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Bài 1:
e; \(\dfrac{10}{21}\) - \(\dfrac{3}{8}\) : \(\dfrac{15}{4}\)
= \(\dfrac{10}{21}\) - \(\dfrac{3}{8}\) x \(\dfrac{4}{15}\)
= \(\dfrac{10}{21}\) - \(\dfrac{1}{10}\)
= \(\dfrac{100}{210}\) - \(\dfrac{21}{210}\)
= \(\dfrac{79}{210}\)
f; (\(\dfrac{2}{3}\) + \(\dfrac{3}{4}\)).(\(\dfrac{5}{7}\) + \(\dfrac{5}{14}\))
= (\(\dfrac{8}{12}\) + \(\dfrac{9}{12}\)).(\(\dfrac{10}{14}\) + \(\dfrac{5}{14}\))
= \(\dfrac{17}{12}\).\(\dfrac{15}{14}\)
= \(\dfrac{85}{56}\)
Trả lời:
\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right)\left(5x+6\right)}=\frac{2005}{2006}\)
\(\Rightarrow1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)
\(\Rightarrow1-\frac{1}{5x+6}=\frac{2005}{2006}\)
\(\Rightarrow\frac{1}{5x+6}=1-\frac{2005}{2006}\)
\(\Rightarrow\frac{1}{5x+6}=\frac{1}{2006}\)
\(\Rightarrow5x+6=2006\)
\(\Rightarrow5x=2000\)
\(\Rightarrow x=400\)
Vậy x = 400
Trả lời:
\(\frac{x}{2008}-\frac{1}{10}-\frac{1}{15}-\frac{1}{21}-...-\frac{1}{120}=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}-\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right)=\frac{5}{8}\)\(\frac{5}{8}\)
Đặt \(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\), ta được : \(\frac{x}{2008}-A=\frac{5}{8}\) (*)
\(\Rightarrow A=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(\Rightarrow A=2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(\Rightarrow A=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(\Rightarrow A=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(\Rightarrow A=2\left(\frac{1}{4}-\frac{1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)
Thay A vào (*) , ta có:
\(\frac{x}{2008}-\frac{3}{8}=\frac{5}{8}\)
\(\Rightarrow\frac{x}{2008}=1\)
\(\Rightarrow x=2008\)
Vậy x = 2008
a)
\(175\cdot19+38\cdot175+43\cdot175\\ =175\cdot19+175\cdot38+175\cdot43\\ =175\cdot\left(19+38+43\right)\\ =175\cdot100\\ =17500\)
b)
\(125\cdot75+125\cdot13-80\cdot125\\ =125\cdot75+125\cdot13-125\cdot80\\ =125\cdot\left(75+13-80\right)\\ =125\cdot10\\ =125\cdot8\\ =1000\)
a, 175. 19 + 38. 175 + 43. 175
= 175. 19 + 175. 38 + 175. 43
= 175.(19 + 38 + 43)
= 175. 100
= 17500
3x . 2 + 15 = 33
3x . 2 = 33 - 15 = 18
3x = 18 : 2 = 9 = 32
=> x = 2
Giải
Theo đề bài ta có:
abc + ab + a = 874
( 100a + 10b + c ) + ( 10a + b ) + a = 874
111a + 11b + c = 874 ( 1 )
Từ ( 1 ) suy ra 6 < a < 8
Vậy a = 7
Thay a = 7 vào ( 1 ) ta được:
11b + c = 874 – 777 = 97 ( 2 )
Từ ( 2 ) suy ra 7 < b < 9
Vậy b = 8
Thay b = 8 vào ( 2 ) ta được:
88 + c = 97
c = 97 – 88 = 9
Vậy a = 7, b = 8, c = 9
Ta có:
abc + ab + a = 874
789 + 78 + 7 = 874
nhớ bấm giúp mình nha bạn...
Chiều rộng của mảnh vườn hình chữ nhật là:
\(\dfrac{21}{4}\) : \(\dfrac{7}{3}\) = \(\dfrac{9}{4}\) (m)
Chu vi của mảnh vườn hìn chữ nhật là:
(\(\dfrac{21}{4}\) + \(\dfrac{9}{4}\)) x 2 = 15 (m)
Diện tích của mảnh vườn hình chữ nhật là:
\(\dfrac{21}{4}\) x \(\dfrac{9}{4}\) = \(\dfrac{189}{16}\) (m2)
b; Số tiền thu được khi trồng hoa để bán trên mảnh đất hình chữ nhật đó là:
80 000 x \(\dfrac{189}{16}\) = 945 000 (đồng)
KL...
