\(Theo \) \(bài \) \(ra \) \(ta \) \(có:\)

\(a\div b\div c\div d=2\div3\div4\div5\)

\(\Rightarrow\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{d}{5}\)

\(a+b+c+d=-42\)

\(Áp \) \(dụng \) \(tính\) \(chất\) \(dãy\) \( tỉ \) \(số \) \(bằng \) \(nhau \) \(ta \) \(được:\)

\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{d}{5}=\dfrac{a+b+c+d}{2+3+4+5}=\dfrac{-42}{14}=-3\)

\(\Rightarrow\dfrac{a}{2}=-3\Rightarrow a=-6\)

\(\Rightarrow\dfrac{b}{3}=-3\Rightarrow b=-9\)

\(\Rightarrow\dfrac{c}{4}=-3\Rightarrow c=-12\)

\(\Rightarrow\dfrac{d}{5}=-3\Rightarrow d=-15\)

\(Vậy\) \(a=-6\)

\(b=-9\)

\(c=-12\)

\(d=-15\)

\(\text{Đặt}\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow\left[{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

\(\text{Ta có:}\)

\(\dfrac{a}{3a+b}=\dfrac{bk}{3bk+b}=\dfrac{bk}{b\left(3k+1\right)}=\dfrac{k}{3k+1}\) \(\left(1\right)\)

\(\dfrac{c}{3c+d}=\dfrac{dk}{3dk+d}=\dfrac{dk}{d\left(3k+1\right)}=\dfrac{k}{3k+1}\) \(\left(2\right)\)

\(Từ\) \(\left(1\right)\) \(và\) \(\left(2\right)\) \(suy\) \(ra:\)

\(\dfrac{a}{3a+b}=\dfrac{k}{3k+1}=\dfrac{c}{3c+d}\)

\(Vậy\) \(\dfrac{a}{3a+b}=\dfrac{c}{3c+d}\) \(\left(ĐPCM\right)\)

\(\left(x-\dfrac{2}{3}\right)\left(x+\dfrac{1}{4}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{2}{3}=0\\x+\dfrac{1}{4}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=\dfrac{-1}{4}\end{matrix}\right.\)

Vậy \(x=\dfrac{2}{3}\) hoặc \(x=-\dfrac{1}{4}\)

Mark the letter A, B, C, or D on your answer sheet to indicate the sentence that is closest in meaning to each of the following questions.

Some people will go any length to lose weight

A. Some people will do anything to lose weight

B. Some people haven’t lost any weight for a long time

C. Losing weight is a long way for some people

D. Some people find it hard to lose weight

Mark the letter A, B, C, or D on your answer sheet to indicate the word(s) OPPOSITE in meaning to the underlined word(s) in each of the following questions.

I could see the finish line and thought I was home and dry

A. hopeless 

B. hopeful  

C. successful  

D. unsuccessful

Trong không gian Oxyz, cho mặt cầu (S):  x 2 + ( y + 2 ) 2 + ( z - 2 ) 2 = 8 . Tính bán kính R của (S)

A. R=8

B. R=4

C. R= 2 2

D. R=64

\(a\)) \(\dfrac{6}{2x+1}=\dfrac{2}{7}\)

\(\Leftrightarrow2\left(2x+1\right)=6\cdot7\)

\(\Leftrightarrow4x+2=42\)

\(\Leftrightarrow4x=40\)

\(\Leftrightarrow x=10\)

Vậy \(x=10\)

\(b\)) \(\dfrac{24}{7x-3}=\dfrac{-4}{25}\)

\(\Leftrightarrow-4\left(7x-3\right)=24\cdot25\)

\(\Leftrightarrow-4\left(7x-3\right)=600\)

\(\Leftrightarrow7x-3=-150\)

\(\Leftrightarrow7x=-147\)

\(\Leftrightarrow x=-21\)

Vậy \(x=-21\)

\(c\)) \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\)

Ta có: \(\dfrac{4}{x-6}=\dfrac{-12}{18}\)

\(\Leftrightarrow-12\left(x-6\right)=72\)

\(\Leftrightarrow x-6=-6\)

