right)\)
b: Diện tích phần trồng hoa là:
\(240:\dfrac{3}{5}=400\left(m^2\right)\)
c: Diện tích trồng hoa bằng:
\(\dfrac{400}{2400-400}=\dfrac{400}{2000}=20\%\)
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\(A=7+7^2+7^3+7^4+7^5+7^6+7^7+7^8\)
\(A=\left(7+7^3\right)+\left(7^2+7^4\right)+\left(7^5+7^7\right)+\left(7^6+7^8\right)\)
\(A=7\cdot\left(7+7^2\right)+7^2\cdot\left(1+7^2\right)+7^5\cdot\left(1+7^2\right)+7^6\cdot\left(1+7^2\right)\)
\(A=7\cdot50+7^2\cdot50+7^5\cdot50+7^6\cdot50\)
\(A=50\cdot\left(7+7^2+7^5+7^6\right)\)
\(A=5\cdot10\cdot\left(7+7^2+7^5+7^6\right)\)
Ta có: 5 ⋮ 5
⇒ \(A=5\cdot10\cdot\left(7+7^2+7^5+7^6\right)\) ⋮ 5 (đpcm)
A = 7 + 72 + 73 + 74 + 75 + 76 + 77 + 78
A = (7 + 73) + (72+ 74) + (75 + 77) + (76 + 78)
A = 7.(1 + 72) + 72.(1 + 72) + 75.(1 + 72) + 76.(1 + 72)
A = 7.( 1 + 49) + 72.( 1 + 49) + 75.(1 + 49) + 76. (1 + 49)
A = 7.50 + 72.50 + 75.50 + 76.50
A = 50.(7 + 72 + 75 + 76)
Vì 50 ⋮ 5 nên A = 50.(7 + 72 + 76) ⋮ 5 đpcm
![](https://rs.olm.vn/images/avt/0.png?1311)
22. \(\dfrac{\dfrac{3}{4}+\dfrac{3}{7}-\dfrac{3}{8}}{\dfrac{5}{4}+\dfrac{5}{7}-\dfrac{5}{8}}+1=\dfrac{3\left(\dfrac{1}{4}+\dfrac{1}{7}-\dfrac{1}{8}\right)}{5\left(\dfrac{1}{4}+\dfrac{1}{7}-\dfrac{1}{8}\right)}+1=\dfrac{3}{5}+1=\dfrac{8}{5}\)
23. \(\dfrac{2}{5}+\dfrac{3}{5}:\left(\dfrac{3}{5}+\dfrac{-2}{3}\right)+\dfrac{7}{2}=\dfrac{2}{5}+\dfrac{3}{5}:\left(\dfrac{9-10}{15}\right)+\dfrac{7}{2}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{-15}{1}+\dfrac{7}{2}=\dfrac{2}{5}-\dfrac{45}{5}+\dfrac{7}{2}\)
\(=\dfrac{4}{10}-\dfrac{90}{10}+\dfrac{35}{10}=\dfrac{4-90+35}{10}=-\dfrac{51}{10}\)
24. \(\dfrac{4+\dfrac{4}{73}-\dfrac{4}{115}}{5+\dfrac{5}{73}-\dfrac{1}{23}}=\dfrac{4\left(1+\dfrac{1}{73}-\dfrac{1}{115}\right)}{5+\dfrac{5}{73}-\dfrac{5}{115}}=\dfrac{4\left(1+\dfrac{1}{73}-\dfrac{1}{115}\right)}{5\left(1+\dfrac{1}{73}-\dfrac{1}{115}\right)}=\dfrac{4}{5}\)
4. \(\dfrac{5}{7}-\dfrac{2}{11}+\dfrac{5}{7}-\dfrac{9}{11}=\dfrac{5}{7}\left(-\dfrac{2}{11}-\dfrac{9}{11}\right)=-\dfrac{5}{7}\)
9. \(\dfrac{5}{9}.\dfrac{7}{13}+\dfrac{5}{9}.\dfrac{9}{13}-\dfrac{5}{9}.\dfrac{3}{13}=\dfrac{5}{9}\left(\dfrac{7}{13}+\dfrac{9}{13}-\dfrac{3}{13}\right)=\dfrac{5}{9}\)
10. \(\dfrac{-5}{9}+\dfrac{8}{15}-\dfrac{2}{11}-\dfrac{4}{9}+\dfrac{7}{15}=\left(-\dfrac{5}{9}-\dfrac{4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)-\dfrac{2}{11}=-\dfrac{2}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
<=>55 - 3x = 25
<=>-3x = 25 - 55
<=>-3x = -30
<=>x=10
55 - 3x = (-5)2
55 - 3x = 25
3x = 55 - 25
3x = 30
x = 30 : 3
x = 10
Vậy x = 10
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Đặt A = 2 + 4 + 8 + ... + 2048
= 2 + 22 + 23 + ... + 211
=> 2A = 22 + 23 + 24 + ... + 212
Lấy 2A trừ A theo vế ta có
2A - A = (22 + 23 + 24 + ... + 212) - (2 + 22 + 23 + ... + 211)
=> A = 212 - 2
Đặt \(A=2+4+8+16+...+1024+2048\)
\(\Rightarrow2A=4+8+16+32+...+2048+4096\)
\(\Rightarrow2A-A=4096-2\)
\(\Rightarrow A=4094\)
\(33\times77+66\times77+77\)
\(=77\times\left(33+66+1\right)\)
\(=77\times100\)
\(=7700\)