\(\dfrac{7^{49}-7^{48}}{7^{48}}\)

\(=\dfrac{7^{49}}{7^{48}}-\dfrac{7^{48}}{7^{48}}\)

\(=7-1\)

\(=6\)

\(\dfrac{7^{49}-7^{48}}{7^{48}}\)

\(=\dfrac{7^{48}\cdot7-7^{48}}{7^{48}}\)

\(=\dfrac{7^{48}\left(7-1\right)}{7^{48}}\)

\(=7-1\)

\(=6\)

13) 

a) \(\left\{{}\begin{matrix}7x+4y=2\\5x-2y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7x+4y=2\\10x-4y=32\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}7x+4y=2\\17x=34\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7\cdot2+4y=2\\x=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}4y=2-14\\x=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4y=-12\\x=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-3\\x=2\end{matrix}\right.\)

Vậy: .... 

b) \(\left\{{}\begin{matrix}2x+3y=19\\3x+4y=-14\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+9y=57\\6x+8y=-28\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+3y=19\\y=85\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+3\cdot85=19\\y=85\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x=19-255\\y=85\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-236\\y=85\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-118\\y=85\end{matrix}\right.\)

Vậy: .... 

c) \(\left\{{}\begin{matrix}2x+2y=3\\3x-2y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x=5\\3x-2y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\3\cdot1-2y=2\end{matrix}\right.\)

 \(\Leftrightarrow\left\{{}\begin{matrix}x=1\\-2y=2-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\-2y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=\dfrac{1}{2}\end{matrix}\right.\)

Vậy: ....

15) 

a) \(\left\{{}\begin{matrix}5\left(x+2\right)=2\left(y+7\right)\\3\left(x+y\right)=17-x\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x+10=2y+14\\3x+3y=17-x\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x-2y=14-10\\3x+3y+x=17\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x-2y=4\\4x+3y=17\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}15x-6y=12\\8x+6y=34\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x-2y=4\\23x=46\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5\cdot2-2y=4\\x=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2y=6\\x=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=3\\x=2\end{matrix}\right.\)

vậy: ... 

Diện tích mảnh đất là:

\(50\times8=400\left(m^2\right)\)

Diện tích đất để xây nhà là:

\(400\times25\%=100\left(m^2\right)\)

Vậy...

diện tích mãnh đất hình chữ nhật là 

\(S=50.8=400m^2\)

100% vuông tương ứng 400 mét vuông nên 25% tương ứng 

\(\dfrac{25.400}{100}=100m^2\)

vậy diện tích đất đai để xây nhà là 100 mét vuông

A là trực tâm của tam giác ABC vì A là giao của 2 đường cao AB và AC

Chọn C

Xét ΔABC có

AC là đường cao ứng với cạnh AB

AB là đường cao ứng với cạnh AC

AC cắt AB tại A

Do đó: A là trực tâm của ΔABC

a: Gọi tử số của phân số cần tìm là a

Theo đề, ta có: \(\dfrac{2}{3}< \dfrac{a}{30}< \dfrac{5}{6}\)

=>\(\dfrac{20}{30}< \dfrac{a}{30}< \dfrac{25}{30}\)

=>20<a<25

Vậy: Các phân số cần tìm có dạng là \(\dfrac{a}{30};20< a< 25\)

b: Gọi mẫu số của phân số cần tìm là a

Theo đề, ta có: \(\dfrac{-5}{6}< \dfrac{-15}{a}< \dfrac{-3}{4}\)

=>\(\dfrac{5}{6}>\dfrac{15}{a}>\dfrac{3}{4}\)

=>\(\dfrac{15}{18}>\dfrac{15}{a}>\dfrac{15}{20}\)

=>18<a<20

Vậy: Các phân số cần tìm có dạng là \(-\dfrac{15}{a};18< a< 20\)

a: Xét ΔBMD và ΔCMA có

MB=MC

\(\widehat{BMD}=\widehat{CMA}\)(hai góc đối đỉnh)

MD=MA

Do đó: ΔBMD=ΔCMA
=>\(\widehat{MBD}=\widehat{MCA}\)

=>BD//AC

=>\(\widehat{ABD}+\widehat{BAC}=180^0\)

mà \(\widehat{BAC}+\widehat{B'A'C'}=180^0\)

nên \(\widehat{ABD}=\widehat{B'A'C'}\)

b: ΔBMD=ΔCMA

=>BD=CA

mà CA=A'C'

nên BD=A'C'

Xét ΔABD và ΔB'A'C' có

AB=B'A'

\(\widehat{ABD}=\widehat{B'A'C'}\)

BD=A'C'

Do đó: ΔABD=ΔB'A'C'

=>AD=B'C'

mà \(AM=\dfrac{1}{2}AD\)

nên \(AM=\dfrac{1}{2}B'C'\)

Q. Do you have many friends?

- Yes, i have a tons of friends, thanks to my great social skills! Also because it's also fun to get around with everyone.

