Help 😭

1. I hope I ___________the exam.

a. will pass b. pass c. will passes d. am passing

2. He’s famous_____________ his invention.

a. of b. about c. for d. on

3. My father will _______________ me to the zoo tomorrow.

a. taking b. to take c. takes d. take

4. He enjoys_____________TV in his free time.

a. watching b. to watch c. watches d. wach

5. She goes swimming________________.

a. everyday b. everydays c. every day d. every Sundays

6. They ____________at home yesterday.

a. were b. was c. are d. is

7. We ______________ some flowers tomorrow.

a. will buy b. buy c. bought d. buying

8. Look! He _____________to music.

a. is listening b. listens c. are listening d. listen

9. _____________he eats breakfast, he will be hungry.

a. If b. Unless c. If not d. Because

10. If you don’t eat, you ____________hungry.

a. will b. are c. will be d. is

11. After supper, he went on_____________________ his homework.

a. do b. doing c. did d. does

12. I will tell him about it as soon as he_________________ back.

a. comes b. will come c. come d. to come

13. It was too late, so I had to go home_____________________ a hurry.

a. with b. on c. in d. for

14. He is working hard now, but he used to__________ very lazy.

a. was b. being c. is d. be

15. His father often makes him__________________ up early.

a. get b. to get c. gets d. getting

16. I like to travel _______________ a train.

a. on b. with c. through d. by

17. When you __________________ her, you will agree with me about it.

a. meet b. have meeting c. are meeting d. would meet

18. Look! Someone ______________________.

a. is coming b. are coming c. come d. coming

\(#FallenAngel\)

1. I hope I ___________the exam.

a. will pass b. pass c. will passes d. am passing

2. He’s famous_____________ his invention.

a. of b. about c. for d. on

3. My father will _______________ me to the zoo tomorrow.

a. taking b. to take c. takes d. take

4. He enjoys_____________TV in his free time.

a. watching b. to watch c. watches d. wach

5. She goes swimming________________.

a. everyday b. everydays c. every day d. every Sundays

6. They ____________at home yesterday.

a. were b. was c. are d. is

7. We ______________ some flowers tomorrow.

a. will buy b. buy c. bought d. buying

8. Look! He _____________to music.

a. is listening b. listens c. are listening d. listen

9. _____________he eats breakfast, he will be hungry.

a. If b. Unless c. If not d. Because

10. If you don’t eat, you ____________hungry.

a. will b. are c. will be d. is

11. After supper, he went on_____________________ his homework.

a. do b. doing c. did d. does

12. I will tell him about it as soon as he_________________ back.

a. comes b. will come c. come d. to come

13. It was too late, so I had to go home_____________________ a hurry.

a. with b. on c. in d. for

14. He is working hard now, but he used to__________ very lazy.

a. was b. being c. is d. be

15. His father often makes him__________________ up early.

a. get b. to get c. gets d. getting

16. I like to travel _______________ a train.

a. on b. with c. through d. by

17. When you __________________ her, you will agree with me about it.

a. meet b. have meeting c. are meeting d. would meet

18. Look! Someone ______________________.

a. is coming b. are coming c. come d. coming

1. I hope I ___________the exam.

a. will pass b. pass c. will passes d. am passing

2. He’s famous_____________ his invention.

a. of b. about c. for d. on

3. My father will _______________ me to the zoo tomorrow.

a. taking b. to take c. takes d. take

4. He enjoys_____________TV in his free time.

a. watching b. to watch c. watches d. wach

5. She goes swimming________________.

a. everyday b. everydays c. every day d. every Sundays

6. They ____________at home yesterday.

a. were b. was c. are d. is

7. We ______________ some flowers tomorrow.

a. will buy b. buy c. bought d. buying

8. Look! He _____________to music.

a. is listening b. listens c. are listening d. listen

9. _____________he eats breakfast, he will be hungry.

