a: \(\overrightarrow{AB}=\left(-3;-2\right)\)

\(\overrightarrow{AC}=\left(1;-4\right)\)

Vì \(\overrightarrow{AB}< >\overrightarrow{AC}\) nên A,B,C ko thẳng hàng

hay A,B,C lập thành 1 tam giác

b: Gọi M là trung điểm của BC

\(\Leftrightarrow\left\{{}\begin{matrix}x_M=\dfrac{2-\left(-2\right)}{2}=2\\y_M=\dfrac{-1-1}{2}=-1\end{matrix}\right.\)

Vậy: M(2;-1)

A(1;3)

\(AM=\sqrt{\left(2-1\right)^2+\left(-1-3\right)^2}=\sqrt{17}\)

Bài 6

\(a,ĐK:x\ne\pm5\\ b,P=\dfrac{x-5+2x+10-2x-10}{\left(x-5\right)\left(x+5\right)}=\dfrac{x-5}{\left(x-5\right)\left(x+5\right)}=\dfrac{1}{x+5}\\ c,P=-3\Leftrightarrow\dfrac{1}{x+5}=-3\Leftrightarrow-3\left(x+5\right)=1\Leftrightarrow x=-\dfrac{16}{3}\\ \Leftrightarrow Q=\left(3x-7\right)^2=\left[3\cdot\left(-\dfrac{16}{3}\right)-7\right]^2=529\)

Bài 7:

\(a,ĐK:x\ne\pm3\\ b,P=\dfrac{3x-9+x+3+18}{\left(x-3\right)\left(x+3\right)}=\dfrac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{4}{x-3}\\ b,P=4\Leftrightarrow4\left(x-3\right)=4\Leftrightarrow x=4\)

Điều kiện (x≠5, x≠-5)

\(P=\dfrac{1}{x+5}+\dfrac{2}{x-5}-\dfrac{2x+10}{\left(x+5\right)\left(x-5\right)}\)

    \(=\dfrac{x-5}{\left(x+5\right)\left(x-5\right)}+\dfrac{2\left(x+5\right)}{\left(x+5\right)\left(x-5\right)}-\dfrac{2\left(x+5\right)}{\left(x+5\right)\left(x-5\right)}\)

    \(=\dfrac{x-5+2\left(x+5\right)-2\left(x+5\right)}{\left(x+5\right)\left(x-5\right)}\)

    \(=\dfrac{x-5}{\left(x+5\right)\left(x-5\right)}=\dfrac{1}{x+5}\)

a: Xét ΔHAC vuông tại H và ΔABC vuông tại A có

\(\widehat{C}\) chung

Do đó: ΔHAC~ΔABC

b: ΔABC vuông tại A

=>\(AB^2+AC^2=BC^2\)

=>\(BC^2=15^2+20^2=625\)

=>BC=25

Xét ΔABC vuông tại A có AH là đường cao

nên \(\left\{{}\begin{matrix}BH\cdot BC=BA^2\\AH\cdot BC=AB\cdot AC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}BH\cdot25=15^2=225\\AH\cdot25=15\cdot20=300\end{matrix}\right.\)

=>BH=9; AH=12

\(a,ĐK:...\\ PT\Leftrightarrow x^2-6x=x^2-7x+10\\ \Leftrightarrow x=10\left(tm\right)\\ b,ĐK:...\\ PT\Leftrightarrow2x\left(4-x\right)-\left(2-2x\right)\left(8-x\right)=\left(8-x\right)\left(4-x\right)\\ \Leftrightarrow8x-2x^2+16+18x-2x^2=32-12x+x^2\\ \Leftrightarrow3x^2-38x+16=0\left(casio\right)\\ c,ĐK:...\\ PT\Leftrightarrow2x\left(x-4\right)-4x=0\\ \Leftrightarrow2x^2-12x=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=6\left(tm\right)\end{matrix}\right.\)

