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21 tháng 9
Bài 10:
1: \(\left(7-\frac15+\frac13\right)-\left(6+\frac95+\frac43\right)\)
\(=7-\frac15+\frac13-6-\frac95-\frac43\)
\(=\left(7-6\right)+\left(-\frac15-\frac95\right)+\left(\frac13-\frac43\right)\)
=1-2-1
=-2
2: \(7+\left(\frac{7}{12}-\frac12+3\right)-\left(\frac{1}{12}+5\right)\)
\(=7+\frac{1}{12}+3-\frac{1}{12}-5\)
=10-5
=5
3: \(\left(\frac12-\frac13\right)-\left(\frac53-\frac32\right)+\left(\frac73-\frac52\right)\)
\(=\frac12-\frac13-\frac53+\frac32+\frac73-\frac52\)
\(=-\frac12+\frac13=\frac{-3+2}{6}=-\frac16\)
4: \(\left(\frac27-\frac94\right)-\left(-\frac37+\frac54\right)-\left(\frac24-\frac97\right)\)
\(=\frac27-\frac94+\frac37-\frac54-\frac24+\frac97\)
\(=\left(\frac27+\frac37+\frac97\right)+\left(-\frac94-\frac54-\frac24\right)=\frac{14}{7}-\frac{16}{4}=2-4=-2\)
5: \(\left(\frac53-\frac37+9\right)-\left(2+\frac57-\frac23\right)+\left(\frac87-\frac43-10\right)\)
\(=\frac53-\frac37+9-2-\frac57+\frac23+\frac87-\frac43-10\)
\(=\left(\frac53+\frac23-\frac43\right)+\left(-\frac37-\frac57+\frac87\right)+\left(9-2-10\right)\)
\(=\frac33+\left(-3\right)=1-3=-2\)
Bài 11:
1: \(\frac25\cdot\frac38_{}+\frac58\cdot\frac25=\frac25\left(\frac38+\frac58\right)=\frac25\cdot\frac88=\frac25\)
2: \(\frac23\cdot\frac52-\frac34\cdot\frac23=\frac23\left(\frac52-\frac34\right)=\frac23\cdot\frac74=\frac{14}{12}=\frac76\)
3: \(\frac57\cdot\frac{19}{23}-\frac{12}{23}\cdot\frac57=\frac57\left(\frac{19}{23}-\frac{12}{23}\right)=\frac57\cdot\frac{7}{23}=\frac{5}{23}\)
4: \(\frac72\cdot\frac{11}{6}-\frac72\cdot\frac56=\frac72\left(\frac{11}{6}-\frac56\right)=\frac72\cdot\frac66=\frac72\)
5: \(\frac{11}{9}\cdot\frac34-\frac29\cdot\frac34=\frac34\left(\frac{11}{9}-\frac29\right)=\frac34\cdot\frac99=\frac34\)
6: \(\frac37\cdot\frac{13}{5}+\frac37\cdot\frac85=\frac37\left(\frac{13}{5}+\frac85\right)=\frac37\cdot\frac{21}{5}=\frac{21}{7}\cdot\frac35=3\cdot\frac35=\frac95\)
7: \(\frac{7}{15}\cdot\frac{16}{13}+\frac{7}{15}\cdot\frac{-3}{13}=\frac{7}{15}\left(\frac{16}{13}-\frac{3}{13}\right)=\frac{7}{15}\cdot\frac{13}{13}=\frac{7}{15}\)
