5:

a: \(\left\{{}\begin{matrix}x-2y=-m-7\\2x+y=3m-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-4y=-2m-14\\2x+y=3m-4\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-5y=-5m-10\\x-2y=-m-7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=m+2\\x=-m-7+2m+4=m-3\end{matrix}\right.\)

Thay x=m-3 và y=m+2 vào y=3x-1, ta được:

3(m-3)-1=m+2

=>3m-10=m+2

=>2m=12

=>m=6

b: A(x,y) nằm trong góc phần tư thứ II

\(\Leftrightarrow\left\{{}\begin{matrix}m-3< 0\\m+2>0\end{matrix}\right.\Leftrightarrow-2< m< 3\)

mà m nguyên

nên \(m\in\left\{-1;0;1;2\right\}\)

cÂU 9.

\(I=\dfrac{\xi}{r+R_N}=\dfrac{20}{5+10}=\dfrac{4}{3}A\)

\(P_R=I^2_R\cdot R=\dfrac{4}{3}\cdot10=\dfrac{40}{3}W\)

\(P=\xi\cdot I=20\cdot\dfrac{4}{3}=\dfrac{80}{3}W\)

\(H=\dfrac{R}{r+R}=\dfrac{10}{5+10}=\dfrac{2}{3}\approx66,67\%\)

1............to work by car everyday

2 ........Khanh does morning exercise, he won't keep fit

3......has a small garden

4 .....has to go to school on time

5 ......she doesn't go to bed early, she will be late for class

6 .......go to the movie tonight

\(\text{⩷!⨙┏⇴⨗⨜}\)

38.

$\sqrt{2006}-\sqrt{2005}=\frac{2006-2005}{\sqrt{2006}+\sqrt{2005}}=\frac{1}{\sqrt{2006}+\sqrt{2005}}< \frac{1}{\sqrt{2005}+\sqrt{2004}}=\frac{2005-2004}{\sqrt{2005}+\sqrt{2004}}=\sqrt{2005}-\sqrt{2004}$

39.

$\sqrt{1998}+\sqrt{2000}-2\sqrt{1999}=(\sqrt{2000}-\sqrt{1999})-(\sqrt{1999}-\sqrt{1998})$

$=\frac{1}{\sqrt{2000}+\sqrt{1999}}-\frac{1}{\sqrt{1999}+\sqrt{1998}}$

$< 0$

$\Rightarrow \sqrt{1998}+\sqrt{2000}<2\sqrt{1999}$

Bài 40 bạn làm tương tự câu 38.

4 If you aren't alert, you computer will be infected with viruses

5 If we use much pesticide on vegetables, they will become poisonous

9 Because Nam needs to improve his social skills, he attends the activity

11 How about using public buses instead of motorbike 

12 They enjoy protecting the environment unpolluted 

15 Mr Brown was disappointed that his son didn't write to him

11:

a: ABCD là hình chữ nhật

=>vecto AB+vecto AD=vecto AC

\(AC=\sqrt{\left(3a\right)^2+\left(4a\right)^2}=5a\)

\(\left|\overrightarrow{AB}+\overrightarrow{AD}\right|=\left|\overrightarrow{AC}\right|=AC=5a\)

b: Gọi M là trung điểm của BC

=>BM=MC=4a/2=2a

Trên tia đối của tia MA lấy D sao cho M là trung điểm của AD

Xét tứ giác ABDC có

M là trung điểm chung của AD và BC

=>ABDC là hình bình hành

=>\(\overrightarrow{AB}+\overrightarrow{AC}=\overrightarrow{AD}=2\cdot\overrightarrow{AM}\)

\(AM=\sqrt{AB^2+BM^2}=\sqrt{\left(3a\right)^2+\left(2a\right)^2}=a\sqrt{13}\)

=>\(\left|\overrightarrow{AB}+\overrightarrow{AC}\right|=2\cdot AM=2a\sqrt{13}\)

d: Ta có: \(12x^2+7x-12\)

\(=12x^2+16x-9x-12\)

\(=4x\left(3x+4\right)-3\left(3x+4\right)\)

\(=\left(3x+4\right)\left(4x-3\right)\)

e: Ta có: \(15x^2+7x-2\)

\(=15x^2+10x-3x-2\)

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