Bài 2 

a: Xét ΔAHB vuông tại H có HM là đường cao

nên \(AM\cdot AB=AH^2\left(1\right)\)

Xét ΔAHC vuông tại H có HN là đường cao

nên \(AN\cdot AC=AH^2\left(2\right)\)

Từ (1) và (2) suy ra \(AM\cdot AB=AN\cdot AC\)

xét tứ giác ANMP có 

góc NAP = 90 độ ( AB vuông góc AC)

góc MPA = 90 độ (MP vuông góc AC)

Góc ANM = 90 độ (MN vuông góc AB)

=> tứ giác AMNP là hình chữ nhật

a. Có 3 góc vuông nên là hcn nha

How often does your father watch the News?

Who is your favorite actor?

When do you usually watch TV?

What is Tim doing?

How much does the new television cost?

Why are you studying?

Where do you buy this dress?

1.How often does your father watch the News?

2.Who is your favorite actor?

3.When do you usually watch TV?

4.What is Tim doing?

5.How much does the new television cost?

6.Why are you studying?

7.Where do you buy this dress?

tách nhỏ câu hỏi ra

bạn có thể cho mình cái đề được không máy của mình nó hay bị mờ ảnh á

1a.

$x^2-5x+6=x^2-2x-(3x-6)=x(x-2)-3(x-2)=(x-2)(x-3)$

1b.

$3x^2+9x-30=3(x^2+3x-10)=3(x^2-2x+5x-10)$

$=3[x(x-2)+5(x-2)]=3(x-2)(x+5)$

1c.
$x^2-3x+2=(x^2-x)-(2x-2)=x(x-1)-2(x-1)=(x-1)(x-2)$

1d.

$x^2-9x+18=x^2-3x-(6x-18)=x(x-3)-6(x-3)=(x-3)(x-6)$

1e.

$x^2-6x+8=x^2-2x-(4x-8)=x(x-2)-4(x-2)=(x-2)(x-4)$

1f.
$x^2-5x-14=x^2-7x+2x-14=x(x-7)+2(x-7)=(x+2)(x-7)$

1g.

$x^2+6x+5=(x^2+x)+(5x+5)=x(x+1)+5(x+1)=(x+1)(x+5)$

1h.

$x^2-7x+12=x^2-3x-(4x-12)=x(x-3)-4(x-3)=(x-3)(x-4)$

1i.

$x^2-7x+10=(x^2-2x)-(5x-10)=x(x-2)-5(x-2)=(x-2)(x-5)$

2a.

$3x^2-5x-2=(3x^2-6x)+(x-2)=3x(x-2)+(x-2)$

$=(x-2)(3x+1)$

2b. 

$2x^2+x-6=(2x^2+4x)-(3x+6)=2x(x+2)-3(x+2)$

$=(2x-3)(x+2)$

2c.

$7x^2+50x+7=(7x^2+49x)+(x+7)$

$=7x(x+7)+(x+7)=(7x+1)(x+7)$

2d. 

$12x^2+7x-12=(12x^2-9x)+(16x-12)$

$=3x(4x-3)+4(4x-3)=(4x-3)(3x+4)$

2e.

$15x^2+7x-2=15x^2-3x+10x-2$

$=3x(5x-1)+2(5x-1)=(5x-1)(3x+2)$

\(1,\left\{{}\begin{matrix}3x-y=5\\5x+2y=23\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=3x-5\\5x+2\left(3x-5\right)=23\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=3x-5\\5x+6x-10=23\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=3x-5\\11x=33\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=3.3-5\\x=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=4\\x=3\end{matrix}\right.\)

\(2,\left\{{}\begin{matrix}5x-4y=3\\2x+y=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5x-4\left(4-2x\right)=3\\y=4-2x\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5x-16+8x=3\\y=4-2x\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}13x=19\\y=4-2x\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{19}{13}\\y=4-2.\dfrac{19}{13}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{19}{13}\\y=\dfrac{14}{13}\end{matrix}\right.\)