Giúp e bài 3 và 5 vs ạ
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Bài 5:
a) Phương trình hoành độ giao điểm của (d1) và (d2) là:
\(2x+1=-x+3\)
\(\Leftrightarrow2x+x=3-1\)
\(\Leftrightarrow3x=2\)
hay \(x=\dfrac{2}{3}\)
Thay \(x=\dfrac{2}{3}\) vào (d1), ta được:
\(y=2\cdot\dfrac{2}{3}+1=\dfrac{4}{3}+1=\dfrac{7}{3}\)
2) Thay \(x=\dfrac{2}{3}\) và \(y=\dfrac{7}{3}\) vào (d3), ta được:
\(\left(m-1\right)\cdot\dfrac{2}{3}+3m-2=\dfrac{7}{3}\)
\(\Leftrightarrow\dfrac{2}{3}m-\dfrac{2}{3}+3m-2=\dfrac{7}{3}\)
\(\Leftrightarrow m\cdot\dfrac{11}{3}=5\)
hay \(m=\dfrac{15}{11}\)
Bài 2:
a: Ta có: ΔABC cân tại A
mà AH là đường cao
nên AH là tia phân giác của góc BAC
b: Xét ΔAMH vuông tại M và ΔANH vuông tại N có
AH chung
\(\widehat{MAH}=\widehat{NAH}\)
Do đó: ΔAMH=ΔANH
Suy ra: AM=AN
hay ΔAMN cân tại A
c: Xét ΔABC có AM/AB=AN/AC
nên MN//BC
d: \(AH^2-AN^2=HN^2\)
\(BH^2-BM^2=MH^2\)
mà HN=MH
nên \(AH^2-AN^2=BH^2-BM^2\)
hay \(AH^2+BM^2=BH^2+AN^2\)
nói c1 với c2 ta có đoạn o1o2
-vẽ đường trung trục của o1o2 .và đườn đó là MN như hình vẽ
-phép đôí xứng trục qua MN sẽ biến (c1) thành (c2).như vậy ta có đc đpcm
\(\left(3\sqrt{7}\right)^2=63>28=\left(\sqrt{28}\right)^2\) hoặc \(3\sqrt{7}>2\sqrt{7}=\sqrt{28}\)
3b.
\(\Delta=m^2+4\left(m+1\right)=\left(m+2\right)^2\)
Pt có 2 nghiệm pb khi \(\left(m+2\right)^2>0\Rightarrow m\ne-2\)
Khi đó theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=-m\\x_1x_2=-\left(m+1\right)\end{matrix}\right.\)
\(x_1+x_2-2x_1x_2=8\)
\(\Leftrightarrow-m+2\left(m+1\right)=8\)
\(\Rightarrow m=6\) (thỏa mãn)
6.
\(M=x-\sqrt{x}+1=\left(x-\sqrt{x}+\dfrac{1}{4}\right)+\dfrac{3}{4}=\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)
\(M_{min}=\dfrac{3}{4}\) khi \(\sqrt{x}=\dfrac{1}{2}\Rightarrow x=\dfrac{1}{4}\)
Bài 5:
1. There are a few students taking part in the event
→ There aren't many students taking part in the event.
2. If he doesn't work hard, he will lose his job
→ Unless he works hard, he will lose his job.
3. Let's write about the three Rs ?
→ Why don't we write about the three Rs?
4. Learning about recyking is fun
→ It's fun to learn about recycling.
5. It's not good to throw old clothes away
→ You shouldn't throw old clothes away
Xếp từ thành câu
Bài 1
1. they / to / movies / do / how / go / the / often ?
→ How often do they go to the movies?
2. your eyes / swimming / should / when goggles / you / you / go / wear / to protect
→ When you go swimming, you should wear goggles to protect your eyes.
3. usually / his / swimming / with / friends / he / goes
→ He usually goes swimming with his friends.
4. go / do / weekend / on / always / fishing / parents / their ?
→ Do their parents always go fishing on the weekend?
5. camping / they / go / do / sometimes
→ Sometimes they go camping.
6. what / TV / you / do / on / sports / watch?
→ What sports do you watch on TV?
Bài 2
1. Our / important / an / sports and games / in play / lives / part
→ Sports and games play an important part in our lives.
2. players / how / match / there / in / many / are / football / a ?
→ How many players are there in a football match?
3. by / she / to keep / every day / tries / fit / jogging
→ She tries to keep fit by jogging every day.
4. yesterday / who / play / football / you / did / with ?
→ Who did you play football with yesterday?
5. sports / building / physical and strength / necessary / are / for
→ Sports are necessary for building physical strength.
6. to switch / before / go / don't / the TV / off / you / forget / to bed
→ Don't forget to switch off the TV before you go to bed.
7. Sunday / I / usually / friends / swimming / on / go / mornings / with / my
→ On Sunday mornings, I usually go swimming with my friends.
8. match / you / on / the / did / television / last night / watch / basketball / the ?
→ Did you watch the basketball match on television last night?
Bài 2: Chọn C
Bài 4:
a: \(\widehat{C}=180^0-80^0-50^0=50^0\)
Xét ΔABC có \(\widehat{A}=\widehat{C}< \widehat{B}\)
nên BC=AB<AC
b: Xét ΔABC có AB<BC<AC
nên \(\widehat{C}< \widehat{A}< \widehat{B}\)