8: \(-\frac{23}{7}\cdot\frac{3}{10}+\frac{13}{7}\cdot\frac{3}{10}=\frac{3}{10}\left(-\frac{23}{7}+\frac{13}{7}\right)=\frac{3}{10}\cdot\frac{-10}{7}=-\frac37\)
9: \(\frac{-11}{8}\cdot\frac{19}{3}+\frac{19}{3}\cdot\frac{-5}{8}=\frac{19}{3}\left(-\frac{11}{8}-\frac58\right)=\frac{19}{3}\cdot\left(-2\right)=-\frac{38}{3}\)
Bài 12: Bài 12:
1: \(\frac{-5}{17}\cdot\frac{31}{33}+\frac{-5}{17}\cdot\frac{2}{33}+1\frac{5}{17}\)
\(=-\frac{5}{17}\cdot\left(\frac{31}{33}+\frac{2}{33}\right)+1+\frac{5}{17}\)
\(=-\frac{5}{17}+1+\frac{5}{17}=1\)
2: \(\frac57\cdot\left(-\frac{3}{11}\right)+\frac57\cdot\left(-\frac{8}{11}\right)+2\frac57\)
\(=-\frac57\left(\frac{3}{11}+\frac{8}{11}\right)+2+\frac57\)
\(=-\frac57+2+\frac57=2\)
3: \(\frac{9}{10}\cdot\frac{23}{11}-\frac{1}{11}\cdot\frac{9}{10}+\frac{9}{10}\)
\(=\frac{9}{10}\left(\frac{23}{11}-\frac{1}{11}+1\right)\)
\(=\frac{9}{10}\cdot\left(2+1\right)=\frac{9}{10}\cdot3=\frac{27}{10}\)
4: \(\frac54\cdot\frac{8}{15}+\frac{-5}{16}\cdot\frac{8}{15}-1\)
\(=\frac{8}{15}\left(\frac54-\frac{5}{16}\right)-1\)
\(=\frac{8}{15}\left(\frac{20}{16}-\frac{5}{16}\right)-1=\frac{8}{16}-1=-\frac{8}{16}=-\frac12\)
5: \(-\frac{19}{3}\cdot\frac{14}{4}+\frac{25}{4}\cdot\frac{-19}{3}+4\frac34\)
\(=-\frac{19}{4}\left(\frac{14}{3}+\frac{25}{3}\right)+4\frac34\)
\(=-\frac{19}{4}\cdot13+\frac{19}{4}=\frac{19}{4}\left(-13+1\right)=\frac{19}{4}\cdot\left(-12\right)=-57\)
6: \(\frac{1}{27}\cdot\frac{-3}{7}-\frac59\cdot\frac{-3}{7}+\frac19\)
\(=-\frac37\left(\frac{1}{27}-\frac59\right)+\frac19\)
\(=-\frac37\left(\frac{1}{27}-\frac{15}{27}\right)+\frac19=-\frac37\cdot\frac{-14}{27}+\frac19=\frac29+\frac19=\frac39=\frac13\) b
20 tháng 9
Câu 37:
a: \(\frac{-7}{15}\cdot\frac{5}{-21}\)
\(=\frac{-7}{-21}\cdot\frac{5}{15}\)
\(=\frac13\cdot\frac13=\frac19\)
b: \(-\frac49:\frac23=-\frac49\cdot\frac32=-\frac{12}{18}=-\frac23\)
c: \(-\frac{3}{15}\cdot\frac{35}{-7}=\frac{3}{15}\cdot\frac{35}{7}=\frac15\cdot5=1\)
d: \(-\frac49:\left(-2\frac23\right)=-\frac49:\frac{-8}{3}=\frac49:\frac83=\frac49\cdot\frac38=\frac{12}{72}=\frac16\)
Câu 36:
a: \(-3,5\cdot\frac{-4}{21}=\frac{-3,5\cdot\left(-4\right)}{21}=\frac{14}{21}=\frac23\)
