d-a-b

1 D

2 A

3 B

Hình đâu rồi bạn?

\(\dfrac{1}{3}\cdot x+\dfrac{2}{5}\cdot\left(x+1\right)=0\\ =>\dfrac{1}{3}\cdot x+\dfrac{2}{5}\cdot x+\dfrac{2}{5}=0\\ =>x\cdot\left(\dfrac{1}{3}+\dfrac{2}{5}\right)+\dfrac{2}{5}=0\\ =>x\cdot\dfrac{11}{15}+\dfrac{2}{5}=0\\ =>x\cdot\dfrac{11}{15}=-\dfrac{2}{5}\\ =>x=\dfrac{-2}{5}:\dfrac{11}{15}\\ =>x=\dfrac{-2}{5}\cdot\dfrac{15}{11}\\ =>x=\dfrac{-6}{11}\)

\(125^7:25^{16}\\ =\left(5^3\right)^7:\left(5^2\right)^{16}\\ =5^{3\cdot7}:5^{2\cdot16}\\ =5^{21}:5^{32}\\ =5^{21-32}\\ =5^{-11}\)

Ta có:

\(\dfrac{1}{2}< \dfrac{x}{10}< \dfrac{4}{5}\\ \Rightarrow\dfrac{5}{10}< \dfrac{x}{10}< \dfrac{8}{10}\\ \Rightarrow5< x< 8\)

Vì \(x\) nguyên nên:

\(x\in\left\{6,7\right\}\)

Vậy \(x\in\left\{6,7\right\}\)

a: Xét ΔAHK vuông tại H và ΔDHB vuông tại H có

HA=HD

HK=HB

Do đó: ΔAHK=ΔDHB

b: ΔAHK=ΔDHB

=>\(\widehat{HAK}=\widehat{HDB}\)

=>AK//DB

c: Xét ΔBAD có

BH là đường cao

BH là đường trung tuyến

Do đó: ΔBAD cân tại B

=>BA=BD

d: Xét ΔHAB vuông tại H và ΔHDK vuông tại H có

HA=HD

HB=HK

Do đó: ΔHAB=ΔHDK

=>\(\widehat{HAB}=\widehat{HDK}\)

=>AB//DK

ta có: IK\(\perp\)AC

AB\(\perp\)AC

Do đó: IK//AB

mà DK//AB

và IK,DK có điểm chung là K

nên I,K,D thẳng hàng

Đặt: \(\dfrac{x}{3}=\dfrac{y}{5}=k=>\left\{{}\begin{matrix}x=3k\\y=5k\end{matrix}\right.\)

Mà:

\(2x^2+y^2=43\\ =>2\cdot\left(3k\right)^2+\left(5k\right)^2=43\\ =>18k^2+25k^2=43\\ =>43k^2=43\\ =>k^2=1\\ =>k=\pm1\\ TH1:k=1=>\left\{{}\begin{matrix}x=3\cdot1=3\\y=5\cdot1=5\end{matrix}\right.\\ TH2:k=-1=>\left\{{}\begin{matrix}x=3\cdot\left(-1\right)=-3\\y=5\cdot\left(-1\right)=-5\end{matrix}\right.\)

Ex1

2 Have you heard the news yet? - Yes, I have already heard it

3 Have you eaten this fruit yet? - Yes, I've already eaten it

4 Has Jill written the report yet? - Yes, she has already written it

5 Has Ted repair his bike yet? - Yes, he has already repaired it

6 Has Messi signed the contract yet? - Yes, he has already signed it

7 Have Vera and Tom got engaged yet? - Yes, they have already done it

8 Has Paul bought a new car yet? - Yes, he has already bought it

9 Has Yen passed her driving test yet? - Yes, she has already passed it

10 Have you sent the invitations yet? - Yes, I have already sent them

Ex1

2 have met

3 has knwon

4 have read

5 haven't seen

6 has never eaten

7 Have you told

8 hasn't rained

9 have had

10 have just sold

\(\left|2\dfrac{1}{5}-x\right|+\left|x-\dfrac{1}{5}\right|+8\dfrac{1}{5}=1,2\\\Rightarrow\left|2\dfrac{1}{5}-x\right|+\left|x-\dfrac{1}{5}\right|=1,2-8\dfrac{1}{5}\\ \Rightarrow \left|2\dfrac{1}{5}-x\right|+\left|x-\dfrac{1}{5}\right|=-7\)

Nhận xét:

\(\left\{{}\begin{matrix}\left|2\dfrac{1}{5}-x\right|\ge0,\forall x\\\left|x-\dfrac{1}{5}\right|\ge0,\forall x\end{matrix}\right.\\ \Rightarrow\left|2\dfrac{1}{5}-x\right|+\left|x-\dfrac{1}{5}\right|\ge0,\forall x\)
Mà \(-7< 0\) nên:
Không tìm được giá trị \(x\) thỏa mãn đề bài
Vậy...