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Bài 7:
a: Xét ΔABE và ΔMBE có
BA=BM
BE chung
EA=EM
Do đó: ΔABE=ΔMBE
\(\left|x+1\right|và\left|x+2\right|\ge0\)
\(\Rightarrow\orbr{\begin{cases}\left(x+1\right)+\left(x+2\right)=3\\\left(x+1\right)+\left(x+2\right)=-3\end{cases}}\)
\(\orbr{\begin{cases}2x+3=3\\2x+3=-3\end{cases}}\)
\(\orbr{\begin{cases}2x=0\\2x=-6\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x=-3\end{cases}}\)
\(\left|x+1\right|+\left|x+2\right|=3\)
Xét \(x+1\ge0;x+2\ge0\Leftrightarrow x\ge-1;x\ge-2\Rightarrow x\ge-1\) ta có : \(\hept{\begin{cases}\left|x+1\right|=x+1\\\left|x+2\right|=x+2\end{cases}}\)
\(\Rightarrow\left|x+1\right|+\left|x+2\right|=3\Leftrightarrow x+1+x+2=3\Leftrightarrow2x+3=3\Rightarrow x=0\)(TM)
Xét \(x+1\le0;x+2\ge0\Leftrightarrow-2\le x\le-1\) ta có : \(\hept{\begin{cases}\left|x+1\right|=-x-1\\\left|x+2\right|=x+2\end{cases}}\)
\(\Rightarrow\left|x+1\right|+\left|x+2\right|=3\Leftrightarrow-x-1+x+2=3\Leftrightarrow1=3\) (loại)
Xét \(x+1\le0;x+2\le0\Leftrightarrow x\le-1;x\le-2\Leftrightarrow x\le-2\) ta có : \(\hept{\begin{cases}\left|x+1\right|=-x-1\\\left|x+2\right|=-x-2\end{cases}}\)
\(\Rightarrow\left|x+1\right|+\left|x+2\right|=-x-1-x-2=-2x-3=3\Rightarrow x=-3\)(TM)
Vậy \(x=\left\{-3;0\right\}\)
Ta có : \(\frac{x}{\frac{1}{3}}=\frac{y}{\frac{1}{5}}\)
\(\Rightarrow\frac{x\times y}{\frac{1}{3}\times\frac{1}{5}}=\frac{1500}{\frac{1}{15}}=22500\)
\(\Rightarrow\frac{x}{\frac{1}{3}}=22500\Rightarrow x=22500\times\frac{1}{3}=7500\)
\(\Rightarrow\frac{y}{\frac{1}{5}}=22500\Rightarrow y=22500\times\frac{1}{5}=4500\)
1.47:
a) Ta có: \(\dfrac{3}{7}x-\dfrac{2}{5}x=-\dfrac{17}{35}\)
\(\Leftrightarrow\dfrac{1}{35}x=\dfrac{-17}{35}\)
hay x=-17
Vậy: x=-17
b) Ta có: \(\left(\dfrac{3}{4}x-\dfrac{9}{16}\right)\left(\dfrac{1}{3}+\dfrac{-3}{5}:x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{3}{4}x-\dfrac{9}{16}=0\\\dfrac{1}{3}+\dfrac{-3}{5}:x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{3}{4}x=\dfrac{9}{16}\\\dfrac{-3}{5}:x=\dfrac{-1}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{16}:\dfrac{3}{4}=\dfrac{9}{16}\cdot\dfrac{4}{3}=\dfrac{36}{48}=\dfrac{3}{4}\\x=\dfrac{-3}{5}:\dfrac{-1}{3}=\dfrac{-3}{5}\cdot\dfrac{-3}{1}=\dfrac{9}{5}\end{matrix}\right.\)
Bài 1.48:
a) Ta có: \(\left(x-\dfrac{1}{3}\right)\left(x+\dfrac{2}{5}\right)>0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}>0\\x+\dfrac{2}{5}< 0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{1}{3}\\x< \dfrac{-2}{5}\end{matrix}\right.\)
b) Ta có: \(\left(x+\dfrac{3}{5}\right)\left(x+1\right)< 0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+1>0\\x+\dfrac{3}{5}< 0\end{matrix}\right.\Leftrightarrow-1< x< \dfrac{-3}{5}\)