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Câu 5:
\(\dfrac{13}{6}+x=-2,4\)
\(\Rightarrow\dfrac{13}{6}+x=-\dfrac{12}{5}\)
\(\Rightarrow x=-\dfrac{12}{5}-\dfrac{13}{6}\)
\(\Rightarrow x=-\dfrac{137}{30}\)
Câu 6:
\(3,7-x=\dfrac{7}{10}\)
\(\Rightarrow\dfrac{37}{10}-x=\dfrac{7}{10}\)
\(\Rightarrow x=\dfrac{37}{10}-\dfrac{7}{10}\)
\(\Rightarrow x=3\)
Câu 7:
\(\dfrac{3}{7}+x=\dfrac{2}{14}\)
\(\Rightarrow\dfrac{3}{7}+x=\dfrac{1}{7}\)
\(\Rightarrow x=\dfrac{1}{7}-\dfrac{3}{7}\)
\(\Rightarrow x=-\dfrac{2}{7}\)
Câu 8:
\(\dfrac{3}{7}\cdot y=\dfrac{-2}{5}\)
\(\Rightarrow y=\dfrac{-2}{5}:\dfrac{3}{7}\)
\(\Rightarrow y=\dfrac{-2}{5}\cdot\dfrac{7}{3}\)
\(\Rightarrow y=-\dfrac{14}{15}\)
Bài 1:
a, \(\dfrac{2}{3}\) + \(\dfrac{1}{5}\). \(\dfrac{10}{7}\)
= \(\dfrac{2}{3}\) + \(\dfrac{2}{7}\)
= \(\dfrac{20}{21}\)
b, \(\dfrac{7}{12}\) - \(\dfrac{27}{7}\). \(\dfrac{1}{18}\)
= \(\dfrac{7}{12}\) - \(\dfrac{3}{14}\)
= \(\dfrac{31}{84}\)
c, \(\dfrac{3}{10}\). \(\dfrac{-5}{6}\) - \(\dfrac{1}{8}\)
= - \(\dfrac{1}{4}\) - \(\dfrac{1}{8}\)
= - \(\dfrac{3}{8}\)
d, - \(\dfrac{4}{9}\): \(\dfrac{8}{3}\) + \(\dfrac{1}{18}\)
= - \(\dfrac{1}{6}\) + \(\dfrac{1}{18}\)
= - \(\dfrac{1}{9}\)
e, {[(\(\dfrac{1}{2}\) - \(\dfrac{2}{3}\))2 : 2 ] - 1}. \(\dfrac{4}{5}\)
= {[ (-\(\dfrac{1}{6}\))2 : 2] - 1}. \(\dfrac{4}{5}\)
= { [\(\dfrac{1}{36}\) : 2] - 1}. \(\dfrac{4}{5}\)
= { \(\dfrac{1}{72}\) - 1}. \(\dfrac{4}{5}\)
=- \(\dfrac{71}{72}\).\(\dfrac{4}{5}\)
= -\(\dfrac{71}{90}\)
Ta có:
\(\dfrac{x}{10}=\dfrac{y}{5}\)
\(\Rightarrow\dfrac{x}{20}=\dfrac{y}{10}\) \(\left(1\right)\)
\(\dfrac{y}{2}=\dfrac{z}{3}\)
\(\Rightarrow\dfrac{y}{10}=\dfrac{z}{15}\) \(\left(2\right)\)
Từ \(\left(1\right)\) và \(\left(2\right)\)
\(\Rightarrow\dfrac{x}{20}=\dfrac{y}{10}=\dfrac{z}{15}\)
Lại có:
\(\dfrac{z}{15}=\dfrac{4z}{60}\)
Áp dụng tính chất của dãy tỉ số bằng nhau,ta có:
\(\dfrac{x}{20}=\dfrac{y}{10}=\dfrac{4z}{60}=\dfrac{x+4z}{20+60}=\dfrac{240}{80}=3\)
\(\Rightarrow x=3\cdot20=60\)
\(y=3\cdot10=30\)
\(z=3\cdot15=45\)
6:
\(2^{225}=\left(2^3\right)^{75}=8^{75}\)
\(3^{150}=\left(3^2\right)^{75}=9^{75}\)
mà 8<9
nên \(2^{225}< 3^{150}\)
4: \(\left|5x+3\right|>=0\forall x\)
=>\(-\left|5x+3\right|< =0\forall x\)
=>\(-\left|5x+3\right|+5< =5\forall x\)
Dấu = xảy ra khi 5x+3=0
=>x=-3/5
1:
\(\left(2x+1\right)^4>=0\)
=>\(\left(2x+1\right)^4+2>=2\)
=>\(M=\dfrac{3}{\left(2x+1\right)^4+2}< =\dfrac{3}{2}\)
Dấu = xảy ra khi 2x+1=0
=>x=-1/2
1: \(\sqrt{11}\) là số vô tỉ
2:
a: 4,9(18)=4,91818...
mà 4,91818<4,928
nên 4,9(18)<4,928
b: 4,315<4,318
=>-4,315>-4,318
=>-4,315...>-4,318...
