Tìm x biết: a) 3/2-1/2x=5/3 b)1/2-2/3+2x=1/2 c)-1/5x-2/3=1/10x+5/6
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Số Hs nam là : 40 - 24 = 16 (Hs)
Tỉ số phần trăm giữa số Hs nam và số Hs cả lớp là:
16 : 40 x 100 = 40%
Đáp số: 40%
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`Answer:`
`(1-5/21).(1-5/32).(1-5/45)...(1-5/320)`
`=(21-5)/21 . (32-5)/32 . (45-5)/45 ... (320-5)/320`
`=16/21 . 27/32 . 40/45 ... 315/320`
`=(16.27.40...315)/(21.32.45...320)`
`=((2.8).(3.9).(4.10)...(15.21))/((3.7).(4.8).(5.9)...(16.20))`
`=(2.8.3.9.4.10...15.21)/(3.7.4.8.5.9...16.20)`
`=((2.3.4...15).(8.9.10...21))/((3.4.5...16).(7.8.9...20))`
`=(2.3.4...15)/(3.4.5...16) . (8.9.10...21)/(7.8.9...20)`
`=2/16 . 21/7`
`=3/8`
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`Answer:`
a) \(x+\frac{2}{5}=-\frac{11}{15}\)
\(\Leftrightarrow x=-\frac{11}{15}-\frac{2}{5}\)
\(\Leftrightarrow x=-\frac{17}{15}\)
b) \(\left(x-\frac{7}{18}\right).\frac{18}{29}=-\frac{12}{29}\)
\(\Leftrightarrow x-\frac{7}{18}=-\frac{12}{29}:\frac{18}{29}\)
\(\Leftrightarrow x-\frac{7}{18}=-\frac{2}{3}\)
\(\Leftrightarrow x=-\frac{2}{3}+\frac{7}{18}\)
\(\Leftrightarrow x=-\frac{5}{18}\)
Bài 3:
Số học sinh Giỏi của lớp `6B` là:
`35.40%=14` học sinh
Số học sinh Khá của lớp `6B` là:
`14. 9/7=18` học sinh
Số học sinh Trung bình của lớp `6B` là:
`35-14-18=3` học sinh
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`Answer:`
Bài 1:
a. \(x:\frac{3}{4}+\frac{1}{4}=-\frac{2}{3}\)
\(\Rightarrow x:\frac{3}{4}=-\frac{2}{3}-\frac{1}{4}\)
\(\Rightarrow x:\frac{3}{4}=-\frac{11}{12}\)
\(\Rightarrow x=-\frac{11}{12}.\frac{3}{4}\)
\(\Rightarrow x=-\frac{11}{16}\)
b. \(\left(2x+\frac{3}{5}\right)^2-\frac{9}{25}=0\)
\(\Rightarrow\left(2x+\frac{3}{5}\right)^2=\frac{9}{25}\)
\(\Rightarrow\left(2x+\frac{3}{5}\right)^2=\left(\pm\frac{3}{5}\right)^2\)
\(\Rightarrow\orbr{\begin{cases}2x+\frac{3}{5}=\frac{3}{5}\\2x+\frac{3}{5}=-\frac{3}{5}\end{cases}}\Rightarrow\orbr{\begin{cases}2x=0\\2x=-\frac{6}{5}\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=-\frac{3}{5}\end{cases}}\)
c. \(\frac{1}{3}x+\frac{2}{5}.\left(x-1\right)=0\)
\(\Rightarrow\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)
\(\Rightarrow\frac{11}{15}x=\frac{2}{5}\)
\(\Rightarrow x=\frac{2}{5}:\frac{11}{15}\)
\(\Rightarrow x=\frac{6}{11}\)
d. \(\left(3x-1\right)\left(-\frac{1}{2}x+5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-1=0\\-\frac{1}{2}x+5=0\end{cases}\Rightarrow\orbr{\begin{cases}3x=1\\-\frac{1}{2}x=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=10\end{cases}}}\)
e. \(3\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)
