Giải:

ΔABC ∼ΔA'B'C' ta có:

Góc A = góc A'; Góc B = góc B'; Góc C = Góc C'

Và các tỉ số:

\(\frac{AB}{A^{\prime}B^{\prime}}=\frac{AC}{A^{\prime}C^{\prime}}=\frac{BC}{B^{\prime}C^{\prime}}\)

Vậy khẳng định không đúng là khẳng định:

C. \(\frac{AB}{A^{\prime}B^{\prime}}\) = \(\frac{A^{\prime}C^{\prime}}{AC}\)

Chọn C nha bạn

Giải:

y = (m -2)\(x\) + 2

⇒ (m- 2)\(x\) - y + 2 = 0

Gốc tọa độ O(0; 0)

Khoảng cách từ gốc tọa độ O(0; 0) đến đường thẳng (d) là:

d(O;d) = \(\frac{\left|\left(m-2\right)\right..0-1.0+2\left|\right.}{\sqrt{\left(m-2\right)^2+1}}\) = \(\frac{2}{\sqrt{\left(m-2\right)^2+1}}\)

Khoảng cách từ gốc tọa độ O đến đường thẳng (d) là lớn nhất khi A = \(\frac{2}{\sqrt{\left(m-2\right)^2+1}}\) lớn nhất.

Vì 2 > 0; \(\sqrt{\left(m-2\right)^2+1}\) > 0 ∀ m nên

A lớn nhất khi (m - 2)\(^2\) + 1 là nhỏ nhất.

(m - 2)\(^2\) ≥ 0 ∀ m

(m - 2)\(^2\) + 1 ≥ 1 ∀ m

\(\sqrt{\left(m-2\right)^2+1}\) ≥ 1 ∀ m

A = \(\frac{2}{\sqrt{\left(m-2^{}\right)^2+1}}\) ≤ \(\frac21=2\) dấu bằng xảy khi m - 2 = 0

suy ra m = 2

Vậy khoảng cách từ gốc tọa độ đến đồ thị lớn nhất là \(2\) khi m = 2

b: a+b+c=0

=>\(\left\{{}\begin{matrix}a+b=-c\\a+c=-b\\b+c=-a\end{matrix}\right.\)

Sửa đề: \(A=\dfrac{a^2}{a^2-b^2-c^2}+\dfrac{b^2}{b^2-c^2-a^2}+\dfrac{c^2}{c^2-a^2-b^2}\)

\(=\dfrac{a^2}{a^2-\left(b^2+c^2\right)}+\dfrac{b^2}{b^2-\left(a^2+c^2\right)}+\dfrac{c^2}{c^2-\left(a^2+b^2\right)}\)

\(=\dfrac{a^2}{a^2-\left(b+c\right)^2+2bc}+\dfrac{b^2}{b^2-\left(a+c\right)^2+2ac}+\dfrac{c^2}{c^2-\left(a+b\right)^2+2ab}\)

\(=\dfrac{a^2}{2bc}+\dfrac{b^2}{2ac}+\dfrac{c^2}{2ab}=\dfrac{a^3+b^3+c^3}{2abc}\)

\(=\dfrac{\left(a+b\right)^3-3ab\left(a+b\right)+c^3}{2abc}\)

\(=\dfrac{\left(-c\right)^3+c^3-3ab\cdot\left(-c\right)}{2abc}=\dfrac{3abc}{2abc}=\dfrac{3}{2}\)

Y = 3x + 2 song song với đường thẳng khác khi a = a' và b ≠ b'

Vậy đường thẳng y = 3x + 2 song song vói đt y = 3x + 4

Chọn C. y = 3x + 4

B =\(\frac{1}{1.5}\) + \(\frac{1}{5.9}\) + ...+ \(\frac{1}{\left(4n-3\right).\left(4n+1\right)}\)

B = \(\frac14\).(\(\frac{4}{1.5}+\frac{4}{5.9}+\cdots+\frac{4}{\left(4n-3\right).\left(4n+1\right)}\)

B = \(\frac14\).(\(\frac11\) - \(\frac15\) + \(\frac15\) - \(\frac19\) + ... + \(\frac{1}{4n-3}-\frac{1}{4n+1}\))

B = \(\frac14\).(\(\frac11\) - \(\frac{1}{4n+1}\))

B = \(\frac14\).\(\frac{4n}{4n+1}\)

B = \(\frac{n}{4n+1}\)

