giúp mk vs ạ mk đag cần gấp
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X. Complete the second sentence
38 We stayed indoors despite the good weather
39 When the children were playing in the playground, it began to rain
40 Before she broke the eggs, she mixed the yolk with flour
41 We won't be able to make coffee until the coffee machine is repaired
42 While I am watching TV, my brother is playing video games
XI. Use suggested words to write sentences
43 Last week, when I went down the street, a small cat suddenly jumped out on the street
44 She thinks I need to focus more on my schoolwork than on the pet
45 My sister once rescued a dog when it was injured badly by its owner
46 We have plans to build an animal hospital in the future
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B=2006^2024
B= ....6
=> B chia 5 dư 1
Có 2006 đồng dư với -1 (mod 223)
=> 2006^2024 đồng dư với (-1)^2024 = 1 (mod 223)
=> B chia 223 dư 1
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Lời giải:
ĐKXĐ: $x\neq \pm \frac{2}{3}$
Gọi biểu thức trên là $A$
\(A=\frac{3x+2}{(3x-2)(3x+2)}-\frac{3x-2}{(3x+2)(3x-2)}+\frac{3x-6}{9x^2-4}\\ =\frac{3x+2}{(3x-2)(3x+2)}-\frac{3x-2}{(3x+2)(3x-2)}+\frac{3x-6}{(3x-2)(3x+2)}\\ =\frac{3x+2-(3x-2)+(3x-6)}{(3x-2)(3x+2)}=\frac{3x-2}{(3x-2)(3x+2)}=\frac{1}{3x+2}\)
Bạn lưu ý lần sau gõ đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để mọi người hiểu đề của bạn hơn nhé.
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Ta có \(2006^{2024}=\left(7.286+4\right)^{2024}\) \(=7A+4^{2024}\). Do đó ta chỉ cần tìm số dư của \(4^{2024}\) khi chia cho 7.
Để ý rằng: \(4^0\equiv1\left[7\right]\); \(4^1\equiv4\left[7\right]\); \(4^2\equiv2\left[7\right]\); \(4^3\equiv1\left[7\right]\); \(4^4\equiv4\left[7\right]\); \(4^5\equiv2\left[7\right]\)
Do đó ta nảy sinh dự đoán rằng \(4^{3k+2}\equiv2\left[7\right]\left(k\inℕ\right)\). Ta sẽ chứng minh điều này bằng phương pháp quy nạp,
Thật vậy, với \(k=0\) thì khẳng định đúng (theo như trên)
Giả sử khẳng định đúng đến \(k=l\ge0\), khi đó \(4^{3l+2}\equiv2\left[7\right]\). Ta cần chứng minh khẳng định đúng với \(k=l+1\), tức là cm \(4^{3\left(l+1\right)+2}\equiv2\left[7\right]\)
Thật vậy, ta có \(4^{3\left(l+1\right)+2}\equiv4^{3l+3+2}\equiv64.4^{3l+2}\equiv1.2\equiv2\left[7\right]\)
Vậy khẳng định đúng với \(k=l+1\Rightarrow4^{3k+2}\equiv2\left[7\right]\)
Vì vậy \(4^{2024}=4^{2022+2}=4^{3.674+2}\equiv2\left[7\right]\)
Vậy số dư của phép chia \(2006^{2024}\) cho 7 là 2.
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X. Complete the second sentence
38 Despite the good weather, we stayed indoors
39 When it began to rain, the children were playing in the playground
40 Before she broke the eggs, she mixed the yolk with flour
41 We won't be able to make coffee until the coffee machine is repaired
42 While I am watching TV, my brother is playing video games
XI. Use suggested words to write sentences
43 Last week, when I went down the street, a small cat suddenly jumped out on the street
44 She thinks I need to focus more on my schoolwork than on the pet
45 My sister once rescued a dog when it was badly injured by its owner
46 We have plans to build an animal hospital in the future
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16. There are only 50 saolas around Viet Nam and they are the most critically _________ animals in Viet Nam.
