Bài 4: 

\(x=130^0\)

`@` `\text {Ans}`

`\downarrow`

`4,`

Vì `\text {MN // BC}`

`=>` $\widehat {B} = \widehat {BMN} = 114^0 (\text {2 góc đối đỉnh})$

Ta có: \(\left\{{}\begin{matrix}\widehat{\text{BMN}}+\widehat{\text{AMN}}=180^0\left(\text{2 góc kề bù}\right)\\\widehat{\text{CNM}}+\widehat{\text{ANM}}=180^0\left(\text{2 góc kề bù}\right)\end{matrix}\right.\)

`=>`\(\left\{{}\begin{matrix}\widehat{\text{AMN}}=180^0-114^0=66^0\\\widehat{\text{ANM}}=180^0-130^0=50^0\end{matrix}\right.\)

Xét `\Delta AMN`:

\(\widehat{\text{A}}+\widehat{\text{M}}+\widehat{\text{N}}=180^0\left(\text{định lý tổng 3 góc trong 1 tgiac}\right)\)

`=>`\(\widehat{\text{A}}+66^0+50^0=180^0\)

`=>`\(\widehat{\text{A}}=180^0-66^0-50^0=64^0\)

Mà \(\widehat{\text{A}}=\widehat{\text{x}}\)

`=>`\(\widehat{\text{x}}=64^0\)

Vậy, số đo của góc `x = 64^0.`

1 are

2 am

3 is

4 are

5 are

6 are

7 is

8 is

9 is

10 are

IV

1 is writing

2 are losing

3 is having

4 is staying

5 am not lying

6 is always using

7 are having

8 Are you playing

9 are not touching

10 Is - listening

11 Is- winning

12 am not staying

13 is not working

14 is not reading

15 isn't raining

16 am not listening

17 Are they making

18 Are you doing

19 Is - sitting

20 is - doing

21 are-putting

22 are-wearing

23 is-studying

2, am

3, is

4,are

5,are

6,are

7,is

8,is

9,is

10,are

IV

1,2,7 OK

3,is having

4,has stayed

5,am not lying

6,always uses

8,Are-playing

9,not to touch

10,Is-listening

11,Are-winning

12,am not staying

13,isn't working

14,isn't reading

15,isn't raining

16,am not listening

17,Are-making

18,Are-doing

19,Is-sitting

20,is-doing

21,do-putting

22,do-wear

23,is-studying

1/ Xét \(\Delta ABC\) và \(\Delta HAC\) có:

∠A = ∠AHC = 90 độ

∠C là góc chung

Do đó: △ABC ∼ △HAC (g . g)

2/ Ta có: \(\Delta HAC\sim\Delta ABC\)

\(\Rightarrow\dfrac{AC}{HC}=\dfrac{BC}{AC}\)

\(\Rightarrow AC.AC=HC.BC\)

\(\Rightarrow AC^2=HC.BC\) (đpcm)

3/ Đặt BD là x, theo tính chất đường phân giác, ta có:

\(\dfrac{AB}{AC}=\dfrac{BD}{DC}\Rightarrow\dfrac{9}{12}=\dfrac{x}{15-x}\)

\(\Rightarrow9\left(15-x\right)=12x\)

\(\Rightarrow135-9x=12x\)

\(\Rightarrow135=12x+9x\)

\(\Rightarrow135=21x\)

\(\Rightarrow x\approx6,4\)

Độ dài của DC là: \(15-x\Rightarrow15-6,4=8,6\)

Vậy BD = 6,4 cm và DC = 8,6 cm

gõ câu hỏi ra đi bạn 

1. a) 6² : 4 . 3 + 2 . 5²

= 36 : 4 . 3 + 2 . 25

= 9 . 3 + 50

= 27 + 50

= 77

b) 5 . 4² - 32 : 4²

= 5 . 16 - 32 : 16

= 80 - 2

= 78

c) 80 - (4 . 5² - 3 .2³)

= 80 - (4 . 25 - 3 . 8)

= 80 - (100 - 24)

= 80 - 76

= 4

d) 2448 : [119 - (23 - 6)]

= 2448 : (119 - 17)

= 2448 : 102

= 24

e) 23 . 85 + 15 . 23 + 170

= 23 . (85 + 15) + 170

= 23 . 100 + 170

= 2300 + 170

= 2470

f) 3³ . 2  - 5 . 2023⁰ + 36 : 3²

= 27 . 2 - 5 . 1 + 36 : 9

= 54 - 5 + 4

= 53

2. a) 123 - 5.(x + 4) = 38

5.(x + 4) = 123 - 38

5.(x + 4) = 85

x + 4 = 85 : 5

x + 4 = 17

x = 17 - 4

x = 13

b) (3.x - 2⁴) . 7³ = 2 . 7⁴

3x - 16 = 2 . 7⁴ : 7³

3x - 16 = 2 . 7

3x = 14 + 16

3x = 30

x = 30 : 3

x = 10

c) (2600 + 6400) - 3.x = 1200

9000 - 3x = 1200

3x = 9000 - 1200

3x = 7800

x = 7800 : 3

x = 2600

d) [(6.x - 72) : 2 - 84] . 28 = 5628

(6x - 72) : 2 - 84 = 5628 : 28

(6x - 72) : 2 - 84 = 201

(6x - 72) : 2 = 201 + 84

(6x - 72) : 2 = 285

6x - 72 = 285 . 2

6x - 72 = 570

6x = 570 + 72

6x = 642

x = 642 : 6

x = 107

e) 70 - 5(x - 3) = 45

5(x - 3) = 70 - 45

5(x - 3) = 25

x - 3 = 25 : 5

x - 3 = 5

x = 5 + 3

x = 8

f) 10 + 2.x = 4⁷ : 4⁵

10 + 2x = 4²

10 + 2x = 16

2x = 16 - 10

2x = 6

x = 6 : 2

x = 3

g) 2.x - 138 = 2³.2²

2x - 138 = 2⁵

2x - 138 = 32

2x = 32 + 138

2x = 170

x = 170 : 2

x = 85

h) 231 - (x - 6) = 1339 : 13

231 - (x - 6) = 103

x - 6 = 231 - 103

x - 6 = 128

x = 128 + 6

x = 134

1.Tính:

a) \(6^2:4.3+2.5^2\)

