1.

\(\Delta'=\left(m+1\right)^2-\left(m^2+3m-7\right)=-m+8\)

Phương trình đã cho vô nghiệm khi và chỉ khi \(\Delta'< 0\)

\(\Rightarrow-m+8< 0\)

\(\Rightarrow m>8\)

Bài 4: 

a: \(A=\left(x-5\right)\left(2x+3\right)-2x\left(x-3\right)+x+7\)

\(=2x^2+3x-10x-15-2x^2+6x+x+7\)

=-8

Vì BC và Cx là 2 tia đối nên \(\widehat{BCA}\) và \(\widehat{ACx}\) là 2 góc kề bù

\(\Rightarrow\widehat{ACB}+\widehat{ACx}=180^o\)

     \(40^o+\widehat{ACx}=180^o\)

     \(\widehat{ACx}=140^o\)

b) Ta có:\(\widehat{ACB}+\widehat{ABC}+\widehat{BAC}=180^o\) (tổng 3 góc trong 1 tam giác)

             ​​​\(40^o+\widehat{ABC}+70^o=180^o\)​

            \(\widehat{ABC}=70^o\)(1)

Vì Oy là phân giác của \(\widehat{ACx}\) nên \(\widehat{xCy}=\dfrac{\widehat{ACx}}{2}=\dfrac{140^o}{2}=70^o\)(2)

Từ (1),(2) => \(\widehat{ABC}=\widehat{xCy}\)

c)Cặp góc đồng vị là \(\widehat{ABC}\) và \(\widehat{xCy}\)

\(5-\left|x-\dfrac{1}{2}\right|=3\)

\(\left|x-\dfrac{1}{2}\right|=5-3\)

\(\left|x-\dfrac{1}{2}\right|=2\)

=>\(x-\dfrac{1}{2}=2\)                      hoặc                      \(x-\dfrac{1}{2}=-2\)

  \(x=2+\dfrac{1}{2}\)                                                       \(x=-2+\dfrac{1}{2}\)

  \(x=\dfrac{5}{2}\)                                                            \(x=\dfrac{-3}{2}\)

Vậy...\(\left(x+\dfrac{1}{3}\right)^2+3=2\)

          \(\left(x+\dfrac{1}{3}\right)^2=2-3\)

          \(\left(x+\dfrac{1}{3}\right)^2=-1\)

Vi \(\left(x+\dfrac{1}{3}\right)^2\) luôn luôn lớn hơn 0 nên

\(\left(x+\dfrac{1}{3}\right)^2=-1\)(vô lý)

Bài 5: 

a: \(x\left(x-1\right)-x^2+4x=-3\)

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

hay x=-1

i: \(x^2-9x+8=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=8\end{matrix}\right.\)

refer

1/ I like table tennis and that’s why I spend a lot of time on that game.
=>I spend a lot of time on table tennis because I like it.
2/ Because the weather was cold, we had to cancel our picnic.
=> The weather was cold, so we had to cancel our picnic.
3/ I won’t forget to phone her. You know, I like her so much.
=> You know I like her so much so I won't forget to phone her
4/ They tried their best to complete the course and that was why they passed.
=> they tried their best to complete the course, so they passed
5/ I love my city so much, so I think I will stay and work here in my city.
=> I think I will stay and word in my city because I love it so much.

1 Because I like table tennis, I spend a lot of time on that game

2 The weather was so cold that we had to cancel our picnic

3 I won't forget to phone her because I like her so mich

4 They pass the course because they tried their best to complete the course

5 Because I love my city so much, I think I will stay and work here in my city

1 Because I like table tennis, I spend a lot of time on that game

2 The weather was so cold that we had to cancel our picnic

3 I won't forget to phone her because I like her so mich

4 They pass the course because they tried their best to complete the course

5 Because I love my city so much, I think I will stay and work here in my city

3.B (thì HTHT với dấu hiệu yet)

4. B

5. B (wish S Ved: ước trong iện tại)

6. D (thì QKĐ với dấu iệu Last night)

a: Xét tứ giác AMHN có 

\(\widehat{MAN}=\widehat{ANH}=\widehat{AMH}=90^0\)

Do đó: AMHN là hình chữ nhật

a) Xét tứ giác AMHN có:

\(\widehat{AMH}=\widehat{MAN}=\widehat{ANH}=90^0\)

=> AMHN là hình chữ nhật

b) Ta có: MH=AN(AMHN là hình chữ nhật)

               AN=DN(D đối xứng với A qua N)

=> MH=DN 

MH//DN(AMHN là hình chữ nhật nên MH//AN,D∈AN)

=> MHDN là hình bình hành

a) - Dùng quỳ tím:

+ Hóa đỏ -> dd H2SO4

+ Hóa xanh -> dd NaOH

+ Không đổi màu -> dd NaCl

b) - Dùng quỳ tím:

+ Hóa xanh -> dd Ca(OH)2

+ Hóa đỏ -> dd H2SO4, dd HCl

- Dùng dd BaCl2:

+ Có kết tủa trắng BaSO4 -> dd H2SO4 

+ Không có kt trắng -> dd HCl

PTHH: H2SO4 + BaCl2 -> BaSO4 (kt trắng) + 2 HCl

c) - Dùng quỳ tím:

+ Hóa xanh : dd KOH 

+ Hóa đỏ : dd HNO3, dd HCl

- Dùng dd AgNO3:

+ Có kt trắng AgCl -> dd HCl

PTHH: HCl + AgNO3 -> AgCl (trắng) + HNO3

+ Còn lại ko ht -> dd AgNO3