2x + 6y + 2z = 60 ( 1 )
x : y : z = 1 : 2 : 3 ( 2 )
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PT
2
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
26 tháng 6 2024
Olm chào em, em cần gõ phân số trên olm thì em chọn biểu tượng \(\Sigma\) góc trái màn hình sau đó chọn biểu tượng phân số rồi chèn phân số em nhé. Cảm ơn em đã đồng hành cùng Olm. Chúc em học tập hiệu quả cùng Olm.vn
26 tháng 6 2024
Nguyễn Thị Thương Hoài : vâng ạ, em hiểu rồi, em cam ơn cô ạ☺
NL
Nguyễn Lê Phước Thịnh
CTVHS
26 tháng 6 2024
\(\left(1+2+3+...+100\right)\cdot\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{8}\right)\cdot\dfrac{\left(1+8+27+64+125+216+343\right)}{1+4+9+16+25+36+49}\)
\(=100\cdot\dfrac{101}{2}\cdot\left(\dfrac{12}{24}+\dfrac{6}{24}+\dfrac{4}{24}+\dfrac{3}{24}\right)\cdot\dfrac{\left(1+2+3+4+5+6+7\right)^2}{140}\)
\(=101\cdot50\cdot\dfrac{25}{24}\cdot\dfrac{784}{140}\)
\(=5050\cdot\dfrac{35}{6}=\dfrac{88375}{3}\)
HN
1
NL
Nguyễn Lê Phước Thịnh
CTVHS
26 tháng 6 2024
\(\dfrac{11}{15}-\dfrac{9}{10}< x< \dfrac{11}{15}:\dfrac{9}{10}\)
=>\(\dfrac{22}{30}-\dfrac{27}{30}< x< \dfrac{11}{15}\cdot\dfrac{10}{9}\)
=>\(-\dfrac{5}{30}< x< \dfrac{22}{27}\)
mà x nguyên
nên x=0
NL
Nguyễn Lê Phước Thịnh
CTVHS
26 tháng 6 2024
b: Đặt \(A=2^{2011}+2^{2010}+...+2+1\)
=>\(2A=2^{2012}+2^{2011}+...+2^2+2\)
=>\(2A-A=2^{2012}+2^{2011}+...+2^2+2-2^{2011}-2^{2010}-...-2-1\)
=>\(A=2^{2012}-1\)
\(x=2^{2012}-2^{2011}-2^{2010}-...-2-1\)
\(=2^{2012}-\left(2^{2012}-1\right)=1\)
=>\(2010\cdot x=2010\)
c: \(A=4^{2015}+4^{2014}-4^{2013}-4^{2012}\)
\(=\left(4^{2015}-4^{2013}\right)+\left(4^{2014}-4^{2012}\right)\)
\(=4^{2013}\left(4^2-1\right)+4^{2012}\left(4^2-1\right)\)
\(=15\cdot\left(4^{2013}+4^{2012}\right)=60\cdot\left(4^{2012}+4^{2011}\right)⋮10\)
=>A có chữ số tận cùng là 0
a: Sửa đề: \(S=1+2+2^2+...+2^{100}\)
=>\(2S=2+2^2+2^3+...+2^{101}\)
=>\(2S-S=2^{101}+2^{100}+...+2^2+2-1-2-2^2-...-2^{100}\)
=>\(S=2^{101}-1\)
26 tháng 6 2024
a,
S=1+2+2\(^2\)+...+2\(^{100}\)
2S=2+2\(^2\)+2\(^3\)+...+2\(^{101}\)
2S-S=(2+2\(^2\)+2\(^3\)+...+2\(^{101}\))-(1+2+2\(^2\)+...+2\(^{100}\))
S= 2\(^{101}\)-1
26 tháng 6 2024
Exercise 1: 1. My sister got married last month.