a. If b. Unless c. If not d. Because

1. I hope I ___________the exam.

a. will pass b. pass c. will passes d. am passing

2. He’s famous_____________ his invention.

a. of b. about c. for d. on

3. My father will _______________ me to the zoo tomorrow.

a. taking b. to take c. takes d. take

4. He enjoys_____________TV in his free time.

a. watching b. to watch c. watches d. wach

5. She goes swimming________________.

a. everyday b. everydays c. every day d. every Sundays

6. They ____________at home yesterday.

a. were b. was c. are d. is

7. We ______________ some flowers tomorrow.

a. will buy b. buy c. bought d. buying

8. Look! He _____________to music.

a. is listening b. listens c. are listening d. listen

9. _____________he eats breakfast, he will be hungry.

a. If b. Unless c. If not d. Because

10. If you don’t eat, you ____________hungry.

a. will b. are c. will be d. is

11. After supper, he went on_____________________ his homework.

a. do b. doing c. did d. does

12. I will tell him about it as soon as he_________________ back.

a. comes b. will come c. come d. to come

13. It was too late, so I had to go home_____________________ a hurry.

a. with b. on c. in d. for

14. He is working hard now, but he used to__________ very lazy.

a. was b. being c. is d. be

15. His father often makes him__________________ up early.

a. get b. to get c. gets d. getting

16. I like to travel _______________ a train.

a. on b. with c. through d. by

17. When you __________________ her, you will agree with me about it.

a. meet b. have meeting c. are meeting d. would meet

18. Look! Someone ______________________.

a. is coming b. are coming c. come d. coming

1. I hope I ___________the exam.

a. will pass b. pass c. will passes d. am passing

2. He’s famous_____________ his invention.

a. of b. about c. for d. on

3. My father will _______________ me to the zoo tomorrow.

a. taking b. to take c. takes d. take

4. He enjoys_____________TV in his free time.

a. watching b. to watch c. watches d. wach

5. She goes swimming________________.

a. everyday b. everydays c. every day d. every Sundays

6. They ____________at home yesterday.

a. were b. was c. are d. is

7. We ______________ some flowers tomorrow.

a. will buy b. buy c. bought d. buying

8. Look! He _____________to music.

a. is listening b. listens c. are listening d. listen

9. _____________he eats breakfast, he will be hungry.

a. If b. Unless c. If not d. Because

\(\dfrac{3}{2\text{x}4}+\dfrac{3}{4\text{x}6}+...+\dfrac{3}{48\text{x}50}\)

\(=\dfrac{3}{2}\text{x}\left(\dfrac{2}{2\text{x}4}+\dfrac{2}{4\text{x}6}+...+\dfrac{2}{48\text{x}50}\right)\)

\(=\dfrac{3}{2}\text{x}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)\)

\(=\dfrac{3}{2}\text{x}\left(\dfrac{1}{2}-\dfrac{1}{50}\right)=\dfrac{3}{2}\text{x}\dfrac{24}{50}=\dfrac{36}{50}=\dfrac{18}{25}\)

\(\dfrac{2}{3}A=\dfrac{2}{2\times4}+\dfrac{2}{4\times6}+...\dfrac{2}{48\times50}\)

\(\dfrac{2}{3}A=\dfrac{4-2}{2\times4}+\dfrac{6-4}{4\times6}+...+\dfrac{50-48}{48\times50}\)

\(\dfrac{2}{3}A=\dfrac{4}{2\times4}-\dfrac{2}{2\times4}+\dfrac{6}{4\times6}-\dfrac{4}{4\times6}+...+\dfrac{50}{48\times50}-\dfrac{48}{48\times50}\)

\(\dfrac{2}{3}A=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}\)

\(\dfrac{2}{3}A=\dfrac{1}{2}-\dfrac{1}{50}\)

\(\dfrac{2}{3}A=\dfrac{12}{25}\)

\(A=\dfrac{12}{25}\div\dfrac{2}{3}\)

