Bẹn tự vẽ hình nhé

1) Ta có: BOC=90 => CON+BON=90

Vì MON =90 (gt)

=> BOM+BON=90 => BOM=CON

+) BD là đường chéo=> BD là phân giác ABC => MBO=CBO = 1/2 BOC=45

Tương tự: NCO=DCO=1/2 BOC=45 

=> MBO=NCO

Xét tam giác OBM và OCN có:

OB=OC

BOM=CON 

MBO=NCO

=> Tam giác OBM=OCN (g.c.g)

=> OM=ON (1)

Lại có: MON =90(gt) (2)

Từ 1,2 => tam giác MON vuông cân (đpcm)

2) tam giác OBM= tam giác OCN(theo 1) 

=> BM=CN

Mà AB=AC ( tứ giác ABCD là hình vuông)

=>AB-BM=BC-CN

=> AM=BM=AM/MB=BN/CN

Ta có: AB//CD (ABCD là hv) => AM//CE => AN/NE=BN/NC

=> AM/BM=AN/NE => MN//BE ( Ta-lét đảo)

3) Vì MN//BE (Theo 2) => BKN=MNO =45 (hai góc đồng vị, tam giác MON vuông cân)

=> tam giác BNK đồng dạng ONC ( BNK=ONK;BKN=OCN=45)

=> NB/NK=NO/NC

Xét tam giác BON và KNC có:

BNO=CNK

NB/NK=NO/NC

=> TAM GIÁC BON đồng dạng tam giác KNC( cgc)

=> NKC=NBO=45

=> BKC=BKN+CKN=90=> CK vuông góc BE (đpcm)

4) Vì KH//OM 

Mà MK vuông góc OK

=> Mk vuôg góc KH 

=> NKH=90

Lại có: NKC=45=> CKH=45=>BKN=NKC=CKH=45

Xét tam giác BKC có: BKN=NKC => KN là phân giác 

Mà KH vuôg góc KN

=> KH là phân giác  ngoài tam giác BKC => KC/KB=HC/HB

CMTT: KN/KH=BN/BH

=> KC/KB+KN/KH+NC/BH=HC/HB+BN/BH+CN/BH=BH/BH=1(ĐPCM)

Phép liên kết trong đoạn văn:

Lặp từ ngữ: thầy, chúng tôi

\(\frac{2}{x-1}+\frac{4}{x+3}=\frac{3x+11}{x^2+2x-3}\)

\(\Leftrightarrow\frac{2}{x-1}+\frac{4}{x+3}=\frac{3x+11}{\left(x-1\right)\left(x+3\right)}\)

\(\Leftrightarrow\frac{2\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}+\frac{4\left(x-1\right)}{\left(x-1\right)\left(x+3\right)}=\frac{3x+11}{\left(x-1\right)\left(x+3\right)}\)

\(\Rightarrow2x+6+4x-4=3x+11\)

\(\Leftrightarrow2x+4x-3x=11-6+4\)

\(\Leftrightarrow3x=9\)

\(\Leftrightarrow x=3\)

Vậy....:)

a bn nhá

tui nhầm

\(25-3\sqrt{x}=6\sqrt{x}+7\left(ĐK:x\ge0\right)\).

\(\Leftrightarrow-3\sqrt{x}-6\sqrt{x}=7-25\).

\(\Leftrightarrow-9\sqrt{x}=-18\).

\(\Leftrightarrow\sqrt{x}=2\).

\(\Leftrightarrow x=2^2=4\)(thỏa mãn điều kiện).

Vậy phương trình có tập nghiệm: \(S=\left\{4\right\}\).