- No, i don't, I'm not really a fan of socializing, plus, I'm shy and introverted so I only have a few friends around.

Q. How often do you go out with friends?

- I often go out with my friends so that we're able to get to know each other more and have some conversations together along the way.

- I don't often go out with friends, I'm always busy, by the way, I would rather stay with my family.

Q. Tell me about your best friend at school.

- My best friend has a nice and bubbly personality. He appears with dark brown hair and large, expressive eyes. He finds himself interested in many fleids such as science and art, he also loves doing researches and create crafts in his free time. He's defintely the best person I've ever known!

Q. How friendly are your neighbours?

- My neighbours? They're the best, they are literally the sweetest and friendliest people on earth, they're always ready to help and are eager to give me tons of presents during my brithday.

- No, my neighbours aren't friendly at all, I don't like how they shout at me whenever I cross by! Another thing that bothers me is that these people are really short-tempered and I'm super scared.

Q. Which is more important to you, friends or family?

- They're equally important to me! They all give me comfort, support, motivation for me to keep up. Meanwhile while I'm more expressive with friends, my family makes me feels more warm and close due to the time we have been spending together.

Q. Who do you spend most time studying/working with?

- I enjoy studying with my friends a lot! I always have my smart dudes to help with my problems while giving really nice advices. Doing stuffs with them is so fun, too, we learn hard yet play hard.

Q. What kinds of things do you study/work with other people?

- I love studying psycology with other people, not just because It's about human behaviors that I could test on humans but also because I have a lot of interest in the field.

Q. Are there times when you study/work better by yourself?

- I have to agree that when I'm by myself, I'm able to focus and concentrate way better, meanwhile, the peaceful, quiet energy helps me a lot with motivation.

- Absolutely not, It's so boring to study alone, I also need the others to teach and guide me so that I wouldn't get into the wrong way.

Q. Is it important to like the person you study/work with?

- Of course, because we would work together more effectively and so that we would have less troubles.

- Well, not really, I think. We should all adapt and manage troubles with hard people because society is not small, there's a high chance we"ll be facing even more difficult people so there's no need to like the person that you work or study with.

25159<x-25160<25161

=>25159+25160<x<25161+25160

=>50319<x<50321

25159 < x - 25160 < 25161 

25159 + 25160 < x < 25161 + 25160

50319 < x < 50321  

1. you / have / terrible / time / Paris ?

➙ Did you have a terrible time in Paris?

2. Why /they / go /for/ twelve  / months?

➙ Why have they gone for twelve months?

3. mountain / climbing / can / very / dangerous.

➙ Mountain climbing can be very dangerous.

4. The/ speed / limit/ be /  lower / in cities / in the countryside

➙ The speed limit is lower in cities than in the countryside.

 5. He/ always /tell / us / things / interesting.

➙ He always tells us interesting things.

6. Jamie /really/ good / at / speak / our club meeting .

➙ Jamie is really good at speaking at our club meetings.

7. they / reach / top / of / mountain  ?

➙ Do they reach the top of the mountain?

8. we / eat / out / restaurant / twice a week.

➙ We eat out at restaurants twice a week.

9. Where / can / you / go / Rickshaw ?

➙ Where can you go in Rickshaw?

10. Your country / have / enormous / public transport system  ?

➙ Does your country have an enormous public transport system?

1 Did you have a terrible time in Paris
2 Why did they go for twelve months
3 Mountain climbing can be very dangerous
4 The speed limit is lower in cities than in the countryside
5 He always tells us interesting things
6 Jamie is really good at speaking at our club meetings
7 Did they reach the top of the mountain
8 We eat out at a restaurant twice a week
9 Where can you go by rickshaw
10 Does your country have an enormous public transport system

\(\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}\right)\cdot x=16\)

=>\(\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}\right)\cdot x=16\)

=>\(x\cdot\dfrac{4}{5}=16\)

=>\(x=16:\dfrac{4}{5}=16\cdot\dfrac{5}{4}=20\)

\(\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}\right).x=16\)

\(\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}\right).x=16\)

\(\left(1-\dfrac{1}{5}\right).x=16\)

\(\dfrac{4}{5}.x=16\)

     \(x=16:\dfrac{4}{5}\)

    \(x=16.\dfrac{5}{4}\)

    \(x=4.5\)

   \(x=20\)