\(A=\dfrac{18}{25}\)

x+(x+1)+(x+2)+...+(x+10)=88

=>11x+(1+2+...+10)=88

=>11x+55=88

=>x+5=8

=>x=3

Bài 1:

\(\dfrac{x-2}{5}=\dfrac{-2}{2y+1}\)

=>\(\left(x-2\right)\left(2y+1\right)=5\cdot\left(-2\right)=-10\)

mà 2y+1 lẻ

nên \(\left(x-2;2y+1\right)\in\left\{\left(2;-5\right);\left(-2;5\right);\left(-10;1\right);\left(10;-1\right)\right\}\)

=>\(\left(x;y\right)\in\left\{\left(4;-3\right);\left(0;2\right);\left(-8;0\right);\left(12;-1\right)\right\}\)

Bài 2:

a: \(\left(2x-1\right)^2+4>=4\forall x\)

=>\(B=\dfrac{20}{\left(2x-1\right)^2+4}< =\dfrac{20}{4}=5\forall x\)

Dấu '=' xảy ra khi 2x-1=0

=>\(x=\dfrac{1}{2}\)

b: \(\left(x^2+1\right)^2>=1\forall x\)

=>\(\left(x^2+1\right)^2+5>=1+5=6\forall x\)

=>\(C=\dfrac{10}{\left(x^2+1\right)^2+5}< =\dfrac{10}{6}=\dfrac{5}{3}\forall x\)

Dấu '=' xảy ra khi x=0

BÀI 4A

\(\dfrac{1}{-2}+\dfrac{1}{-6}+\dfrac{1}{-12}+\dfrac{1}{-20}+\dfrac{1}{-30}+\dfrac{1}{-42}+\dfrac{1}{-56}+\dfrac{1}{-72}+\dfrac{1}{-90}\\ =-1\cdot\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\right)\\ =-1\cdot\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =-1\cdot\left(\dfrac{1}{1}-\dfrac{1}{10}\right)=-1\cdot\dfrac{9}{10}=-\dfrac{9}{10}\)

2,34+1,28=3,62

2,34 + 1,28 3,62

\(\dfrac{3}{5}:\dfrac{7}{3}+\dfrac{3}{5}:\dfrac{7}{4}-1\dfrac{3}{5}\)

\(=\dfrac{3}{5}\cdot\dfrac{3}{7}+\dfrac{3}{5}\cdot\dfrac{4}{7}-1-\dfrac{3}{5}\)

\(=\dfrac{3}{5}-1-\dfrac{3}{5}=-1\)

 Giả sử tồn tại một số tự nhiên \(a\) để với mọi số tự nhiên \(b\), \(ab+4\) không phải là số chính phương. Điều này có nghĩa là phương trình \(ab+4=k^2\left(k\inℕ,k\ge2\right)\) không có nghiệm tự nhiên \(\left(b,k\right)\).

 \(\Leftrightarrow b=\dfrac{k^2-4}{a}\) không có nghiêm tự nhiên. 

 Điều này tương đương với việc không tồn tại số tự nhiên \(k\) nào để \(k^2-4⋮a\).     (*)

 Ta sẽ chứng minh (*) vô lý.

 Thật vậy, nếu \(a\ge4\) thì tồn tại số tự nhiên \(k=am+2\left(m\inℕ\right)\) thỏa mãn:

\(k^2-4=\left(am+2\right)^2-4=a^2m^2+4am+4-4=a\left(am^2+4m\right)⋮a\)

 Nếu \(a=3\) thì tồn tại số \(k=3n+1\left(n\inℕ\right)\) để:

 \(k^2-4=\left(3n+1\right)^2-4=9n^2+6n+1-4=9n^2+6n-3⋮3\)

 Nếu \(a=2\) thì chỉ cần chọn \(k\) chẵn là xong.

 Như vậy ta đã chỉ ra rằng (*) vô lý. Do đó điều ta giả sử ban đầu là sai.

 Vậy ta có đpcm.