\(\Leftrightarrow x=0\)

\(\dfrac{y}{24}=\dfrac{4}{x-6}\)

\(\Leftrightarrow\dfrac{y}{24}=\dfrac{-2}{3}\)

\(\Leftrightarrow y=\dfrac{-2}{3}\cdot24\)

\(\Leftrightarrow y=-16\)

Vậy \(x=0\)

\(y=-16\)

\(d\)) \(-\dfrac{1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\)

\(\Leftrightarrow-0,2\le x\le0,25\)\(\)

Mà \(x\in Z\)

\(\Leftrightarrow x=0\)

Vậy \(x=0\)

\(e\)) \(\dfrac{x+46}{20}=x\dfrac{2}{5}\)

\(\Leftrightarrow\dfrac{x+46}{20}=\dfrac{5x+2}{5}\)

\(\Leftrightarrow5\left(x+46\right)=20\left(5x+2\right)\)

\(\Leftrightarrow5x+230=100x+40\)

\(\Leftrightarrow5x-100x=40-230\)

\(\Leftrightarrow-95x=-190\)

\(\Leftrightarrow x=\dfrac{-190}{-95}\)

\(\Leftrightarrow x=2\)

Vậy \(x=2\)

\(f\)) \(y\dfrac{5}{y}=\dfrac{56}{y}\)

\(\Leftrightarrow\dfrac{y^2+5}{y}=\dfrac{56}{y}\)

\(\Leftrightarrow\left(y^2+5\right)y=56y\)

\(\Leftrightarrow y^3+5y=56y\)

\(\Leftrightarrow y^3=56y-5y\)

\(\Leftrightarrow y^3=51y\)

\(\Leftrightarrow\dfrac{y^3}{y}=51\)

\(\Leftrightarrow y^2=51\)

\(\Leftrightarrow y=\sqrt{51}\)

\(\Leftrightarrow y=7,141...\)

Mà \(y\in Z\)

Vậy \(y\) không có giá trị

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions.

What picture do you have of the future? Will life in the future be better, worse or the same as now? What do you hope about the future?

Futurologists predict that life will probably be very different in 2050 in all the fields, from entertainment to technology. First of all, it seems that TV channels will have disappeared. Instead, people will choose a program from a 'menu' and a computer will send the program directly to the television. Today, we can use the World Wide Web to read newspaper stories and see pictures on a computer thousands of kilometers away. By 2050, music, films, programs, newspapers and books will come to us by computer.

In what concerns the environment, water will have become one of our most serious problems. In many places, agriculture is changing and farmers are growing fruit and vegetables to export. This uses a lot of water. Demand for water will increase ten times between now and 2050 and there could be serious shortages. Some futurologists predict that water could be the cause of war if we don't act now.

In transport, cars running on new, clean fuels will have computers to control the speed and there won't be any accidents. Today, many cars have computers that tell drivers exactly where they are. By 2050, the computer will control the car and drive it to your destination. On the other hand, space planes will take people halfway around the world in two hours. Nowadays, the United States Shuttle can go into space and land on Earth again. By 2050, space planes will fly all over the world and people will fly from Los Angeles to Tokyo in just two hours.

In the domain of technology, robots will have replaced people in factories. Many factories already use robots. Big companies prefer robots - they do not ask for pay rises or go on strike, and they work 24 hours a day. By 2050, we will see robots everywhere - in factories, schools, offices, hospitals, shops and homes.

Last but not least, medicine technology will have conquered many diseases. Today, there are electronic devices that connect directly to the brain to help people hear. By 2050, we will be able to help blind and deaf people see and hear again. Scientists have discovered how to control genes. They have already produced clones of animals. By 2050, scientists will be able to produce clones of people and decide how they look, how they behave and how much intelligence they have.

The word "This" in paragraph 3 refers to __________________. 

A. the possible war 

B. the cash crop planting 

C. the serious shortage 

D. the demand for water

=> a-2010=2009       hoặc          a-2010=-2009

=>         a=2009+2010                       a=-2009+2010

=>         a=4019                                a=1

vậy a=4019  hoặc a= 1