\(=36:4.3+2.25\)

\(=9.3+50\)

\(=27+50\)

\(=77\)

b) \(5.4^2-32:4^2\)

\(=5.16-32:16\)

\(=80-2\)

\(=78\)

c) \(80-\left(4.5^2-3.2^3\right)\)

\(=80-\left(4.25-3.8\right)\)

\(=80-\left(100-24\right)\)

\(=80-76\)

\(=4\)

d) \(2448:\left[119-\left(23-6\right)\right]\)

\(=2448:\left[119-17\right]\)

\(=2448:102\)

\(=24\)

e) \(23.85+15.23+170\)

\(=23\left(85+15\right)+170\)

\(=23.100+170\)

\(=2300+170\)

\(=2470\)

f) \(3^3.2-5.2023^0+36:3^2\)

\(=27.2-5.1+36:9\)

\(=54-5+4\)

\(=53\)

2. Tìm x biết:

a) \(123-5.\left(x+4\right)=38\)

\(=>5.\left(x+4\right)=123-38\)

\(=>5.\left(x+4\right)=85\)

\(=>x+4=85:5\)

\(=>x+4=17\)

\(=>x=17-4\)

\(=>x=13\)

b) \(\left(3.x-2^4\right).7^3=2.7^4\)

\(=>3.x-2^4=2.7^4:7^3\)

\(=>3.x-2^4=2.7\)

\(=>3.x-16=14\)

\(=>3.x=14+16\)

\(=>3.x=30\)

\(=>x=30:3\)

\(=>x=10\)

c) \(\left(2600+6400\right)-3.x=1200\)

\(=>9000-3.x=1200\)

\(=>3.x=9000-1200\)

\(=>3.x=7800\)

\(=>x=7800:3\)

\(=>x=2600\)

d) \(\left[\left(6.x-72\right):2-84\right].28=5628\)

\(=>\left(6.x-72\right):2-84=5628:28\)

\(=>\left(6.x-72\right):2-84=201\)

\(=>\left(6.x-72\right):2=201+84\)

\(=>\left(6.x-72\right):2=285\)

\(=>6.x-72=285\times2\)

\(=>6.x-72=570\)

\(=>6.x=570+72\)

\(=>6.x=642\)

\(=>x=642:6\)

\(=>x=107\)

e) \(70-5.\left(x-3\right)=45\)

\(=>5.\left(x-3\right)=70-45\)

\(=>5.\left(x-3\right)=25\)

\(=>x-3=25:5\)

\(=>x-3=5\)

\(=>x=5+3\)

\(=>x=8\)

f) \(10+2.x=4^7:4^5\)

\(=>10+2.x=4^2\)

\(=>10+2.x=16\)

\(=>2.x=16-10\)

\(=>2.x=6\)

\(=>x=6:2\)

\(=>x=3\)

g) \(2.x-138=2^3.3^2\)

\(=>2.x-138=8.9\)

\(=>2.x-138=72\)

\(=>2.x=72+138\)

\(=>2.x=210\)

\(=>x=210:2\)

\(=>x=105\)

h) \(231-\left(x-6\right)=1339:13\)

\(=>231-\left(x-6\right)=103\)

\(=>x-6=231-103\)

\(=>x-6=128\)

\(=>x=128+6\)

\(=>x=134\)

Chúc bạn học tốt

Câu 3: 

a: Ta có: \(2x\left(3x-1\right)-\left(x-3\right)\left(6x+2\right)\)

\(=6x^2-2x-6x^2-2x+18x+6\)

=14x+6

b: Ta có: \(2x\left(x+7\right)-3x\left(x+1\right)\)

\(=2x^2+14x-3x^2-3x\)

\(=-x^2+11x\)

Câu 2: 

a: Ta có: \(\left(-8x^5+12x^3-16x^2\right):4x^2\)

\(=-8x^5:4x^2+12x^3:4x^2-16x^2:4x^2\)

\(=-2x^3+3x-4\)

b: Ta có: \(\left(12x^3y^3-18x^2y+9xy^2\right):6xy\)

\(=12x^3y^3:6xy-18x^2y:6xy+9xy^2:6xy\)

\(=2x^2y^2-3x+\dfrac{3}{2}y\)

c: Ta có: \(\dfrac{x^3-11x^2+27x-9}{x-3}\)

\(=\dfrac{x^3-3x^2-8x^2+24x+3x-9}{x-3}\)

\(=x^2-8x+3\)

d: Ta có: \(\dfrac{6x^4-13x^3+7x^2-x-5}{3x+1}\)

\(=\dfrac{6x^4+2x^3-15x^3-5x^2+12x^2+4x-5x-\dfrac{5}{3}-\dfrac{10}{3}}{3x+1}\)

\(=2x^3-5x^2+4x-\dfrac{5}{3}-\dfrac{\dfrac{10}{3}}{3x+1}\)

\(D=10\cdot\left(-2.5\right)\cdot0.4\cdot\left(-0.1\right)\)

\(=10\cdot1\cdot2.5\cdot0.4\)

=10

???