\(a,=x^2+x+4x+4=\left(x+1\right)\left(x+4\right)\\ b,=x^2+2x-3x-6=\left(x-3\right)\left(x+2\right)\\ c,=x^2-2x-3x+6=\left(x-2\right)\left(x-3\right)\\ d,=3\left(x^2-2x+5x-10\right)=3\left(x-2\right)\left(x+5\right)\\ e,=-3x^2+6x-x+2=\left(x-2\right)\left(1-3x\right)\\ f,=x^2-x-6x+6=\left(x-1\right)\left(x-6\right)\\ h,=4\left(x^2-3x-6x+18\right)=4\left(x-3\right)\left(x-6\right)\\ i,=3\left(3x^2-3x-8x+5\right)=3\left(x-1\right)\left(3x-8\right)\\ k,=-\left(2x^2+x+4x+2\right)=-\left(2x+1\right)\left(x+2\right)\\ l,=x^2-2xy-5xy+10y^2=\left(x-2y\right)\left(x-5y\right)\\ m,=x^2-xy-2xy+2y^2=\left(x-y\right)\left(x-2y\right)\\ n,=x^2+xy-3xy-3y^2=\left(x+y\right)\left(x-3y\right)\)

Bào quan riboxom trong chất tế bào có chức năng gì? 

a) \(=\left(x^2+x\right)+\left(4x+4\right)=x\left(x+1\right)+4\left(x+1\right)=\left(x+1\right)\left(x+4\right)\)

b) \(=\left(x^2+2x\right)-\left(3x+6\right)=x\left(x+2\right)-3\left(x+2\right)=\left(x+2\right)\left(x-3\right)\)

c) \(=\left(x^2-2x\right)-\left(3x-6\right)=x\left(x-2\right)-3\left(x-2\right)=\left(x-2\right)\left(x-3\right)\)

d) \(3x^2+9x-30=3\left(x^2+3x-10\right)=3\left[\left(x^2+5x\right)-\left(2x+10\right)\right]=3\left[x\left(x+5\right)-2\left(x+5\right)\right]=3\left(x-2\right)\left(x+5\right)\)

e) \(=-\left(3x^2-5x-2\right)=-\left[\left(3x^2-6x\right)+\left(x-2\right)\right]=-\left[3x\left(x-2\right)+\left(x-2\right)\right]=-\left(3x+1\right)\left(x-2\right)\)

f) \(x^2-7x+6=\left(x^2-x\right)-\left(6x-6\right)=x\left(x-1\right)-6\left(x-1\right)=\left(x-1\right)\left(x-6\right)\)

h) \(=4\left(x^2-9x+14\right)=4\left[\left(x^2-7x\right)-\left(2x-14\right)\right]=4\left[x\left(x-7\right)-2\left(x-7\right)\right]=4\left(x-2\right)\left(x-7\right)\)

i) \(=3\left(3x^2-8x+5\right)=3\left[\left(3x^2-3x\right)-\left(5x-5\right)\right]=3\left[3x\left(x-1\right)-5\left(x-1\right)\right]=3\left(x-1\right)\left(3x-5\right)\)

k) \(=-\left(2x^2+5x+2\right)=-\left[\left(2x^2+4x\right)+\left(x+2\right)\right]=-\left[2x\left(x+2\right)+\left(x+2\right)\right]=-\left(x+2\right)\left(2x+1\right)\)

l) \(=\left(x^2-5xy\right)-\left(2xy-10y^2\right)=x\left(x-5y\right)-2y\left(x-5y\right)=\left(x-5y\right)\left(x-2y\right)\)

m) \(=\left(x^2-2xy\right)-\left(xy-2y^2\right)=x\left(x-2y\right)-y\left(x-2y\right)=\left(x-2y\right)\left(x-y\right)\)

n) \(=\left(x^2-3xy\right)+\left(xy-3y^2\right)=x\left(x-3y\right)+y\left(x-3y\right)=\left(x+y\right)\left(x-3y\right)\)