b: \(1\frac23\cdot\left(-2\frac13\right)=-\frac53\cdot\frac73=-\frac{35}{9}\)
c: \(\left(-2,5\right):\frac{3}{-4}=\left(-2,5\right)\cdot\frac{\left(-4\right)}{3}=\frac{10}{3}\)
d: \(\left(-8\frac25\right):\left(-2\frac45\right)=\frac{-42}{5}:\frac{-14}{5}=\frac{42}{14}=3\)
Câu 35:
a: \(\frac32\cdot\frac{-2}{25}=\frac{3}{25}\cdot\frac{-2}{2}=-\frac{3}{25}\)
b: \(\frac{-8}{5}\cdot\frac{-3}{4}=\frac85\cdot\frac34=\frac{24}{20}=\frac65\)
c: \(-\frac{15}{4}:\frac{-21}{10}=\frac{15}{4}:\frac{21}{10}=\frac{15}{4}\cdot\frac{10}{21}=\frac{10}{4}\cdot\frac{15}{21}=\frac52\cdot\frac57=\frac{25}{14}\)
d: \(-\frac{15}{7}:\frac{5}{14}=-\frac{15}{7}\cdot\frac{14}{5}=\frac{-210}{35}=-6\)
Câu 34:
\(-3\frac15\cdot2,5=-\frac{16}{5}\cdot\frac52=-\frac{16}{2}=-8\)
Câu 33:
a: \(\frac{-1}{21}+\frac{-1}{14}=\frac{-2}{42}+\frac{-3}{42}=\frac{-2-3}{42}=-\frac{5}{42}\)
b: \(\frac{-3}{7}+\frac{-2}{9}=\frac{-27}{63}+\frac{-14}{63}=-\frac{27+14}{63}=-\frac{41}{63}\)
c: \(\frac{-5}{12}+\frac{7}{18}=-\frac{15}{36}+\frac{14}{36}=\frac{-15+14}{36}=\frac{-1}{36}\)
d: \(\frac{-4}{15}+0,75=-\frac{4}{15}+\frac34=-\frac{16}{60}+\frac{45}{60}=\frac{45-16}{60}=\frac{29}{60}\)
e: \(-\frac23+1,1=-\frac23+\frac{11}{10}=-\frac{20}{30}+\frac{33}{30}=\frac{33-20}{30}=\frac{13}{30}\)
f: \(-3\frac12-4\frac14=-\frac72-\frac{17}{4}=\frac{-14}{4}-\frac{17}{4}=-\frac{31}{4}\)
Câu 32:
a: \(\frac{1}{12}+\frac{-3}{12}=\frac{1-3}{12}=-\frac{2}{12}=-\frac16\)
b: \(\frac78-\frac54=\frac78-\frac{10}{8}=\frac{7-10}{8}=-\frac38\)
c: \(1\frac25+3\frac35=1+\frac25+3+\frac35=4+1=5\)
d: \(\frac{-14}{20}+0,6=-\frac{14}{20}+\frac{12}{20}=-\frac{2}{20}=-\frac{1}{10}\)
Câu 31:
\(A=-\frac15+\frac{8}{15}\)
\(=-\frac{3}{15}+\frac{8}{15}=\frac{5}{15}=\frac13\)
20 tháng 9
Bài 3:
a: \(A=3^2\cdot\frac{1}{243}\cdot81^2\cdot\frac{1}{3^3}\)
\(=\frac{9}{243}\cdot81\cdot81\cdot\frac{1}{27}\)
\(=\frac{1}{27}\cdot81\cdot3=3\cdot3=9\)
b: \(B=\left(4\cdot2^5\right):\left(2^3\cdot\frac{1}{16}\right)\)
\(=2^2\cdot2^5:\left(\frac{2^3}{16}\right)=2^7:\frac12=2^7\cdot2=2^8=256\)
Bài 2:
a: \(A=\left(3^2\right)^2-\left(-2^3\right)^2-\left(-5^2\right)^2\)
\(=3^4-2^6-\left(-25\right)^2\)
=81-64-625
=17-625
=-608
