a/ Tam giác AMN cân tại A (gt). \(\Rightarrow\) \(\widehat{AMN}=\widehat{ANM};AM=AN.\)

Xét tam giác AMB và tam giác ANC có:

+ AM = AN (cmt).

+ \(\widehat{AMB}=\widehat{ANC}\left(\widehat{AMN}=\widehat{ANM}\right).\)

+ MB = NC (gt).

\(\Rightarrow\) Tam giác AMB = Tam giác ANC (c - g - c).

\(\Rightarrow\) AB = AC (cặp cạnh tương ứng).

Xét tam giác ABC có: AB = AC (cmt).

\(\Rightarrow\) Tam giác ABC cân tại A.

b/ Tam giác ABC cân tại A (cmt) \(\Rightarrow\) \(\widehat{ABC}=\widehat{ACB}.\)

Mà \(\widehat{ABC}=\widehat{MBH;}\widehat{ACB}=\widehat{NCK}\text{​​}\) (đối đỉnh).

\(\Rightarrow\) \(\widehat{MBH}=\widehat{NCK}.\)

Xét tam giác MBH và tam giác NCK \(\left(\widehat{BHM}=\widehat{CKN}=90^o\right)\)có:

+ MB = NC (gt).

+ \(\widehat{MBH}=\widehat{NCK}\left(cmt\right).\)

\(\Rightarrow\) Tam giác MBH = Tam giác NCK (cạnh huyền - góc nhọn).

c/ Tam giác MBH = Tam giác NCK (cmt).

\(\Rightarrow\) \(\widehat{BMH}=\widehat{CNK}\) (cặp góc tương ứng).

Xét tam giác OMN có: \(\widehat{NMO}=\widehat{MNO}\) (do \(\widehat{BMH}=\widehat{CNK}\)).

\(\Rightarrow\) Tam giác OMN tại O.

1:

1: \(=3\sqrt{3}-12\sqrt{3}+10\sqrt{3}=\sqrt{3}\)

2: \(=6\sqrt{2}+10\sqrt{2}-35\sqrt{2}=-19\sqrt{2}\)

3: \(=4\sqrt{2a}+15\sqrt{2a}-5\sqrt{2a}=14\sqrt{2a}\)

4: \(=7\sqrt{a}-8\sqrt{a}+5\sqrt{a}=4\sqrt{a}\)

5: \(=\sqrt{a}\cdot\dfrac{\sqrt{2}}{2}-\sqrt{a}\cdot\dfrac{\sqrt{3}}{3}+3\sqrt{3}\cdot\sqrt{a}-2\sqrt{2}\cdot\sqrt{a}\)

\(=\sqrt{a}\cdot\left(-\dfrac{3}{2}\sqrt{2}+\dfrac{8\sqrt{3}}{3}\right)\)

\(a.A=\left(\dfrac{x}{x^2-4}+\dfrac{1}{x+2}-\dfrac{2}{x-2}\right):\left(1-\dfrac{x}{x+2}\right)\left(đk:x\ne\pm2\right)\)

\(=\left[\dfrac{x}{x^2-4}+\dfrac{x-2}{x^2-4}-\dfrac{2\left(x+2\right)}{x^2-4}\right]:\left(\dfrac{x+2}{x+2}-\dfrac{x}{x+2}\right)\)

\(=\dfrac{x+x-2-2x-4}{x^2-4}:\dfrac{x+2-x}{x+2}\)

\(=\dfrac{-6}{\left(x+2\right)\left(x-2\right)}.\dfrac{x+2}{2}\)

\(=\dfrac{-3}{x-2}\left(1\right)\)

\(b.\) Thay x = 2023 vào (1), ta được:

\(\dfrac{-3}{2023-2}=-\dfrac{3}{2021}\)

\(c.\) Để A là một số nguyên thì \(x-2\inƯ_{\left(-3\right)}\)

Vậy x - 2 có các giá trị sau:

\(\left[{}\begin{matrix}x-2=1\\x-2=-1\\x-2=3\\x-2=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\\x=5\\x=-1\end{matrix}\right.\)

Bài 6:

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{a}{41}=\dfrac{b}{29}=\dfrac{c}{30}=\dfrac{a+b}{41+29}=\dfrac{700}{70}=10\)

