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Bài 1 :
\(a,-1\frac{1}{4}+\frac{1}{4}+50\%\)
\(=-\frac{3}{4}+\frac{1}{4}+\frac{1}{2}\)
\(=-\frac{1}{2}+\frac{1}{2}\)
\(=0\)
\(b,0,5+0,5.\left(-80\right).0,01-10\%\)
\(=0,5-40.0,01-10\%\)
\(=0,5-0,4-\frac{1}{10}\)
\(=0,1-\frac{1}{10}\)
\(=\frac{1}{10}-\frac{1}{10}\)
\(=0\)
\(c,\frac{4}{30}\times\frac{2}{5}+\frac{2}{15}\times\frac{4}{5}+\frac{2}{15}\times\left(-\frac{1}{5}\right)\)
\(=\frac{2}{15}\times\frac{2}{5}+\frac{2}{15}\times\frac{4}{5}+\frac{2}{15}\times\left(-\frac{1}{5}\right)\)
\(=\frac{2}{15}\left(\frac{2}{5}+\frac{4}{5}-\frac{1}{5}\right)\)
\(=\frac{2}{15}\times\frac{5}{5}\)
\(=\frac{2}{15}\times1\)
\(=\frac{2}{15}\)
\(xy-x-y+1=0\)
\(\Rightarrow x.\left(y-1\right)-\left(y-1\right)=0\)
\(\Rightarrow\left(y-1\right).\left(x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}y-1=0\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)
Vậy \(x=y=1\)
Chúc bạn học tốt!!!
Tìm x,y biết:
xy-x-y+1=0
=> x(y-1)-y=0-1
=> x(y-1)- (y-1)= (-1)
=> (y-1)(x-1)=(-1)
\(\Rightarrow\left[{}\begin{matrix}y-1=1;x-1=-1\\y-1=-1;x-1=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}y=2;x=0\\y=0;x=2\end{matrix}\right.\)
Vì \(\widehat{BAD}\)+\(\widehat{CDA}\)= 1800 \(\Rightarrow\)\(\widehat{BAD}\)Và \(\widehat{CDA}\)Là hai góc trong cùng phía bù nhau\(\Rightarrow\)Ax song song với Dy
\(\Rightarrow\)\(\widehat{ABC}\)VÀ \(\widehat{BCD}\)Cũng là hai góc trong cung phía bù nhau\(\Rightarrow\)\(\widehat{BCD}\)=1800-600 =1200
\(\widehat{BCD}\)=1200
Gọi đường thẳng cắt Ax và Dy là b
Theo đề bài ta có b vuông góc vs D , b vuông góc vs A
Suy ra Ax || dy
Vì Ax || dy nên ta có
ABC^ + BCD^ = 180 độ (so le trong)
60* + BCD^ = 180*
BCD^ = 180* - 60*
BCD^ = 120*
Vậy BCD^ = 120*
4.
\(\left(0,36\right)^8=\left(\left(0,6\right)^2\right)^8=\left(0,6\right)^{16}\)
\(\left(0,216\right)^4=\left(\left(0,6\right)^3\right)^4=\left(0,6\right)^{12}\)
5.
a, \(\left(3\times5\right)^3=15^3=1125\)
b, \(\left(\frac{-4}{11}\right)^2=\frac{16}{121}\)
c, \(\left(0,5\right)^4\times6^4=\left(0,5\times6\right)^4=3^4=81\)
d, \(\left(\frac{-1}{3}\right)^5\div\left(\frac{1}{6}\right)^5=\left(\frac{-1}{3}\right)^5\times6^5=\left(\frac{-1}{3}\times6\right)^5=\left(-2\right)^5=-32\)
6.
a, \(\frac{6^2\times6^3}{3^5}=\frac{6^5}{3^5}=\frac{2^5\times3^5}{3^5}=2^5=32\)
b, \(\frac{25^2\times4^2}{5^5\times\left(-2\right)^5}=\frac{100^2}{\left(-10\right)^5}=\frac{10^4}{\left(-10\right)^5}=\frac{-1}{10}\)
c, Mình không nhìn rõ đề
d, \(\left(-2\frac{3}{4}+\frac{1}{2}\right)^2=\left(\frac{-11}{4}+\frac{1}{2}\right)^2=\left(\frac{-9}{4}\right)^2=\frac{81}{16}\)
7.
a, \(\left(\frac{1}{3}\right)^m=\frac{1}{81}\Rightarrow\left(\frac{1}{3}\right)^m=\left(\frac{1}{3}\right)^4\Rightarrow m=4\)
b, \(\left(\frac{3}{5}\right)^n=\left(\frac{9}{25}\right)^5\Rightarrow\left(\frac{3}{5}\right)^n=\left(\left(\frac{3}{5}\right)^2\right)^5\Rightarrow\left(\frac{3}{5}\right)^n=\left(\frac{3}{5}\right)^{10}\Rightarrow n=10\)
c, \(\left(-0,25\right)^p=\frac{1}{256}\Rightarrow\left(-0,25\right)^p=\left(\frac{1}{4}\right)^4\Rightarrow\left(-0,25\right)^p=\left(0,25\right)^4\Rightarrow p=4\)
8.
a, \(\left(\frac{2}{5}+\frac{3}{4}\right)^2=\left(\frac{23}{20}\right)^2=\frac{529}{400}\)
b, \(\left(\frac{5}{4}-\frac{1}{6}\right)^2=\left(\frac{1}{2}\right)^2=\frac{1}{4}\)