b: \(B=2^3+3\cdot\left(\frac12\right)^0\cdot\left(\frac12\right)^2\cdot4+\left\lbrack\left(-2\right)^2:\frac12\right\rbrack:8\)
\(=8+3\cdot1\cdot\frac14\cdot4+4\cdot\frac28\)
=8+3+1
=11+1
=12
Bài 1:
a: \(\left(\frac23\right)^3\cdot\left(-\frac34\right)^2\cdot\left(-1\right)^5:\left(\frac25\right)^2\cdot\left(-\frac{5}{12}\right)^2\)
\(=\frac{2^3}{3^3}\cdot\frac{3^2}{4^2}\cdot\left(-1\right):\frac{4}{25}\cdot\frac{25}{144}\)
\(=\frac{2^3}{2^4}\cdot\frac13\cdot\left(-1\right)\cdot\frac{25}{4}\cdot\frac{25}{144}=\frac16\cdot\left(-1\right)\cdot\frac{625}{576}=\frac{-625}{3456}\)
b:Sửa đề: \(\frac{\left(6^6+6^3\cdot3^3+3^6\right)}{-73}\)
\(=\frac{3^6\cdot2^6+3^6\cdot2^3+3^6}{-73}\)
\(=\frac{3^6\left(2^6+2^3+1\right)}{-73}=\frac{3^6\cdot73}{-73}=-3^6=-729\)
12 tháng 9
Bài 1:
a: \(M=\frac13xy\left(-\frac12xy^2z^3\right)^2\cdot x^3y\)
\(=\frac13x^4y^2\cdot\frac14x^2y^4z^6\)
\(=\left(\frac13\cdot\frac14\right)\cdot\left(x^4\cdot x^2\right)\cdot\left(y^4\cdot y^2\right)\cdot z^6=\frac{1}{12}x^6y^6z^6\)
Bậc là 6+6+6=18
Hệ số là 1/12
Phần biến là \(x^6;y^6;z^6\)
b: \(M=\frac{1}{12}x^6y^6z^6=\frac{1}{12}\cdot\left(xyz\right)^6\)
Thay x=-4;y=0,5;z=-0,5 vào M, ta được:
\(M=\frac{1}{12}\cdot\left\lbrack-4\cdot0,5\cdot\left(-0,5\right)\right\rbrack^6=\frac{1}{12}\cdot\left(2\cdot0,5\right)^6=\frac{1}{12}\)
Bài 2:
a: \(\left(xy^2-6x^2y\right)-\left(-2xy^2-5x^2y\right)+\left(x^2y-6xy^2\right)\)
\(=xy^2-6x^2y+2xy^2+5x^2y+x^2y-6xy^2=-3xy^2\)
b: \(N=\left(15x^5y^4-20x^3y^2+5x^2y^3\right):5x^2y\)
\(=\frac{15x^5y^4}{5x^2y}-\frac{20x^3y^2}{5x^2y}+\frac{5x^2y^3}{5x^2y}=3x^3y^3-4xy+y^2\)
Thay x=1;y=1 vào N, ta được:
\(N=3\cdot1^3\cdot1^3-4\cdot1\cdot1+1^2\)
=3-4+1
=0
c: \(\left(3x^2-x-3\right)-2x\left(x+2\right)-\left(x+4\right)\left(x-5\right)=1\)
=>\(3x^2-x-3-2x^2-4x-\left(x^2-x-20\right)=1\)
=>\(x^2-5x-3-x^2+x+20=1\)
=>-4x+17=1
=>-4x=-16
=>x=4
Bài 3:
a: AC//BD
AC⊥BA
Do đó: BD⊥BA
b: AC//BD
=>\(\hat{ACD}+\hat{CDB}=180^0\) (hai góc trong cùng phía)
=>\(\hat{CDB}=180^0-120^0=60^0\)
c: CI là phân giác của góc ACD
=>\(\hat{ACI}=\hat{DCI}=\frac12\cdot\hat{ACD}=60^0\)
Xét ΔCID có \(\hat{CID}+\hat{DCI}+\hat{CDI}=180^0\)
=>\(\hat{CID}=180^0-60^0-60^0=60^0\)