Do đó: a=410; b=290; c=300

dạ ko ạ, làm dạng 1 và 2 ạ

Science and technology has become a debated topic in the society. On one hand, it is necessary for the modern life where other countries are continuously developing in the field of science and technology. It becomes very necessary for other countries too to grow in the same way to be strong and well developed other countries for the future safety and security. It is science and technology which helps other weak countries to develop and be strong. We have to take support of science and technology forever to improve the way of life for the betterment of mankind. If we do not take the help of technologies such as computer, internet, electricity, etc we cannot be economically strong in the future and would be backward forever even we cannot survive in such a competitive and technological world.

Advancement in the field of medical, agriculture, education, economy, sports, games, jobs, tourism, etc are the examples of science and technology. All such advancements show us that how both are equally beneficial for our life. We can see a clear difference in our life style while matching the ancient and modern way of life. High level of scientific and technological advancement in the field of medicine has made easy the treatment of various lethal diseases which was earlier not possible. It has helped a lot to the doctors to find effective ways to cure diseases through medicine or operations as well as research vaccines to cure diseases such as cancer, AIDS, diabetes, Alzheimer’s, Leukemia, etc.

bạn ơi bạn lấy từ đâu vậy ạ

Today, international relations in science and technology is both cooperative and competitive, so in essence, international cooperation is a manifestation of international integration, targeting the following objectives: Development of science and technology: This requires countries, organizations and individuals to cooperate and collaborate to conduct joint research to mobilize more resources, shorten time, reduce costs; Strengthening role and influence: International and regional organizations implementing S & T policy not only help developing countries but also through it to enhance the role and influence of Myself; Expand production, expand markets and increase profits: Developed countries, transnational companies expand cooperation to maintain, enhance their monopoly position, to expand production, expand Market and increase profits; Improving Competitiveness: Foreign investors must train science and technology staff, skilled workers and technology transfer to their home country. Developing countries must prepare resources, strengthen material and technical foundations for research and training, improve information and communication infrastructure, and regulate regulatory requirements. this target.

The tendency for the establishment of forms of international cooperation in science and technology is becoming more widespread with the paripation of many companies and countries in fields such as electronics, informas and telecommunications, Transportation, marine, environmental and other high-tech areas. The above cooperation is often assessed through key indicators such as the growth of incoming and outgoing traffic Of foreign direct investment; Number of laboratories, R & D centers invested or joint ventured; Mergers, joint ventures, and joint ventures between some large companies of international scale have confirmed the trend of increasing cooperation and internationalization in the manufacturing sector. Scientific research and technological development aimed at improving the capacity and competitiveness in the international market.

For developing countries, international integration in science and technology is a driving force for domes scientific and technological activities in order to effectively exploit the world's science and technology achievements. To attract foreign resources and technology to raise and develop the level of S & T in the country, contributing to the achievement of socio-economic development strategy objectives and step by step integrating into the knowledge economy of the country. world.

In our country, the Prime Minister has approved the project of international integration in science and technology to 2020 with the aim of making Vietnam a strong country in a number of science and technology fields by 2020.

what is her mother going to prepare for her bỉthdat party

there are three sticks of butter in the cupboard

i have enough food for the first three day of your stay

`@` `\text {Ans}`

`\downarrow`

`1,`

`a)`

\(\dfrac{x}{2}=\dfrac{y}{3}\text{ và }x+y=50\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

`x/2 = y/3 = (x+y)/(2 + 3) = 50/5 = 10`

`=> x/2 = y/3 = 10`

`=> x = 10*2 = 20; y = 3*10 = 30`

Vậy, `x = 20; y = 30`

`b)`

\(\dfrac{x}{2}=\dfrac{y}{3}\text{ và }5x+4y=110\)

Ta có:

`x/2 = y/3` `=> (5x)/10 = (4y)/12`

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

`(5x)/10 = (4y)/12 = (5x+4y)/(10 + 12) = 110/22 = 5`

`=> x/2 = y/3 = 5`

`=> x = 2*5 = 10; y = 3*5 = 15`

Vậy, `x = 10; y = 15`

`c)`

\(5x=11y\text{ và }2x+3y=37\)