Bài 5:
a, Chiều rộng mảnh vườn:
\(\dfrac{21}{4}:\dfrac{7}{3}=\dfrac{9}{4}\left(m\right)\)
Chu vi mảnh đất:
\(2\times\left(\dfrac{21}{4}+\dfrac{9}{4}\right)=15\left(m\right)\)
Diện tích mảnh đất:
\(\dfrac{21}{4}\times\dfrac{9}{4}=\dfrac{189}{16}\left(m^2\right)\)
b, Số tiền thu được khi bán hoa:
\(\dfrac{189}{16}\times80000=945000\left(đồng\right)\)
\(\frac{27^{20}+9^{20}}{9^{25}+81^5}=\frac{3^{60}+3^{60}}{3^{50}+3^{20}}=\frac{3^{20}\left(3^{40}+3^{40}\right)}{3^{20}\left(3^{30}+1\right)}=\frac{3^{40}.2}{3^{30}+1}\)
1: \(\dfrac{21}{-20}-\dfrac{11}{5}-\dfrac{-5}{4}\)
\(=-\dfrac{21}{20}-\dfrac{11}{5}+\dfrac{5}{4}\)
\(=-\dfrac{21}{20}-\dfrac{44}{20}+\dfrac{25}{20}=\dfrac{-40}{20}=-2\)
2: \(\dfrac{-1}{6}-\dfrac{4}{-3}-\dfrac{11}{18}\)
\(=\dfrac{-1}{6}+\dfrac{4}{3}-\dfrac{11}{18}\)
\(=-\dfrac{3}{18}+\dfrac{24}{18}-\dfrac{1}{18}=\dfrac{10}{18}=\dfrac{5}{9}\)
3: \(\dfrac{7}{17}-\dfrac{5}{-2}+\dfrac{13}{34}\)
\(=\dfrac{7}{17}+\dfrac{5}{2}+\dfrac{13}{34}\)
\(=\dfrac{14}{34}+\dfrac{85}{34}+\dfrac{13}{34}=\dfrac{112}{34}=\dfrac{56}{17}\)
4: \(\left(\dfrac{3}{29}-\dfrac{1}{5}\right)\cdot\dfrac{29}{3}\)
\(=\left(\dfrac{15}{145}-\dfrac{29}{145}\right)\cdot\dfrac{29}{3}\)
\(=\dfrac{-14}{145}\cdot\dfrac{29}{3}=-\dfrac{14}{3}\cdot\dfrac{29}{145}=\dfrac{-14}{15}\)
5: \(\dfrac{3}{4}:\dfrac{7}{8}-3\dfrac{1}{4}+1\)
\(=\dfrac{3}{4}\cdot\dfrac{8}{7}-\dfrac{13}{4}+1\)
\(=\dfrac{6}{7}-\dfrac{9}{4}\)
\(=\dfrac{24}{28}-\dfrac{54}{28}=\dfrac{-30}{28}=-\dfrac{15}{14}\)
6: \(\left(0,75+\dfrac{-1}{3}-\dfrac{5}{8}\right):\dfrac{-5}{6}\)
\(=\left(\dfrac{3}{4}-\dfrac{1}{3}-\dfrac{5}{8}\right):\dfrac{-5}{6}\)
\(=\left(\dfrac{18}{24}-\dfrac{8}{24}-\dfrac{15}{24}\right):\dfrac{-5}{6}\)
\(=\dfrac{-5}{24}\cdot\dfrac{6}{-5}=\dfrac{6}{24}=\dfrac{1}{4}\)
7: \(3\dfrac{1}{7}-\dfrac{1}{4}\cdot\dfrac{2}{9}+25\%\)
\(=\dfrac{22}{7}-\dfrac{1}{18}+\dfrac{1}{4}\)
\(=\dfrac{841}{252}\)
8: \(4\dfrac{1}{5}-\dfrac{1}{5}\cdot\dfrac{10}{11}+15\%\)
\(=\dfrac{21}{5}-\dfrac{2}{11}+\dfrac{3}{20}\)
\(=\dfrac{924}{220}-\dfrac{40}{220}+\dfrac{66}{220}=\dfrac{950}{220}=\dfrac{95}{22}\)
9: \(1\dfrac{1}{2}-1\dfrac{2}{5}\cdot1,5-2,2:\dfrac{11}{4}\)
\(=\dfrac{3}{2}-\dfrac{7}{5}\cdot\dfrac{3}{2}-2,2\cdot\dfrac{4}{11}\)
\(=\dfrac{3}{2}\left(1-\dfrac{7}{5}\right)-\dfrac{8.8}{11}\)
\(=\dfrac{3}{2}\cdot\dfrac{-2}{5}-\dfrac{4}{5}=-\dfrac{3}{5}-\dfrac{4}{5}=-\dfrac{7}{5}\)
10: \(\dfrac{3}{17}\cdot\dfrac{13}{15}+\dfrac{3}{17}\cdot\dfrac{2}{15}\)
\(=\dfrac{3}{17}\left(\dfrac{13}{15}+\dfrac{2}{15}\right)=\dfrac{3}{17}\cdot\dfrac{15}{15}=\dfrac{3}{17}\)
11: \(\dfrac{7}{19}\cdot\dfrac{8}{11}+\dfrac{7}{19}\cdot\dfrac{3}{11}+\dfrac{-14}{19}\)
\(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)-\dfrac{14}{19}=\dfrac{7}{19}-\dfrac{14}{19}=-\dfrac{7}{19}\)
12: \(\dfrac{-4}{5}\cdot\dfrac{7}{11}+\dfrac{-4}{5}\cdot\dfrac{4}{11}+1\dfrac{2}{11}\)
\(=\dfrac{-4}{5}\left(\dfrac{7}{11}+\dfrac{4}{11}\right)+1+\dfrac{2}{11}=-\dfrac{4}{5}+1+\dfrac{2}{11}\)
\(=\dfrac{1}{5}+\dfrac{2}{11}=\dfrac{11}{55}+\dfrac{10}{55}=\dfrac{21}{55}\)