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9) Theo bài, ta có : 5x = 4y
\(\Rightarrow\dfrac{x}{4}=\dfrac{y}{5}\)
Mà y - x = 7
Theo tính chất dãy tỉ số bằng nhau, ta có :
\(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{y-x}{5-4}=\dfrac{7}{1}=7\)
Do đó : \(\dfrac{x}{4}=7\Rightarrow x=7.4=28\)
\(\dfrac{y}{5}=7\Rightarrow y=7.5=35\)
Vậy x = 28 ; y = 35
\(1,\)\(a,\dfrac{2+3}{9+3}=\dfrac{5}{12}\)
\(\Leftrightarrow\dfrac{5}{12}=\dfrac{5.3}{12.3}=\dfrac{15}{36}\) và \(\dfrac{6}{9}=\dfrac{24}{36}\)
\(\dfrac{15}{36}< \dfrac{24}{36}\Rightarrow\dfrac{5}{12}< \dfrac{6}{9}\) hay \(\dfrac{2+3}{9+3}< \dfrac{6}{9}\)
\(\dfrac{2}{3}=\dfrac{8}{12}\Rightarrow\dfrac{5}{12}< \dfrac{2}{3}\) hay \(\dfrac{2+3}{9+3}< \dfrac{2}{3}\)
\(b,\dfrac{6-2}{9-3}=\dfrac{4}{6}=\dfrac{2}{3}\Rightarrow\dfrac{6-2}{9-3}=\dfrac{2}{3}\)
\(\dfrac{2}{3}=\dfrac{6}{9}\Rightarrow\dfrac{6-2}{9-3}=\dfrac{6}{9}\)
\(2,a,\dfrac{3+12}{5+20}=\dfrac{15}{25}=\dfrac{3}{5}\Rightarrow\dfrac{3+12}{5+20}=\dfrac{3}{5}\)
\(\dfrac{3}{5}=\dfrac{3.4}{5.4}=\dfrac{12}{20}\Rightarrow\dfrac{3+12}{5+20}=\dfrac{12}{20}\)
\(b,\dfrac{3-12}{5-20}=\dfrac{-9}{-15}=\dfrac{9}{15}=\dfrac{3}{5}\Rightarrow\dfrac{3-12}{5-20}=\dfrac{3}{5}\)
\(\dfrac{3}{5}=\dfrac{3.4}{5.4}=\dfrac{12}{20}\Rightarrow\dfrac{3-12}{5-20}=\dfrac{12}{20}\)
| lũy thừa |
cơ số |
cơ số |
giá trị lũy thừa |
| (4/5)n | 4 | 5 | (4/5)n = 4n/5n |
| (-3/4)n | -3 | 4 | (-3/4)n= -3n/4n |
| (5/-7)n | 5 | -7 | (5/-7)n=5n/-7n |
\(B=\dfrac{1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}}{4+\dfrac{4}{7}+\dfrac{4}{7^2}-\dfrac{4}{7^3}}\cdot\dfrac{858585}{313131}\cdot\left(-1\dfrac{14}{17}\right)\)
\(=\dfrac{1}{4}\cdot\dfrac{85}{31}\cdot\dfrac{-31}{17}\)
\(=\dfrac{-5}{4}\)
\(A=\dfrac{10}{7.12}+\dfrac{10}{12.17}+\dfrac{10}{17.22}+...+\dfrac{10}{502.507}\) (sửa 502+507 thành 503.507)
\(\Rightarrow A=10\left(\dfrac{1}{7.12}+\dfrac{1}{12.17}+\dfrac{1}{17.22}+...+\dfrac{1}{502.507}\right)\)
\(\Rightarrow A=10.\dfrac{1}{5}\left(\dfrac{1}{7}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{22}+...+\dfrac{1}{502}-\dfrac{1}{507}\right)\)
\(\Rightarrow A=2.\left(\dfrac{1}{7}-\dfrac{1}{507}\right)=2.\left(\dfrac{500}{3549}\right)=\dfrac{1000}{3549}\)
\(B=\dfrac{4}{8.13}+\dfrac{4}{13.18}+\dfrac{4}{18.23}+...+\dfrac{4}{253.258}\)
\(\Rightarrow B=4\left(\dfrac{1}{8.13}+\dfrac{1}{13.18}+\dfrac{1}{18.23}+...+\dfrac{1}{253.258}\right)\)
\(\Rightarrow B=4.\dfrac{1}{5}\left(\dfrac{1}{8}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{23}+...+\dfrac{1}{253}-\dfrac{1}{258}\right)\)
\(\Rightarrow B=\dfrac{4}{5}\left(\dfrac{1}{8}-\dfrac{1}{258}\right)=\dfrac{4}{5}\left(\dfrac{129}{1032}-\dfrac{8}{1032}\right)=\dfrac{4}{5}.\dfrac{121}{1032}=\dfrac{121}{1290}\)
Khi thể tích là 2m3 thì khối lượng là 997*2:1=1994m3
Khi khối lượng là 1994kg thì thể tích là 1994*1:997=2m3
\(\dfrac{50-\dfrac{4}{15}+\dfrac{2}{15}-\dfrac{2}{17}}{100-\dfrac{8}{15}+\dfrac{4}{15}-\dfrac{4}{17}}\) \(=\dfrac{1.\left(50-\dfrac{4}{15}+\dfrac{2}{15}-\dfrac{2}{17}\right)}{2.\left(50-\dfrac{4}{15}+\dfrac{2}{15}-\dfrac{2}{17}\right)}=\dfrac{1}{2}\)