A. threatening B. popular C. endangered D. dangerous
17. The sun _________ at 5 a.m. tomorrow according to the weather forecast.
A. is going to rise B. rises C. rise D. will rise
18. Local officials posted a flood __________ yesterday, so many are moving to safer areas and using more flood-prevention methods today. A. damage B. warning C. property D. emergency
19. While my mother __________ dinner, my father _________ home from work yesterday.
A. was made/ came B. was making/ came C. was making/ was coming D. made/ came
20. I __________ on the sofa when suddenly the cat ___________ on me.
A. was sitting/ jumped B. was sitting/ was jumping C. sat/ jumped D. sat/ was jumping
21. My dentist __________ checks my teeth. I don’t often go to the dentist.
A. never B. sometimes C. always D. usually
22. The students ___________ on their field trip to the Happy Farm next day.
A. will go B. goes C. go D. is going
23. I have to pass the entrance test ________ I can apply to that university.
A. after B. as soon as C. while D. before
24. My family was having dinner _________ it was raining outside.
A. till B. while C. until D. as soon as
16c
17a
18b
19b
20a
21b
22d
23d
24b
Đáp án nhé e chúc e may mắn chạy deadline
Trả công a nha
Bài 6:
a: Xét ΔAHB vuông tại H và ΔBCD vuông tại C có
\(\widehat{ABH}=\widehat{BDC}\)(hai góc so le trong, AB//CD)
Do đó: ΔAHB~ΔBCD
b: Xét ΔHDA vuông tại H và ΔADB vuông tại A có
\(\widehat{HDA}\) chung
Do đó: ΔHDA~ΔADB
=>\(\dfrac{DH}{DA}=\dfrac{DA}{DB}\)
=>\(DA^2=DH\cdot DB\)
c: Ta có: ΔADB vuông tại A
=>\(AB^2+AD^2=BD^2\)
=>\(BD^2=3^2+4^2=25=5^2\)
=>BD=5(cm)
=>\(DH=\dfrac{DA^2}{DB}=\dfrac{3^2}{5}=1,8\left(cm\right)\)
ΔDHA vuông tại H
=>\(HD^2+HA^2=DA^2\)
=>\(HA^2+1,8^2=3^2\)
=>\(HA^2=2,4^2\)
=>HA=2,4(cm)
Bài 4:
a: Xét ΔABC vuông tại A và ΔHBA vuông tại H có
\(\widehat{ABC}\) chung
Do đó: ΔABC~ΔHBA
=>\(\dfrac{BA}{BH}=\dfrac{BC}{BA}\)(1)
=>\(BA^2=BH\cdot BC\)
c: Xét ΔBAH có BI là phân giác
nên \(\dfrac{IA}{IH}=\dfrac{BA}{BH}\left(2\right)\)
Xét ΔBCA có BD là phân giác
nên \(\dfrac{DC}{DA}=\dfrac{BC}{BA}\left(3\right)\)
Từ (1),(2),(3) suy ra \(\dfrac{IA}{IH}=\dfrac{DC}{DA}\)
=>\(\dfrac{IH}{IA}=\dfrac{DA}{DC}\)
c: Xét ΔBAC vuông tại A có \(BA^2+AC^2=BC^2\)
=>\(BC^2=6^2+8^2=100=10^2\)
=>BC=10(cm)
Xét ΔBAC có BD là phân giác
nên \(\dfrac{AD}{AB}=\dfrac{CD}{CB}\)
=>\(\dfrac{AD}{6}=\dfrac{CD}{10}\)
=>\(\dfrac{AD}{3}=\dfrac{CD}{5}\)
mà AD+CD=AC=8cm
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{AD}{3}=\dfrac{CD}{5}=\dfrac{AD+CD}{3+5}=\dfrac{8}{8}=1\)
=>\(AD=3\left(cm\right)\)
ΔBAD vuông tại A
=>\(S_{BAD}=\dfrac{1}{2}\cdot BA\cdot AD=\dfrac{1}{2}\cdot6\cdot3=9\left(cm^2\right)\)
ΔBAC vuông tại A
=>\(S_{BAC}=\dfrac{1}{2}\cdot BA\cdot AC=\dfrac{1}{2}\cdot6\cdot8=24\left(cm^2\right)\)
\(S_{BAD}+S_{BDC}=S_{BAC}\)
=>\(S_{BDC}=24-9=15\left(cm^2\right)\)