Ta có:

`5x = 11y -> x/11 = y/5 -> (2x)/22 = (3y)/15`

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

`(2x)/22 = (3y)/15 = (2x+3y)/(22+15) = 37/37 = 1`

`=> x/11 = y/5 = 1`

`=> x = 11; y = 5`

Vậy, `x = 11; y = 5`

`d)`

\(\dfrac{x}{2}=\dfrac{y}{1}\text{và }x+y-63=0\)

Ta có: `x + y - 63 = 0 -> x + y = 63`

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

`x/2 = y/1 = (x+y)/(2+1) = 63/3 = 21`

`=> x/2 = y/1 = 21`

`=> x = 21*2 =42; y = 21`

Vậy, `x = 42; y = 21.`

`2,`

`a)`

\(\dfrac{a}{14}=\dfrac{b}{2}=\dfrac{c}{4}\text{ và }a+b+c=5\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

`a/14 = b/2 = c/4 = (a+b+c)/(14+2+4)=5/20=1/4=0,25`

`=> a/14 = b/2 = c/4 = 0,25`

`=> a = 14*0,25 = 3,5` `; b = 2*0,25 = 0,5;` `c = 4*0,25 = 1`

Vậy, `a = 3,5`; `b = 0,5`; `c = 1`

`b)`

\(\dfrac{a}{3}=\dfrac{b}{5}=\dfrac{c}{8}\text{ và }7a+3b-5c=7\)

Ta có:

`a/3 = b/5 = c/8 => (7a)/21 = (3b)/15 = (5c)/40`

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

`(7a)/21 = (3b)/15 = (5c)/40 = (7a + 3b - 5c)/(21 + 15 - 40)=7/-4 = -1,75`

`=> a/3 = b/5 = c/8 = -1,75`

`=> a = 3*(-1,75) = -5,25`

`b = 5*(-1,75) = -8,75`

`c = 8*(-1,75) = -14`

Vậy, `a = -5,25; b = -8,75`; `c = -14`

`c)`

\(\dfrac{a}{3}=\dfrac{b}{8}=\dfrac{c}{5}\text{và }3a+b-2c=14\)

Ta có:

`a/3 = b/8 = c/5 -> (3a)/9 = b/8 = (2c)/10`

Câu này bạn làm tương tự nha

`d)`

\(\dfrac{a}{3}=\dfrac{b}{2};\dfrac{b}{7}=\dfrac{c}{5}\text{ và }3a+5c-7b=30\)

Ta có:

`a/3 = b/2 -> a/21 = b/14`/

`b/7 = c/5 -> b/14 = c/10`

`=> a/21 = b/14 = c/10`

`=> (3a)/63 = (7b)/98 = (5c)/50`

Câu này bạn cũng làm tương tự.

Bài 5:

f(x) có 1 nghiệm x - 2

=> f (2) = 0

\(\Rightarrow a.2^2-a.2+2=0\)

\(\Rightarrow4a-2a+2=0\)

=> 2a + 2 = 0

=> 2a = -2

=> a = -1

Vậy:....

P/s: Mỗi lần chỉ đc đăng 1 câu hỏi thôi! Bạn vui lòng đăng bài hình trên câu hỏi khác nhé!

a)Ta có  △MIP cân tại M nên ˆMNI=ˆMPIMNI^=MPI^

Xét △MIN và △MIP có: 

ˆNMI=ˆPMINMI^=PMI^

MI : cạnh chung

ˆMNI=ˆMPIMNI^=MPI^

Nên △MIN = △MIP (c.g.c)

b)Gọi O là giao điểm của EF và MI

Vì △MNP là  tam giác cân và MI là đường phân giác của △MIP

Suy ra MI đồng thời là đường cao của △MNP

Nên ˆMOE=ˆMOF=90oMOE^=MOF^=90o

Xét △MOE vuông tại O và △MOF vuông tại O có:

OM : cạnh chung

ˆEMO=ˆFMOEMO^=FMO^(vì MI là đường phân giác của △MIP và OMI)

Suy ra △MOE = △MOF (cạnh góc vuông – góc nhọn kề)

Nên ME = MF

Vậy △MEF cân

tham khảo