\(\left|x-2\right|=12\\ =>\left[{}\begin{matrix}x-2=12\\x-2=-12\end{matrix}\right.\\ =>\left[{}\begin{matrix}x=12+2=14\left(ktm\right)\\x=-12+2=-10\left(tm\right)\end{matrix}\right.\\ \left|y+1\right|=2025\\ =>\left[{}\begin{matrix}y+1=2025\\y+1=-2025\end{matrix}\right.\\ =>\left[{}\begin{matrix}y=2025-1=2024\left(tm\right)\\y=-2025-1=-2026\left(ktm\right)\end{matrix}\right.\)

\(A=202x+y-4=202\cdot-10+2024-4=-2020+2024-4=0\)

\(\dfrac{9}{x-2}=\dfrac{x-2}{4}\left(ĐK:x\ne2\right)\\ =>\left(x-2\right)\cdot\left(x-2\right)=9\cdot4\\ =>\left(x-2\right)^2=36\\ =>\left(x-2\right)^2=6^2\\ TH1:x-2=6\\ =>x=6+2\\ =>x=8\\ TH2:x-2=-6\\ =>x=-6+2\\ =>x=-4\)

Ta có: 

\(1+2+3+...+n\)

Số lượng số hạng là: `(n-1):1+1=n` (số hạng) 

Tổng của dãy số là: `(n+1)*n/2` 

Áp dụng ta có:

\(\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+....+\dfrac{1}{1+2+3+...+100}\\ =\dfrac{1}{\dfrac{3\cdot\left(3+1\right)}{2}}+\dfrac{1}{\dfrac{4\cdot\left(4+1\right)}{2}}+...+\dfrac{1}{\dfrac{100\cdot\left(100+1\right)}{2}}\\ =\dfrac{2}{3\cdot4}+\dfrac{2}{4\cdot5}+...+\dfrac{2}{100\cdot101}\\ =2\left(\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{100\cdot101}\right)\\ =2\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{100}-\dfrac{1}{101}\right)\\ =2\left(\dfrac{1}{3}-\dfrac{1}{101}\right)\\ =2\cdot\dfrac{98}{303}\\ =\dfrac{196}{303}\)

\(\dfrac{-5}{7}\cdot\dfrac{2}{11}+\dfrac{-5}{7}\cdot\dfrac{9}{14}+1\dfrac{5}{7}\\ =\dfrac{-5}{7}\cdot\dfrac{2}{11}+\dfrac{-5}{7}\cdot\dfrac{9}{14}+\dfrac{5}{7}+1\\ =\dfrac{5}{7}\cdot\left(\dfrac{-2}{11}+\dfrac{-9}{14}+1\right)+1\\ =\dfrac{5}{7}\cdot\dfrac{27}{154}+1\\ =\dfrac{135}{1078}+1\\ =\dfrac{1213}{1078}\)

\(x^3+ax+b\\ =\left(x^3+4x^2+3x\right)+\left(-4x^2-16x-12\right)+\left(a+13\right)x+\left(b+12\right)\\ =x\left(x^2+4x+3\right)-4\left(x^2+4x+3\right)+\left(a+13\right)x+\left(b+12\right)\\ =\left(x-4\right)\left(x^2+4x+3\right)+\left(a+13\right)x+\left(b+12\right)\)

Để `x^3+ax+b` chia hết cho `x^2+4x+3` thì:

\(\left\{{}\begin{matrix}a+13=0\\b+12=0\end{matrix}\right.=>\left\{{}\begin{matrix}a=-13\\b=-12\end{matrix}\right.\)

Gọi cạnh của hình lập phương đó là `x (cm)`

Điều kiện: `x > 0`

Diện tích toán phần của hình lập phương là: 

`x . x . 6 = 6x^2`

Thể tích hình lập phương là: 

`x . x . x = x^3`

Mà diện tích toàn phần của hình lập phương bằng thể tích của nó

`=> x^3 = 6x^2`

`=> x^3 - 6x^2 = 0`

`=> x^2 (x - 6) = 0`

`=> x = 0` hoặc `x = 6`

Mà `x > 0` nên `x = 6`

Vậy cạnh của hình lập phương là `6cm`

Thể tích hình lập phương là: 

`6^3 = 216 (cm^3)`

Vậy ....

Bài 3: Các cặp góc so le trong là: \(\widehat{tBO};\widehat{BOC}\); \(\widehat{OBC};\widehat{yOB}\); \(\widehat{BCO};\widehat{x'OC}\); \(\widehat{t'CO};\widehat{BOC}\)

Các cặp góc đồng vị là:

\(\widehat{xBt};\widehat{xOy}\); \(\widehat{tBO};\widehat{x'Oy}\); \(\widehat{y'Ct'};\widehat{x'Oy'}\); \(\widehat{t'CO};\widehat{x'Oy}\)

Bài 2: 

Các cặp góc so le trong là \(\widehat{FEC};\widehat{ACB}\)

Các cặp góc đồng vị là \(\widehat{ADE};\widehat{ABC}\); \(\widehat{AED};\widehat{ACB}\)

Các cặp góc trong cùng phía là: \(\widehat{BDE};\widehat{B}\); \(\widehat{DEC};\widehat{ECB}\)

15 I have black hair. Alice's hair is also black.
-> Alice's hair is the same color as mine.

16 The station was nearer than I thought.
-> The station was not as far as I thought.

17 Our neighbours have lived here for quite a long time, but we have lived here longer.
-> Our neighbours haven't lived here as long as we have.

18 My mother's favourite food is noodles. My favourite food is bread.
-> My mother likes noodles, but I like bread.

19 The number of students in this class is 40. That class also has 40 students.
-> This class has the same number of students as that class.

20 My favourite subject is English. My sister is also interested in Math.
-> I like English, and my sister likes Math.

15.i have black hair.alice is houris also black (same)

->......My hair's color is the same as alice's...............

16.the station was nearer than I thought (as)

->....The station was not as far as I thought..............

17.our neighbours have lived here for quite a long time,but we have lived here longer(as).

-->......Out neighbours haven't lived here as long as us.............

18.my mother is favourite food is noodles.my favourite food is bread.(like).

-->.........My mother's favorite food is not like mine......................

19.the number of student in this class is 40.thas class also has 40 students(same_

-->.......The number of students in this class is the same as that class................................

20.my favourite subject is english.My sister is also interested in Math (like)

-->......I don't like the same subject as my sister.................................

`-1/3<=x/3<=-1/6`

`=>-2/6<=2x/3<=-1/6`

`=>-2<=2x<=-1`

`=>-2/2<=x<=-1/2`

`=>-1<=x<=-1/2` 

\(\dfrac{-1}{2}< \dfrac{x}{3}< \dfrac{-1}{6}\)

`=>` \(\dfrac{-3}{6}< \dfrac{2x}{6}< \dfrac{-1}{6}\)

`=> -3 < 2x < -1`

Mà `2x` là số nguyên

`=> 2x = -2`

`=> x = -1`

Vậy `x = -1`

`4^3<=2^x<=2^10`

`=>(2^2)^3<=2^x<=2^10`

`=>2^(2*3)<=2^x<=2^10`

`=>2^6<=2^x<=2^10`

`=>6<=x<=10` 

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