c: \(\sqrt{3}=\sqrt{\dfrac{6}{2}}< \sqrt{\dfrac{7}{2}}\)
3:
a: \(6=\sqrt{3};-1,7=-\sqrt{2,89}\)
0<2,89<3
=>\(0< \sqrt{2,89}< \sqrt{3}\)
=>\(-\sqrt{3}< -\sqrt{2,89}< 0\)
0<35<36<47
=>\(0< \sqrt{35}< \sqrt{36}< \sqrt{47}\)
=>\(-\sqrt{3}< -\sqrt{2,89}< 0< \sqrt{35}< \sqrt{36}< \sqrt{47}\)
=>\(-\sqrt{3}< -\sqrt{2,89}< 0< \sqrt{35}< 6< \sqrt{47}\)
b: \(-\sqrt{2\dfrac{1}{3}}=-\sqrt{2,\left(3\right)}\)
\(-1,5=-\sqrt{2,25}\)
2,25<2,3<2,(3)
=>\(\sqrt{2.25}< \sqrt{2.3}< \sqrt{2.\left(3\right)}\)
=>\(0>-1.5>-\sqrt{2.3}>-\sqrt{2\dfrac{1}{3}}\)
\(0< \sqrt{5\dfrac{1}{6}}=\sqrt{5,1\left(6\right)}< \sqrt{5,3}\)
=>\(\sqrt{5.3}>\sqrt{5\dfrac{1}{6}}>0>-1.5>-\sqrt{2.3}>-\sqrt{2\dfrac{1}{3}}\)
a) Ta có:
\(\widehat{yOu}+\widehat{xOy}=180^o\) (kề bù)
\(\Rightarrow\widehat{yOu}=180^o-\widehat{xOy}\)
\(\Rightarrow\widehat{yOu}=180^o-60^o=120^o\)
Mà: \(\widehat{xOt}+\widehat{tOu}=180^o\) (kề bù)
\(\Rightarrow\widehat{xOt}=180^o-\widehat{tOu}\)
\(\Rightarrow\widehat{xOt}=180^o-30^o=150^o\)
b) Ta có:
\(\widehat{xOy}+\widehat{yOt}+\widehat{tOu}=\widehat{xOu}\)
\(\Rightarrow\widehat{yOt}=\widehat{xOu}-\widehat{xOy}-\widehat{tOu}\)
\(\Rightarrow\widehat{yOt}=180^o-60^o-30^o\)
\(\Rightarrow\widehat{yOt}=90^o\)
\(c,-\dfrac{8}{13}+\left(-\dfrac{7}{5}-x\right)=-\dfrac{1}{2}\\ -\dfrac{7}{5}-x=-\dfrac{1}{2}-\dfrac{8}{13}\\ -\dfrac{7}{5}-x=-\dfrac{29}{26}\\ x=-\dfrac{7}{5}-\left(-\dfrac{29}{26}\right)=-\dfrac{37}{130}\\ d,-1\dfrac{1}{7}-\left[-\dfrac{5}{3}+\left(x-\dfrac{7}{3}\right)\right]=-\dfrac{4}{21}\\ -\dfrac{8}{7}-\left[-\dfrac{5}{3}+\left(x-\dfrac{7}{3}\right)\right]=-\dfrac{4}{21}\\ -\dfrac{5}{3}+\left(x-\dfrac{7}{3}\right)=-\dfrac{8}{7}-\left(-\dfrac{4}{21}\right)\\ -\dfrac{5}{3}+\left(x-\dfrac{7}{3}\right)=-\dfrac{20}{21}\\ x-\dfrac{7}{3}=-\dfrac{20}{21}-\left(-\dfrac{5}{3}\right)\\ x-\dfrac{7}{3}=\dfrac{5}{7}\\ x=\dfrac{5}{7}+\dfrac{7}{3}=\dfrac{64}{21}\\ e,-\dfrac{2}{3}-x:\dfrac{1}{2}=\dfrac{2}{5}\\ x:\dfrac{1}{2}=-\dfrac{2}{3}-\dfrac{2}{5}\\ x:\dfrac{1}{2}=-\dfrac{16}{15}\\ x=-\dfrac{16}{15}\times\dfrac{1}{2}=-\dfrac{8}{15}\)
c: -8/13+(-7/5-x)=-1/2
=>x+7/5+8/13=1/2
=>x=1/2-7/5-8/13=-197/130
d: \(\Leftrightarrow-\dfrac{8}{7}+\dfrac{5}{3}-\left(x-\dfrac{7}{3}\right)=\dfrac{-4}{21}\)
=>\(x-\dfrac{7}{3}=\dfrac{-8}{7}+\dfrac{5}{3}+\dfrac{4}{21}=\dfrac{-24+35+4}{21}=\dfrac{18}{21}=\dfrac{6}{7}\)
=>x=6/7+7/3=18/21+49/21=67/21
e: =>x:1/2=-2/3-2/5=-16/15
=>x=-16/15*1/2=-8/15
f: =>-8/5*x=-1/3+4/9=1/9
=>x=-1/9:8/5=-1/9*5/8=-5/72
g: =>-4/5x-1/4+x=-13/3
=>1/5x=-13/3+1/4=-52/12+3/12=-49/12
=>x=-49/12*5=-245/12
h: =>12/7:x-1/2=0 hoặc 2/5x-3/2=0
=>12/7:x=1/2 hoặc 2/5x=3/2
=>x=12/7:1/2=24/7 hoặc x=3/2:2/5=3/2*5/2=15/4