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.`

Câu 3: 

a: \(BD=\sqrt{BC^2-DC^2}=4\left(cm\right)\)

b: \(\widehat{A}=180^0-2\cdot70^0=40^0< \widehat{B}\)

nên BC<AC=AB

c: Xét ΔEBC vuông tại E và ΔDCB vuông tại D có

BC chung

\(\widehat{EBC}=\widehat{DCB}\)

Do đó:ΔEBC=ΔDCB

d: Xét ΔOBC có \(\widehat{OBC}=\widehat{OCB}\)

nên ΔOBC cân tại O

Câu 2

a) Thay y = -2 vào biểu thức đã cho ta được:

2.(-2) + 3 = -1

Vậy giá trị của biểu thức đã cho tại y = -2 là -1

b) Thay x = -5 vào biểu thức đã cho ta được:

2.[(-5)² - 5] = 2.(25 - 5) = 2.20 = 40

Vậy giá trị của biểu thức đã cho tại x = -5 là 40

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) 

\(4Fe+3O_{2\left(dư\right)}\xrightarrow[]{t^o}2Fe_2O_3\)

\(Fe_2O_3+6HCl\rightarrow2FeCl_3+3H_2O\)

\(FeCl_3+3KOH\rightarrow Fe\left(OH\right)_3\downarrow+3KCl\)

\(2Fe\left(OH\right)_3\xrightarrow[]{t^o}Fe_2O_3+3H_2O\)

\(Fe_2O_3+CO\xrightarrow[]{500-600^oC}2FeO+CO_2\)

My grandma often works in the garden in her free time.

What are you doing with the stove?

3. My grandma often works in the garden in her free time.

4. What are you doing with the stove?

3. My grandma often works in the garden in her free time.

4. What are you doing with the stove?

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

Bài 4

uses crt;
var a,b: integer;
c,s,d:real;
begin
clrscr;
readln(a,b);
if (a>0) and (b>0) then
begin
c:=sqrt(a*a+b*b);
d:=(a+b+c)/2;
s:=sqrt(d*(d-a)*(d-b)*(d-c));
writeln(c:4:2,'  ',s:4:2);
end
else writeln('nhap lai');
readln
end.

Bài 5

uses crt;
var r: integer;
s,t: real;
begin
clrscr;
readln(r);
s:=r*r*3.14;
t:=2*3.14*r;
writeln(s:4:2,'  ',t:4:2);
readln
end.

bài 6

uses crt;
var a,b,x: INTEGER;
s,v,t: real;
begin
clrscr;
readln(a,b,x);
s:=a*b;
v:=(x*(b-x))/2;
t:=s/2;
writeln(s:4:1);
writeln(v:4:1);
write(t:4:1);
readln
end.

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

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

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

\(A=\left(4x-1\right)\left(3x+1\right)-5x\left(x-3\right)-\left(x-4\right)\left(x-3\right)\)

\(=\left(4x-1\right)\left(3x+1\right)-\left(5x+x-4\right)\left(x-3\right)\)

\(=12x^2+4x-3x-1-6x^2+4x+18x-12\)

\(=18x^2+19x-13\)