Bài 3:

Chiều rộng là:

\(\dfrac{11}{4}-\dfrac{3}{2}=\dfrac{11}{4}-\dfrac{6}{4}=\dfrac{5}{4}\left(m\right)\)

Chu vi là:

\(\left(\dfrac{11}{4}+\dfrac{5}{4}\right)\cdot2=\dfrac{16}{4}\cdot2=4\cdot2=8\left(m\right)\)

Diện tích là:

\(\dfrac{11}{4}\cdot\dfrac{5}{4}=\dfrac{55}{16}\left(m^2\right)\)

bài 1 :

a) \(3\dfrac{4}{5}\)= \(\dfrac{19}{5}\)                                   b) \(4\dfrac{3}{5}\)=\(\dfrac{23}{5}\)

c) \(11\dfrac{12}{13}\)= \(\dfrac{155}{13}\)                              d) 12 \(\dfrac{11}{13}\)= \(\dfrac{167}{13}\)

bài 1
a)
\(3\dfrac{4}{5}=\dfrac{3x5+4}{5}=\dfrac{19}{5}\)
b)
\(4\dfrac{3}{5}=\dfrac{4x5+3}{5}=\dfrac{23}{5}\)
c)
\(11\dfrac{12}{13}=\dfrac{11x13+12}{13}=\dfrac{155}{13}\)
d)
\(12\dfrac{11}{13}=\dfrac{12x13+11}{13}=\dfrac{167}{13}\)
bài 2
a)\(3\dfrac{3}{4}+1\dfrac{1}{2}=\dfrac{3x4+3}{4}+\dfrac{1x2+1}{2}=\dfrac{15}{4}+\dfrac{3}{2}=\dfrac{21}{4}\)
b)\(3\dfrac{3}{4}-1\dfrac{1}{2}=\dfrac{15}{4}-\dfrac{3}{2}=\dfrac{15}{4}-\dfrac{6}{4}=\dfrac{9}{4}\)
c)\(3\dfrac{3}{4}x1\dfrac{1}{2}=\dfrac{15}{4}x\dfrac{3}{2}=\dfrac{45}{8}\)
d)\(3\dfrac{3}{4}:1\dfrac{1}{2}=\dfrac{15}{4}:\dfrac{3}{2}=\dfrac{15}{4}.\dfrac{2}{3}=\dfrac{5}{2}\)

1 fun (make fun of sb: trêu chọc, biến ai thành trò đùa)

2 down (put sb down = criticise sb)

3 might have (I might have known -> show rằng tôi ko thấy bất ngờ tí nào về sự việc đc nhắc đến)

4 as I may (try as sb may/might = despite one's best efforts)

5 accept (accept an invitation = chấp nhận lời mời)

6 do as it was (do as sb be told = obey, làm như đc bảo)

7 waste of (be a waste of money = chỉ tổ phí tiền)

8 of looking after (look after one's interests = quan tâm đến lợi ích của ai)

9 have fell (fall asleep = start to sleep)

10 earth are you (what on earth are you doing? = m đang làm cái quái gì vậy? :'D)

1 him

2 her down

3 have

4 out

5 accept

6 be

7 waste of

8 of protecting

9 fall

10 chưa nghĩ ra

1 là fun

a: =(-3/2)*(-2/3)+(5/2-3/4):7/4

=1+7/4:7/4=1+1=2

b: \(=\dfrac{1}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{100\cdot103}\right)\)

\(=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{100}-\dfrac{1}{103}\right)\)

=1/3*102/103=34/103

1 B

2 A

3 B

4 D

5 D

6 B

7 A

8 B

9 C

10 C

11 D

12 B

13 D

14 B

15 C

16 B

17 C

Trả lời :

1. B

2. A

3. B

4. D

5. D

6. B

7. A

8. B

9. C

10. C

11. D

12. B

13. D

14. B

15. C

16. B

17. C

Áp dụng tc dtsbn:

\(\dfrac{2y+z-x}{x}=\dfrac{2z-y+x}{y}=\dfrac{2x+y-z}{z}=\dfrac{2x+2y+2z}{x+y+z}=\dfrac{2\left(x+y+z\right)}{x+y+z}=2\\ \Rightarrow\left\{{}\begin{matrix}2y+z-x=2x\\2z-y+x=2y\\2x+y-z=2z\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}2y+z=3x\\2z+x=3y\\2x+y=3z\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3x-2y=z\\3y-2z=x\\3z-2x=y\end{matrix}\right.;\left\{{}\begin{matrix}3x-z=2y\\3y-x=2z\\3z-y=2z\end{matrix}\right.\\ \Rightarrow P=\dfrac{xyz}{2x\cdot2y\cdot2z}=\dfrac{1}{8}\)

Chọn D

\(\dfrac{2y+z-x}{x}=\dfrac{2z-y+x}{y}=\dfrac{2x+y-z}{z}=\dfrac{2\left(x+y+z\right)}{x+y+z}=2\)

\(\Rightarrow\left\{{}\begin{matrix}2y+z-x=2x\\2z-y+x=2y\\2x+y-z=2z\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}2y+z=3x\\2z+x=3y\\2x+y=3z\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}3x-2y=z\\3y-2z=x\\3z-2x=y\end{matrix}\right.\) và \(\left\{{}\begin{matrix}3x-z=2y\\3y-x=2z\\3z-y=2x\end{matrix}\right.\)

Thay vào A:

\(A=\dfrac{z.x.y}{2y.2z.2x}=\dfrac{1}{8}\)

Vì x>0, y>0, z>0 ⇒ x+y+z>0

Áp dụng t/c dtsbn ta có:

\(\dfrac{2y+z-x}{x}=\dfrac{2z-y+x}{y}=\dfrac{2x+y-z}{z}=\dfrac{2y+z-x+2z-y+x+2x+y-z}{x+y+z}=\dfrac{2\left(x+y+z\right)}{x+y+z}=2\)

\(\dfrac{2y+z-x}{x}=2\Rightarrow2y+z-x=2x\Rightarrow2y+z=3x\\ \dfrac{2z-y+x}{y}=2\Rightarrow2z-y+x=2y\Rightarrow2z+x=3y\\ \dfrac{2x+y-z}{z}=2\Rightarrow2x+y-z=2z\Rightarrow2x+y=3z\)

\(A=\dfrac{\left(3x-2y\right)\left(3y-2z\right)\left(3z-2x\right)}{\left(3x-z\right)\left(3y-x\right)\left(3z-y\right)}\)

\(\Rightarrow A=\dfrac{\left(2y+z-2y\right)\left(2z+y-2z\right)\left(2x+y-2x\right)}{\left(2y+z-z\right)\left(2z+x-x\right)\left(2x+y-y\right)}\)

\(\Rightarrow A=\dfrac{xyz}{2x.2y.2z}\)

\(\Rightarrow A=\dfrac{1}{8}\)

Câu I:

1) Ta có: \(P=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{\sqrt{x}+2}{\sqrt{x}}-\dfrac{x+\sqrt{x}-4}{x-\sqrt{x}}\right):\left(\dfrac{1}{\sqrt{x}+1}+\dfrac{2}{x-1}\right)\)

\(=\left(\dfrac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{x+\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\sqrt{x}-1+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\)

\(=\dfrac{x+x+\sqrt{x}-2-x-\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(=\dfrac{x+2}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{\sqrt{x}-1}{1}\)

\(=\dfrac{x+2}{\sqrt{x}}\)

2) Để P=3 thì \(\dfrac{x+2}{\sqrt{x}}=3\)

\(\Leftrightarrow x+2=3\sqrt{x}\)

\(\Leftrightarrow x-3\sqrt{x}+2=0\)

\(\Leftrightarrow x-\sqrt{x}-2\sqrt{x}+2=0\)

\(\Leftrightarrow\sqrt{x}\cdot\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-1\right)=0\)

\(\Leftrightarrow\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}-2=0\\\sqrt{x}-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=2\\\sqrt{x}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\left(nhận\right)\\x=1\left(loại\right)\end{matrix}\right.\)
Vậy: Để P=3 thì x=4