b: Để (d)//(d') thì m+3=4

hay m=1

\(a,\Leftrightarrow\left\{{}\begin{matrix}m+2=-1\\-2m\ne5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m=-3\\m\ne-\dfrac{5}{2}\end{matrix}\right.\Leftrightarrow m=-3\\ b,\text{PTHDGD: }2x+1=\left(m+2\right)x-2m\\ \text{Thay }x=-2\Leftrightarrow-2m-4-2m=-3\\ \Leftrightarrow-4m=1\Leftrightarrow m=-\dfrac{1}{4}\)

a: Thay x=2 và y=-3 vào (d), ta được:

\(2\left(2m-1\right)-2m+5=-3\)

=>\(4m-2-2m+5=-3\)

=>2m+3=-3

=>2m=-6

=>\(m=-\dfrac{6}{2}=-3\)

b: Để (d)//(d') thì \(\left\{{}\begin{matrix}2m-1=2\\-2m+5\ne1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2m=3\\-2m\ne-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m=\dfrac{3}{2}\\m\ne2\end{matrix}\right.\)

=>m=3/2

Thay m=3/2 vào (d), ta được:

\(y=\left(2\cdot\dfrac{3}{2}-1\right)x-2\cdot\dfrac{3}{2}+5=2x+2\)

y=2x+2 nên a=2

Gọi \(\alpha\) là góc tạo bởi (d) với trục Ox

\(tan\alpha=2\)

=>\(\alpha\simeq63^026'\)

1.

\(a,\Leftrightarrow2m-1+m-2=6\Leftrightarrow3m=9\Leftrightarrow m=3\\ b,2x+3y-5=0\Leftrightarrow3y=-2x+5\Leftrightarrow y=-\dfrac{2}{3}x+\dfrac{5}{3}\)

Để \(\left(d\right)\text{//}y=-\dfrac{2}{3}x+\dfrac{5}{3}\Leftrightarrow\left\{{}\begin{matrix}2m-1=-\dfrac{2}{3}\\m-2\ne\dfrac{5}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m=\dfrac{1}{6}\\m\ne\dfrac{11}{3}\end{matrix}\right.\Leftrightarrow m=\dfrac{1}{6}\)

\(c,x+2y+1=0\Leftrightarrow2y=-x-1\Leftrightarrow y=-\dfrac{1}{2}x-\dfrac{1}{2}\\ \left(d\right)\bot y=-\dfrac{1}{2}x-\dfrac{1}{2}\Leftrightarrow\left(-\dfrac{1}{2}\right)\left(2m-1\right)=-1\\ \Leftrightarrow\dfrac{1}{2}\left(2m-1\right)=1\Leftrightarrow m-\dfrac{1}{2}=1\Leftrightarrow m=\dfrac{3}{2}\)

2.

Gọi điểm cố định đó là \(A\left(x_0;y_0\right)\)

\(\Leftrightarrow y_0=\left(2m-1\right)x_0+m-2\\ \Leftrightarrow2mx_0+m-x_0-2-y_0=0\\ \Leftrightarrow m\left(2x_0+1\right)-\left(x_0+y_0+2\right)=0\\ \Leftrightarrow\left\{{}\begin{matrix}2x_0=-1\\x_0+y_0+2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x_0=-\dfrac{1}{2}\\y_0=-\dfrac{3}{2}\end{matrix}\right.\)

a: Để hàm số y=(2m+3)x-2m+5 nghịch biến trên R thì 2m+3<0

=>2m<-3

=>\(m< -\dfrac{3}{2}\)

b: Để (d)//(d1) thì

\(\left\{{}\begin{matrix}2m+3=3m-2\\-2m+5\ne1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-m=-5\\-2m\ne-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m=5\\m\ne2\end{matrix}\right.\)

=>m=5

c: Thay y=5 vào y=3x-1, ta được:

3x-1=5

=>3x=6

=>x=6/3=2

Thay x=2 và y=5 vào (d), ta được:

\(2\left(2m+3\right)-2m+5=5\)

=>\(4m+6-2m+5=5\)

=>2m+11=5

=>2m=-6

=>m=-6/2=-3

d: Tọa độ A là:

\(\left\{{}\begin{matrix}y=0\\\left(2m+3\right)x-2m+5=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=0\\x\left(2m+3\right)=2m-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=0\\x=\dfrac{2m-5}{2m+3}\end{matrix}\right.\)

=>\(A\left(\dfrac{2m-5}{2m+3};0\right)\)

\(OA=\sqrt{\left(\dfrac{2m-5}{2m+3}-0\right)^2+\left(0-0\right)^2}=\sqrt{\left(\dfrac{2m-5}{2m+3}\right)^2}=\left|\dfrac{2m-5}{2m+3}\right|\)

Tọa độ B là:

\(\left\{{}\begin{matrix}x=0\\y=x\left(2m+3\right)-2m+5=0\left(2m+3\right)-2m+5=-2m+5\end{matrix}\right.\)

=>\(B\left(-2m+5;0\right)\)

\(OB=\sqrt{\left(-2m+5-0\right)^2+\left(0-0\right)^2}\)

\(=\sqrt{\left(-2m+5\right)^2}=\left|2m-5\right|\)

Vì Ox\(\perp\)Oy

nên OA\(\perp\)OB

=>ΔOAB vuông tại O

=>\(S_{OAB}=\dfrac{1}{2}\cdot\left|2m-5\right|\cdot\dfrac{\left|2m-5\right|}{\left|2m+3\right|}\)

\(=\dfrac{1}{2}\cdot\dfrac{\left(2m-5\right)^2}{\left|2m+3\right|}\)

Để \(S_{AOB}=1\) thì \(\dfrac{\dfrac{1}{2}\left(2m-5\right)^2}{\left|2m+3\right|}=1\)

=>\(\dfrac{\left(2m-5\right)^2}{\left|2m+3\right|}=2\)

=>\(\left(2m-5\right)^2=2\left|2m+3\right|\)

=>\(\left(2m-5\right)^2=2\left(2m+3\right)\)

=>\(4m^2-20m+25-4m-6=0\)

=>\(4m^2-24m+19=0\)

=>\(m=\dfrac{6\pm\sqrt{17}}{2}\)

a, d1//d2 <=> 2m-1= m+1 <=> 2m-m = 1+1 <=> m=2

a: Để (d1)//(d2) thì \(\left\{{}\begin{matrix}2m-1=m+1\\-2m+5< >m-1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2m-m=1+1\\-2m-m< >-1-5\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}m=2\\-3m\ne-6\end{matrix}\right.\)

=>\(m\in\varnothing\)

b: Để (d1) cắt (d2) thì \(2m-1\ne m+1\)

=>\(2m-m\ne1+1\)

=>\(m\ne2\)

Đáp án C

Bạn ơi, giữa -2x và số 3 là dấu gì?