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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 |
a. = 1/20 + 5 - 1/2
= 101/20 - 1/2
= 91/20
b. = ( 6/15 - 3/5) - ( 7/8 + 2/16) + 3
= -1/5 - 1 + 3
= 9/5
c. = 15/7 . ( 3/5 - 8/5)
= 15/7 . ( -1)
= - 15/7
e. = -14/9 - 3/9
= -17/9
f. = 19/21 . ( 15/17 + 2/17) + 13/21
= 19/21 . 1 + 13/21
= 32/21
g. = 43/12 : 2 + 5/24
= 43/24 + 5/24
= 2
\(1,\)
\(a,\dfrac{11}{125}-\dfrac{17}{18}-\dfrac{5}{7}+\dfrac{4}{9}+\dfrac{17}{14}\)
\(=\dfrac{11}{125}+\left(\dfrac{4}{9}-\dfrac{17}{18}\right)+\left(\dfrac{17}{14}-\dfrac{5}{7}\right)\)
\(=\dfrac{11}{125}+\left(\dfrac{-1}{2}\right)+\dfrac{1}{2}\)
\(=\dfrac{11}{125}\)
\(b,-1\dfrac{5}{7}.15+\dfrac{2}{7}.\left(-15\right)+\left(-105\right).\left(\dfrac{2}{3}-\dfrac{4}{5}+\dfrac{1}{7}\right)\)
\(=\dfrac{-12}{7}.15+\dfrac{2}{7}.\left(-15\right)+\left(105\right).\left(\dfrac{2}{3}-\dfrac{4}{5}+\dfrac{1}{7}\right)\)
\(=-15.\left[\dfrac{12}{7}+\dfrac{2}{7}+\left(-5\right).\left(\dfrac{2}{3}-\dfrac{4}{5}+\dfrac{1}{7}\right)\right]\)
\(=-15.\left[2+\left(-5\right).\dfrac{1}{105}\right]\)
\(=-15.\left(2-\dfrac{1}{21}\right)\)
\(=-15.\dfrac{41}{21}=\dfrac{-615}{21}\)
\(2,\)
\(a,\dfrac{11}{13}-\left(\dfrac{5}{42}-x\right)=-\left(\dfrac{15}{28}-\dfrac{11}{13}\right)\)
\(\Leftrightarrow\dfrac{11}{13}-\dfrac{5}{42}+x=\dfrac{-15}{28}+\dfrac{11}{13}\)
\(\Leftrightarrow x=\dfrac{-15}{28}+\dfrac{11}{13}-\dfrac{11}{13}+\dfrac{5}{42}\)
\(\Leftrightarrow x=\left(\dfrac{11}{13}-\dfrac{11}{13}\right)+\left(\dfrac{5}{42}+\dfrac{-15}{28}\right)\)
\(\Leftrightarrow x=\dfrac{5}{12}\)
Vậy \(x=\dfrac{5}{12}\)
\(b,\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)
\(\Leftrightarrow\left|x+\dfrac{4}{15}\right|-3,75=-2,15\)
\(\Leftrightarrow\left|x+\dfrac{4}{15}\right|=-2,15+3,75=1,6=\dfrac{16}{10}=\dfrac{8}{5}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{4}{15}=\dfrac{8}{5}\\x+\dfrac{4}{15}=\dfrac{-8}{5}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{8}{5}-\dfrac{4}{15}=\dfrac{4}{3}\\x=\dfrac{-8}{5}-\dfrac{4}{15}=\dfrac{-28}{15}\end{matrix}\right.\)
Vậy \(x\in\left\{\dfrac{4}{3};\dfrac{-28}{15}\right\}\)
\(c,7^{x+2}+2.7^{x-1}=345\)
\(\Leftrightarrow7^{x-1}.\left(7^3+2\right)=345\)
\(\Leftrightarrow7^{x-1}.\left(343+2\right)=345\)
\(\Leftrightarrow7^{x-1}.345=345\)
\(\Leftrightarrow7^{x-1}=345:345=1\)
\(\Leftrightarrow x-1=0\)
\(x=0+1=1\)
Vậy \(x=1\)
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
e)\(16\dfrac{2}{7}:\left(-\dfrac{3}{5}\right)+28\dfrac{2}{7}:\left(-\dfrac{3}{5}\right)\)
=\(\left(16\dfrac{2}{7}+28\dfrac{2}{7}\right):\left(-\dfrac{3}{5}\right)\)
=\(\dfrac{312}{7}\)\(:\left(-\dfrac{3}{5}\right)\)
=\(-\dfrac{516}{7}\)
a)\(\dfrac{7}{8}.\left(\dfrac{2}{12}+\dfrac{4}{10}\right)\)
=\(\dfrac{7}{8}.\left(\dfrac{1}{6}+\dfrac{2}{5}\right)\)
=\(\dfrac{7}{8}.\)\(\dfrac{17}{30}\)
=\(\dfrac{119}{240}\)
\(\dfrac{50-\dfrac{4}{15}+\dfrac{2}{15}-\dfrac{2}{17}}{100-\dfrac{8}{15}+\dfrac{4}{15}-\dfrac{4}{17}}\) \(=\dfrac{1.\left(50-\dfrac{4}{15}+\dfrac{2}{15}-\dfrac{2}{17}\right)}{2.\left(50-\dfrac{4}{15}+\dfrac{2}{15}-\dfrac{2}{17}\right)}=\dfrac{1}{2}\)