\(25-3\sqrt{x}=6\sqrt{x}+7\)(\(x\ge0\))

<=>\(-3\sqrt{x}-6\sqrt{x}=-18\)

<=>\(-9\sqrt{x}=-18\)

<=>\(\sqrt{x}=2\)

<=> \(x=\pm4\)

Gọi quãng đường là x ( x > 0 , km )

Thời gian lúc đi là : \(\frac{x}{50}\)giờ 

Thời gian lúc về là \(\frac{x}{40}\)giờ

Vì tổng thời gian cả đi cả ề là \(12-7-\frac{1}{2}=\frac{9}{2}\)giờ

nên ta có pt : 

\(\frac{x}{40}+\frac{x}{50}=\frac{9}{2}\Leftrightarrow x=100\)km 

Vậy quãng đường AB dài 100 km 

đây là toán lớp 5 mà

III. Choose the best answer A, B, C or D to complete the sentences:

1. What can be done to protect people from __________ disasters?

A. environment                 B. environmental          C. environmentally       D. environmentalist

2. All our English teachers are __________ speakers.

A. native                            B. original                    C. foreign                      D. foreigns

3. The heavy rain has caused __________ in many parts of the country.

A. storms                           B. floods                       C. drought                     D. flood

4. Science is used in all corners of the world for the __________ of people.

A. interest                          B. need                          C. profits                       D. benefit

5. The new invention could have a wide range of __________ in industry.

A. applications                   B. concerns                   C. goodness                   D. advance

6. Too much carbon dioxide in the air can be __________ for humans to breathe.

A. poisonous                      B. unfriendly                 C. healthy                      D. poison

7. Teenagers often use abbreviations when ___________.

A. texting                          B. video conferencing      C. sending letters          D. talking

8. The ___________ in technology allow astronomers to know more about outer space.

A. developments               B. science                         C. exploration                D. discovery

9. To generate cheap and clean energy, instead of burning fossil fuels, scientists have developed____.

A. oil                                  B. solar panels                  C. electricity                  D. coal burning

10. Mary wondered if Neptune __________ larger than Saturn.

A. was                                B. being                            C. is                                D. be

III. Choose the best answer A, B, C or D to complete the sentences:

1. What can be done to protect people from __________ disasters?

A. environment                 B. environmental          C. environmentally       D. environmentalist

2. All our English teachers are __________ speakers.

A. native                            B. original                    C. foreign                      D. foreigns

3. The heavy rain has caused __________ in many parts of the country.

A. storms                           B. floods                       C. drought                     D. flood

4. Science is used in all corners of the world for the __________ of people.

A. interest                          B. need                          C. profits                       D. benefit

5. The new invention could have a wide range of __________ in industry.

A. applications                   B. concerns                   C. goodness                   D. advance

6. Too much carbon dioxide in the air can be __________ for humans to breathe.

A. poisonous                      B. unfriendly                 C. healthy                      D. poison

7. Teenagers often use abbreviations when ___________.

A. texting                          B. video conferencing      C. sending letters          D. talking

8. The ___________ in technology allow astronomers to know more about outer space.

A. developments               B. science                         C. exploration                D. discovery

9. To generate cheap and clean energy, instead of burning fossil fuels, scientists have developed____.

A. oil                                  B. solar panels                  C. electricity                  D. coal burning

10. Mary wondered if Neptune __________ larger than Saturn.

A. was                                B. being                            C. is                                D. be

\(x^2+4y^2-4\left(x-y\right)+2=x^2-4x+4+4y^2+4y+1-3\)

\(=\left(x-2\right)^2+\left(2y+1\right)^2-3\ge-3\)

Dấu ''='' xảy ra khi \(x=2;y=-\frac{1}{2}\)

Vậy GTNN biểu thức trên là -3 khi \(x=2;y=-\frac{1}{2}\)

Ta có

 \(x^2+4y^2-4\left(x-y\right)+2=\left(x^2-4x+4\right)+\left(4y^2+4y+1\right)-3=\left(x-2\right)^2+\left(2y+1\right)^2-3\)

Vì \(\hept{\begin{cases}\left(x-2\right)^2\ge0\\\left(2y+1^2\right)\ge0\end{cases}}\)

\(\Rightarrow\left(x-2\right)^2+\left(2y+1\right)^2-3\ge-3\)

Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x=2\\y=-\frac{1}{2}\end{cases}}\)

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