\(\Rightarrow3\left(3x-\frac{1}{2}\right)^3=-\frac{1}{9}\)
\(\Rightarrow\left(3x-\frac{1}{2}\right)^3=\left(-\frac{1}{3}\right)^3\)
\(\Rightarrow3x-\frac{1}{2}=-\frac{1}{3}\)
\(\Rightarrow3x=\frac{1}{6}\)
\(\Rightarrow x=\frac{1}{18}\)
Bài 2:
a. \(\frac{2}{5}.\frac{1}{3}-\frac{2}{25}:\frac{1}{5}+\frac{3}{5}.\frac{1}{3}\)
\(=\frac{2}{15}-\frac{2}{3}+\frac{3}{15}\)
\(=\frac{5}{15}-\frac{2}{3}\)
\(=-\frac{1}{3}\)
b. \(\left(3\frac{1}{3}+2,5\right):\left(3\frac{1}{6}-4\frac{1}{5}\right)-\frac{11}{31}\)
\(=\left(\frac{10}{3}+2,5\right):\left(\frac{19}{6}-\frac{21}{5}\right)-\frac{11}{31}\)
\(=\frac{35}{6}:\left(-\frac{31}{30}\right)-\frac{11}{31}\)
\(=-6\)
c. \(\left(-2\right)^3.\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)
\(=\left(-8\right).\left(\frac{3}{4}-\frac{1}{4}\right):\left(\frac{9}{4}-\frac{7}{6}\right)\)
\(=\left(-8\right).\frac{1}{2}:\frac{13}{12}\)
\(=-\frac{48}{13}\)
d. \(E=-\frac{11}{12}.\frac{7}{8}+\frac{11}{12}.\left(-\frac{15}{17}\right)-\frac{11}{12}\)
\(=\frac{11}{12}.\left(-1\right).\frac{7}{8}+\frac{11}{12}.\left(-\frac{15}{16}\right)-\frac{11}{12}\)
\(=\frac{11}{12}.\left(-\frac{7}{8}+-\frac{15}{16}-1\right)\)
\(=\frac{11}{12}.-\frac{45}{16}\)
\(=-\frac{165}{64}\)
e. \(F=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(=\frac{1004}{1005}\)
g. \(\left(1-\frac{5}{21}\right)\left(1-\frac{5}{32}\right)\left(1-\frac{5}{45}\right)...\left(1-\frac{5}{320}\right)\)
\(=\frac{21-5}{21}.\frac{32-5}{32}.\frac{45-5}{45}...\frac{320-5}{320}\)
\(=\frac{16}{21}.\frac{27}{32}.\frac{40}{45}...\frac{315}{320}\)
\(=\frac{\left(2.8\right)\left(3.9\right)\left(4.10\right)...\left(15.21\right)}{\left(3.7\right)\left(4.8\right)\left(5.9\right)...\left(16.20\right)}\)
\(=\frac{2.8.3.9.4.10...15.21}{3.7.4.8.5.9...16.20}\)
\(=\frac{\left(2.3.4...15\right)\left(8.9.10...21\right)}{\left(3.4.5...16\right)\left(7.8.9...20\right)}\)
\(=\frac{2.3.4...15}{3.4.5...16}.\frac{8.9.10...21}{7.8.9...20}\)
\(=\frac{2}{16}.\frac{21}{7}\)
\(=\frac{3}{8}\)
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\(\left(a^2+3b^2\right)\left(1+3\right)\ge\left(a+3b\right)^2\)
\(\Rightarrow\sqrt{a^2+3b^2}\ge\sqrt{\dfrac{\left(a+3b\right)^2}{4}}=\dfrac{a+3b}{2}\)
Tương tự:
\(\sqrt{b^2+3c^2}\ge\dfrac{b+3c}{2}\) ; \(\sqrt{c^2+3a^2}\ge\dfrac{c+3a}{2}\)
Cộng vế \(\Rightarrow VT\ge\dfrac{4\left(a+b+c\right)}{2}=6\)
Dấu "=" xảy ra khi \(a=b=c=1\)
a) \(\dfrac{1}{2}x=\dfrac{3}{2}-\dfrac{5}{3}=-\dfrac{1}{6}\)
\(x=-\dfrac{1}{6}:\dfrac{1}{2}=-\dfrac{1}{3}\)
b) \(-\dfrac{1}{6}+2x=\dfrac{1}{2}\)
\(x=\left(\dfrac{1}{2}+\dfrac{1}{6}\right):2=\dfrac{1}{3}\)