anh chị giải giúp e bài này giùm nha
em cảm ơn nhiều lắm em đg gấp
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\(a,=x^2+x+4x+4=\left(x+1\right)\left(x+4\right)\\ b,=x^2+2x-3x-6=\left(x-3\right)\left(x+2\right)\\ c,=x^2-2x-3x+6=\left(x-2\right)\left(x-3\right)\\ d,=3\left(x^2-2x+5x-10\right)=3\left(x-2\right)\left(x+5\right)\\ e,=-3x^2+6x-x+2=\left(x-2\right)\left(1-3x\right)\\ f,=x^2-x-6x+6=\left(x-1\right)\left(x-6\right)\\ h,=4\left(x^2-3x-6x+18\right)=4\left(x-3\right)\left(x-6\right)\\ i,=3\left(3x^2-3x-8x+5\right)=3\left(x-1\right)\left(3x-8\right)\\ k,=-\left(2x^2+x+4x+2\right)=-\left(2x+1\right)\left(x+2\right)\\ l,=x^2-2xy-5xy+10y^2=\left(x-2y\right)\left(x-5y\right)\\ m,=x^2-xy-2xy+2y^2=\left(x-y\right)\left(x-2y\right)\\ n,=x^2+xy-3xy-3y^2=\left(x+y\right)\left(x-3y\right)\)
1. A. celebrate B. together C. restaurant D. organize
2. A. pollution B. awareness C. disappear D. addition
3. A. apple B. butter C. mother D. advance
4. A. protection B. referee C. dictation D. increasing
5. A. carriage B. damage C. survive D. lightning
6. A. generosity B. occurrence C. priority D. memorial
1. A. celebrate B. together C. restaurant D. organize
2. A. pollution B. awareness C. disappear D. addition
3. A. apple B. butter C. mother D. advance
4. A. protection B. referee C. dictation D. increasing
5. A. carriage B. damage C. survive D. lightning
6. A. generosity B. occurrence C. priority D. memorial
a) \(\left(2m-1\right)sinx+1-m=0\Rightarrow sinx=\dfrac{m-1}{2m-1}\)
Pt có nghiệm: \(-1\le\dfrac{m-1}{2m-1}\le1\)
\(\Rightarrow1-2m\le m-1\le2m-1\Rightarrow m\ge\dfrac{2}{3}\)
b) \(\left(m+1\right)sin3x-cos3x=m+2\)
Pt có nghiệm: \(\left(m+1\right)^2+\left(-1\right)^2\ge\left(m+2\right)^2\)
\(\Rightarrow m^2+2m+1+1\ge m^2+4m+4\)
\(\Rightarrow-2m\ge2\Rightarrow m\le-1\)
a) \(A=\dfrac{\left(2x^2+2x\right)\left(x-2\right)^2}{\left(x^3-4x\right)\left(x+1\right)}=\dfrac{2x\left(x+1\right)\left(x-2\right)^2}{x\left(x-2\right)\left(x+2\right)\left(x+1\right)}\)
\(=\dfrac{2\left(x-2\right)}{x+2}\)
Thay \(x=\dfrac{1}{2}\) vào A ta được:
\(A=\dfrac{2\cdot\left(\dfrac{1}{2}-2\right)}{\dfrac{1}{2}+2}=\dfrac{-3}{\dfrac{5}{2}}=-\dfrac{6}{5}\)
b) \(B=\dfrac{x^3-x^2y+xy^2}{x^3+y^3}=\dfrac{x\left(x^2-xy+y^2\right)}{\left(x+y\right)\left(x^2-xy+y^2\right)}=\dfrac{x}{x+y}\)
Thay \(x=-5,y=10\) vào B ta đc:
\(B=\dfrac{-5}{-5+10}=-1\)
a,\(n_{Na}=\dfrac{4,6}{23}=0,2\left(mol\right)\)
PTHH: 2Na + 2H2O → 2NaOH + H2
Mol: 0,2 0,2 0,1
\(V_{H_2}=0,1.22,4=2,24\left(l\right)\)
b,mNaOH=0,2.40=8 (g)
\(C\%_{ddNaOH}=\dfrac{8.100\%}{4,6+200-0,1.2}=3,91\%\)
\(d,=\dfrac{3y}{5x\left(x-y\right)}\\ e,=\dfrac{5x\left(x+2\right)\left(2-x\right)}{4\left(x-2\right)\left(x+2\right)}=\dfrac{-5x}{4}\\ f,=\dfrac{3\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)\left(6-x\right)}=\dfrac{-3\left(x+6\right)}{2\left(x+5\right)}\\ g,=\dfrac{3xy\left(x-3y\right)\left(x+3y\right)}{2x^2y^2\left(x-3y\right)}=\dfrac{3\left(x+3y\right)}{2xy}\\ h,=\dfrac{45x^2y\left(x-y\right)\left(x+y\right)}{10xy\left(y-x\right)}=\dfrac{-9x\left(x+y\right)}{2}\\ i,=\dfrac{12\left(a-b\right)\left(a+b\right)\left(a^2+ab+b^2\right)}{3\left(a+b\right)\left(a-b\right)^2}=\dfrac{4\left(a^2+ab+b^2\right)}{a-b}\)
e: \(=\dfrac{5\left(x+2\right)}{4\left(x-2\right)}\cdot\dfrac{-2\left(x-2\right)}{x+2}=\dfrac{-10}{4}=-\dfrac{5}{2}\)
Gọi M là trung điểm EG \(\Rightarrow AM\perp EG\) (tam giác cân)
\(\Rightarrow AM\perp\left(EFGH\right)\Rightarrow AM=d\left(A;\left(EFGH\right)\right)\)
\(EG=30-2x\Rightarrow EM=\dfrac{1}{2}EG=15-x\)
\(\Rightarrow AM=\sqrt{AE^2-EM^2}=\sqrt{x^2-\left(15-x\right)^2}=\sqrt{30x-225}\)
Do AEG là tam giác, theo BĐT tam giác: \(\left\{{}\begin{matrix}AE+AG>EG\\\left|AG-AE\right|< EG\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x+x>30-2x\\0< 30-2x\end{matrix}\right.\) \(\Rightarrow\dfrac{15}{2}< x< 15\)
\(V=AD.S_{\Delta AEG}=30.\dfrac{1}{2}AM.EG=15.\left(30-2x\right)\sqrt{30x-225}\)
\(V^2=15^3.4\left(15-x\right)^2\left(2x-15\right)=15^3.4.\left(15-x\right)\left(15-x\right)\left(2x-15\right)\)
\(\le15^3.4.\left(\dfrac{15-x+15-x+2x-15}{3}\right)^3=...\)
Dấu "=" xảy ra khi \(15-x=2x-15\Rightarrow x=10\)
\(\Rightarrow d\left(A;\left(EFGH\right)\right)=AM=\sqrt{30.10-225}=5\sqrt{3}\)