Câu 13:
a) \(A=\left(\dfrac{5}{2}\right)^2+\left(-\dfrac{1}{2}\right)\)
\(=\dfrac{25}{4}-\dfrac{1}{2}\)
\(=\dfrac{23}{4}\)
b) \(B=\dfrac{3}{7}.\left(-\dfrac{1}{9}\right)+\dfrac{3}{7}.\left(-\dfrac{2}{3}\right)\)
\(=\dfrac{3}{7}.\left(-\dfrac{1}{9}-\dfrac{2}{3}\right)\)
\(=\dfrac{3}{7}.\left(-\dfrac{7}{9}\right)\)
\(=-\dfrac{1}{3}\)
c) \(-\dfrac{5}{2}.\sqrt{\dfrac{9}{25}}-2^2.\left(-\dfrac{1}{4}\right)\)
\(=-\dfrac{5}{2}.\dfrac{3}{5}+4.\dfrac{1}{4}\)
\(=-\dfrac{3}{2}+1\)
\(=-\dfrac{1}{2}\)
d) \(\dfrac{5}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)+\dfrac{5}{9}:\left(\dfrac{1}{15}-\dfrac{2}{3}\right)\)
\(=\dfrac{5}{9}:\left(-\dfrac{3}{22}\right)+\dfrac{5}{9}:\left(-\dfrac{3}{5}\right)\)
\(=\dfrac{5}{9}.\left(-\dfrac{22}{3}\right)+\dfrac{5}{9}.\left(-\dfrac{5}{3}\right)\)
\(=\dfrac{5}{9}.\left(-\dfrac{22}{3}-\dfrac{5}{3}\right)\)
\(=\dfrac{5}{9}.\left(-9\right)\)
\(=-5\)
Câu 17:
a: Ta có: AB\(\perp\)AC
CD\(\perp\)AC
Do đó: AB//CD
b: Ta có: AB//CD
=>\(\widehat{ABD}+\widehat{BDC}=180^0\)(hai góc trong cùng phía)
=>\(\widehat{ABD}+72^0=180^0\)
=>\(\widehat{ABD}=108^0\)
c: Ta có: BE là phân giác của góc ABD
=>\(\widehat{ABE}=\dfrac{1}{2}\cdot\widehat{ABD}=\dfrac{1}{2}\cdot108^0=54^0\)
Câu 14:
a: \(\dfrac{3}{4}+\dfrac{1}{4}x=0,25\)
=>\(\dfrac{1}{4}x=0,25-\dfrac{3}{4}=-\dfrac{2}{4}=-\dfrac{1}{2}\)
=>\(x=-\dfrac{1}{2}:\dfrac{1}{4}=-\dfrac{1}{2}\cdot4=-2\)
b: \(\left|x+1\right|=3,4\)
=>\(\left[{}\begin{matrix}x+1=3,4\\x+1=-3,4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2,4\\x=-4,4\end{matrix}\right.\)
c: \(\left(x+\dfrac{1}{2}\right)^3:3=-\dfrac{1}{81}\)
=>\(\left(x+\dfrac{1}{2}\right)^3=-\dfrac{1}{81}\cdot3=-\dfrac{1}{27}\)
=>\(x+\dfrac{1}{2}=-\dfrac{1}{3}\)
=>\(x=-\dfrac{1}{3}-\dfrac{1}{2}=-\dfrac{5}{6}\)