2. Daisy came to her grandparents’ house 3 days ago.
3. My computer was broken yesterday.
4. He bought me a big teddy bear on my birthday last week.
5. My friend gave me a bar of chocolate when I was at school yesterday.
6. My children did not do their homework last night.
7. Did you live here five years ago?
8. They watched TV late at night yesterday.
9. Was your friend at your house last weekend?
10. They were not excited about the film last night.
11. Yesterday, I went to the restaurant with a client.
12. We drove around the parking lot for 20 mins to find a parking space.
13. When we arrived at the restaurant, the place was full.
14. The waitress asked us if we had reservations.
15. I said, "No, my secretary forgets to make them."
16. The waitress told us to come back in two hours.
17. My client and I slowly walked back to the car.
18. Then we saw a small grocery store.
19. We stopped in the grocery store and bought some sandwiches.
20. That was better than waiting for two hours.
21. Yesterday, I went to the park with my brother.
22. The cashier told us to come back in two hours.
23. When we arrived at the stadium, the place was full.
24. Then we saw a small store.
25. We drove around the parking lot for 30 minutes to find a parking space.
26. I visited my friends last week. [câu này được chia sẵn rồi]
27. He stayed up late last night.
28. I drank wine, sang a song, and played the piano yesterday.
29. I turned off the light, went to bed, and fell asleep.
30. When I was singing, my friends came.
\(#FallenAngel\)
mn lm giup e bai nay ik a
NL
Nguyễn Lê Phước Thịnh
CTVHS
26 tháng 6 2024
b1: \(\dfrac{1}{-3}=\dfrac{-1}{3}=\dfrac{-10}{30}\)
\(\dfrac{-1}{4}=\dfrac{-10}{40}\)
=>3 số hữu tỉ xen giữa là \(-\dfrac{10}{31};-\dfrac{10}{33};-\dfrac{10}{37}\)
b2: \(\dfrac{-3}{7}=\dfrac{-3\cdot5}{7\cdot5}=\dfrac{-15}{35}=\dfrac{-150}{350};\dfrac{-2}{5}=\dfrac{-2\cdot7}{5\cdot7}=\dfrac{-14}{35}=-\dfrac{140}{350}\)
=>3 số hữu tỉ xen giữa là \(-\dfrac{149}{350};-\dfrac{147}{350};-\dfrac{145}{350}\)
P
26 tháng 6 2024
Ta có: \(x+y=\dfrac{a}{m}+\dfrac{b}{m}=\dfrac{a+b}{m}\)
\(\Rightarrow\dfrac{1}{2}\left(x+y\right)=\dfrac{1}{2}\cdot\dfrac{a+b}{m}=\dfrac{a+b}{2m}\)
\(\Rightarrow\dfrac{1}{2}\left(x+y\right)=z\)
\(\Rightarrow\dfrac{x+y}{2}=z\)
=> `z` là trung bình cộng của `x` và `y`
=> `z` nằm giữa `x` và `y`
Mà: `x<y`
=> `x<z<y`
x:y:z=1:2:3
=>\(\dfrac{x}{1}=\dfrac{y}{2}=\dfrac{z}{3}\)
mà 2x+6y+2z=60
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{1}=\dfrac{y}{2}=\dfrac{z}{3}=\dfrac{2x+6y+2z}{2\cdot1+6\cdot2+2\cdot3}=\dfrac{60}{20}=3\)
=>\(x=3\cdot1=3;y=3\cdot2=6;z=3\cdot3=9\)
Ta có: \(\dfrac{x}{1}=\dfrac{y}{2}=\dfrac{z}{3}\Rightarrow\dfrac{2x}{2}=\dfrac{6y}{12}=\dfrac{2z}{6}\)
Áp dụng tính chất dãy tỉ sống bằng nhau, ta có:
\(\dfrac{2x}{2}=\dfrac{6y}{12}=\dfrac{2z}{6}=\dfrac{2x+6y+2z}{2+12+6}=\dfrac{60}{20}=3\)
Do đó:
\(\dfrac{x}{1}=3\Rightarrow x=1.3=3\)
\(\dfrac{y}{2}=3\Rightarrow y=2.3=6\)
\(\dfrac{z}{3}=3\Rightarrow z=3.3=9\)
Vậy x = 3; y = 6; z = 9.
\(#NqHahh\)