Bài 28:

C = 4/3.5 + 4/5.7 + ... + 4/97.99

C = 2.(2/3.5 + 2/5.7 + ...+ 2/97.99)

C = 2.(1/3 - 1/5 + 1/5 - 1/7 + ... + 1/97 - 1/99)

C = 2.(1/3 - 1/99)

C = 2.32/99

C = 64/99

D = 18/2.5 + 18/5.8 + ... + 18/203.306

D = 6.(3/2.5 + 3/5.8 + ... + 3/203.206)

D = 6.(1/2 - 1/5 + 1/5 - 1/8 + ... + 1/203 - 1/206)

D = 6.(1/2 - 1/206)

D = 306/103

C/D = 64/99 : 306/103

C/D = 64/99.103/306

C/D = 3296/15147

Cho A = (196 + 197) / 198 ; B = (196 + 197) / (197 + 198). So sánh A và B

B = \(\frac{196+197}{197+198}\) = \(\frac{196}{197+198}+\) \(\frac{197}{197+198}\)

\(\frac{196}{197+198}\) < \(\frac{196}{198}\)

\(\frac{197}{197+198}\) < \(\frac{197}{198}\)

Cộng vế với vế ta có:

B = \(\frac{196}{197+198}+\) \(\frac{197}{197+198}\) < \(\frac{196}{198}+\frac{197}{198}\) = A

Vậy A > B

Bài 1:

1. most delicious
2. smartest
3. hottest
4. worst
5. most interesting
6. highest

Bài 2: 1 - B 2 - B 3 - B 4 - A

Bài 3:

1. Nam is the fastest in the team.
2. The red dress is the most expensive.
3. This is the most beautiful house I have ever seen.
   
   HI hi

1. This is the most delicious cake I have ever tasted.
2. Who is the smartest student in your group?
3. Yesterday was the hottest day of the summer.
4. It was the worst movie I've ever seen.
5. This is the most interesting book in the library.
6. Which is the highest mountain in the world?

1. Jupiter is the ________ planet in our solar system.
2. • Đáp án: B. largest
3. She is the ________ girl in the school.
4. • Đáp án: B. most beautiful
5. That was the ________ exam I've ever taken.
6. • Đáp án: B. most difficult
7. My brother is the ________ person I know.
8. • Đáp án: A. busiest

1. No one in the team is faster than Nam.
2. • \(\rightarrow \) Nam is the fastest person/player in the team.
3. This dress is \(\$50\). The blue one is \(\$70\). The red one is \(\$100\).
4. • \(\rightarrow \) The red dress is the most expensive (of the three).
5. I have never seen a more beautiful house than this one.
6. • \(\rightarrow \) This is the most beautiful house I have ever seen.

1. \(3n + 1 = x^2\) (1)
2. \(4n + 1 = y^2\) (2)

• Bước 1: Giới hạn giá trị của \(y\)
  Vì \(10 \le n \le 99\), ta có:
  \(4 \cdot 10 + 1 \le 4n + 1 \le 4 \cdot 99 + 1\)
  \(41 \le y^2 \le 397\)
  \(\Rightarrow 7 \le y \le 19\)
• Bước 2: Xét phương trình (2)
  Từ \(4n + 1 = y^2\), ta thấy \(y^{2}\) phải là số lẻ, nên \(y\) là số lẻ.
  Các giá trị \(y\) có thể là: \(\{7, 9, 11, 13, 15, 17, 19\}\).
• Bước 3: Thử chọn giá trị
  Ta lập bảng để kiểm tra điều kiện \(3n + 1\) là số chính phương:

Ta có:
\(x^2-x=x\left(x-1\right)\) với mọi x thuộc số nguyên dương
Khi đó
\(\left(a^2+b^2+c^2+d^2\right)-\left(a+b+c+d\right)=a\left(a-1\right)+b\left(b-1\right)+c\left(c-1\right)+d\left(d-1\right)\)
Và:
\(a\left(a-1\right)+b\left(b-1\right)+c\left(c-1\right)+d\left(d-1\right)\) chia hết 2
\(\Rightarrow\left(a^2+b^2+c^2+d^2\right)-\left(a+b+c+d\right)\) chia hết 2

Mà : \(a^2+b^2+c^2+d^2\) chia hết 2
\(\Rightarrow a+b+c+d\) chia hết 2
Với \(a+b+c+d\ge1+1+1+1=4\)
Vậy , a+b+c+d là hợp số

• If we recycle more, the environment will be cleaner.
• This is the most modern house in my town.

\(\rarr\)

1. If we recycle more, the environment will be cleaner.

2. This house is the most modern house in my town.

Giải:

Tiền bán bằng: 100% + 20% = 120%

Giá mua của chiếc máy là:

10500000 : 120 x 100 = 8 750 000 (đồng)

Kết luận:

Giá mua của chiếc máy là 8 750 000 đồng.

\(-\frac14.\left(12\frac34-7,75\right)-25\%-3+\frac12\)

Phần 1: \(-\frac14=-0,25\)

Phần 2: \(12\frac34=\frac{48}{4}=12\)

Phần 3: \(25\%=0,25\)

Phần 4: \(\frac12=0,5\)

Kết quả cuối cùng: \(-0,25.\left(12-7,75\right)-0,25-3+0,5=\)

\(-0,25.4,25-0,25-3+0,5=\)

\(-1,0625-0,25-3+0,5=\)

\(-1,3125-3+0,5=-4,3125+0,5=-3,8125\)

\(\)

- 1/4 x (12\(\frac34\) - 7,75) - 25% - 3 + 1/2

= - 1/4 x (12,75 - 7,75) - 1/4 - 3 + 1/2

= - 1/4 x 5 - 1/4 - 3 + 1/2

= - 1/4(5 + 1) - 3 + 1/2

= - 1/4.6 - 3 + 1/2

= - 3/2 + 1/2 - 3

= - 1 - 3

= - 4

1. Write about a city you would like to visit / natural wonder

I would like to visit Paris one day. It is a beautiful city with famous places, delicious food, and rich culture. I want to see the Eiffel Tower and walk along the lovely streets. I also want to try French bread and learn more about the history of this city. I think visiting Paris would be an amazing experience.

2. Write about your dream house

My dream house is a big and modern house in the countryside. It has a beautiful garden with many flowers and trees. Inside, there are four bedrooms, a large living room, and a cozy kitchen. I also want a small library to read books and a swimming pool in the backyard. My dream house is peaceful, comfortable, and full of happiness.

• This question is formed by asking "What" about the action "will stay at".
• The phrase "will stay at" is replaced by "will you do".
• The remaining part of the sentence ("if it rain") is adjusted to "if it rains" to follow correct English grammar.

What will you do if it rains?

75% - 1 1/2 + 0,5 : 5/12
= 3/4 - 3/2 + 1/2 × 12/5
= 3/4 - 6/4 + 6/5
= -3/4 + 6/5
= -15/20 + 24/20
​= 9/20

\(75\%-1\frac12+0,5:\frac{5}{12}\)

\(=\frac{75}{100}-\frac32+\frac12:\frac{5}{12}\)

\(=\frac34-\frac32+\frac12.\frac{12}{5}\)

\(=\left(\frac34.\frac{12}{5}\right)+\left(-\frac32+\frac12\right)\)

\(=\frac95-1\)

\(=\frac45\) hoặc 0,8.