Bài 1:

a; 20 - 4x = 0

4x = 20

x = 20 : 4

x = 5

Vậy x = 5

b; 3.(2x - 1) - 3x + 1 = 0

6x - 3 - 3x + 1 = 0

6x - 3x = 3 - 1

3x = 2

x = 2/3

Vậy x = 2/3

a; 7x - 8 = 4x + 7

7x - 4x = 8 + 7

3x = 15

x = 15: 3

x = 5

Vậy x = 5

Bài 1:

b; 2x + 5 = 20 - 3x

2x + 3x = 20 - 5

5x = 15

x = 15: 5

x = 3

Vậy x = 3

c; 5y + 12 = 8y + 27

8y - 5y = 12 - 27

3y = - 15

y = -15: 3

y = -5

Vậy y = - 5

d; 13 - 2y = y - 2

y + 2y = 13+ 2

3y = 15

y = 15 : 3

y = 5

Vậy y = 5

a: \(\dfrac{1}{2x-3}-\dfrac{1}{2x+3}=\dfrac{2x+3-2x+3}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{6}{4x^2-9}\)

b: \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)

\(=\dfrac{1}{x\left(y-x\right)}-\dfrac{1}{y\left(y-x\right)}=\dfrac{y-x}{xy\left(y-x\right)}=\dfrac{1}{xy}\)

c: \(\dfrac{x+1}{x+4}-\dfrac{x^2-4}{x^2-16}\)

\(=\dfrac{x+1}{x+4}-\dfrac{x^2-4}{\left(x-4\right)\left(x+4\right)}\)

\(=\dfrac{\left(x+1\right)\left(x-4\right)-x^2+4}{\left(x+4\right)\left(x-4\right)}=\dfrac{x^2-3x-4-x^2+4}{\left(x+4\right)\left(x-4\right)}=\dfrac{-3x}{x^2-16}\)

d: \(\dfrac{x+1}{2x+6}+\dfrac{2x+3}{x\left(x+3\right)}\)

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

\(=\dfrac{x\left(x+1\right)+2\left(2x+3\right)}{2x\left(x+3\right)}=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}\)

\(=\dfrac{x^2+5x+6}{2x\left(x+3\right)}=\dfrac{\left(x+3\right)\left(x+2\right)}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)

e: \(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)

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

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

\(=\dfrac{-6x^2+3x+2x-1+6x^2-4x-3x+2}{2x\left(2x-1\right)}\)

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

a: \(\dfrac{2}{x+3}+\dfrac{1}{x}=\dfrac{2x+x+3}{x\left(x+3\right)}=\dfrac{3x+3}{x\left(x+3\right)}\)

b: \(\dfrac{x+1}{2x-2}+\dfrac{-2x}{x^2-1}\)

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

\(=\dfrac{\left(x+1\right)^2-2\cdot2x}{2\left(x-1\right)\left(x+1\right)}=\dfrac{\left(x-1\right)^2}{2\left(x-1\right)\left(x+1\right)}=\dfrac{x-1}{2\left(x+1\right)}\)

c: Sửa đề: \(\dfrac{x-12}{6x-36}+\dfrac{4}{x^2-6x}\)

\(=\dfrac{x-12}{6\left(x-6\right)}+\dfrac{4}{x\left(x-6\right)}\)

\(=\dfrac{x\left(x-12\right)+24}{6x\left(x-6\right)}=\dfrac{x^2-12x+24}{6x\left(x-6\right)}\)

d: \(\dfrac{6-x}{x^2+3x}+\dfrac{3}{2x+6}\)

\(=\dfrac{-x+6}{x\left(x+3\right)}+\dfrac{3}{2\left(x+3\right)}\)

\(=\dfrac{2\left(-x+6\right)+3x}{2x\left(x+3\right)}=\dfrac{x+12}{2x\left(x+3\right)}\)

e: \(\dfrac{3}{2y+4}-\dfrac{1}{3y+6}\)

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

\(=\dfrac{9-2}{6\left(y+2\right)}=\dfrac{7}{6\cdot\left(y+2\right)}\)

kho nha bro

\(-\dfrac{15x^2y^3}{18x^3y^5}=-\dfrac{15}{18}\cdot\dfrac{x^2}{x^3}\cdot\dfrac{y^3}{y^5}=\dfrac{-5}{6\cdot x\cdot y^2}\)

a: Ta có: \(AM=MB=\dfrac{AB}{2}\)

\(BN=NC=\dfrac{BC}{2}\)

mà AB=BC(ABCD là hình vuông)

nên AM=MB=BN=NC

Xét ΔMBC vuông tại B và ΔNCD vuông tại C có

MB=NC

BC=CD

Do đó: ΔMBC=ΔNCD

=>\(\widehat{BMC}=\widehat{CND}\)

=>\(\widehat{CND}+\widehat{NCO}=90^0\)

=>CM\(\perp\)DN tại O

b: \(BM=\dfrac{AB}{2}=\dfrac{4}{2}=2\left(cm\right)\)

ΔMBC vuông tại B

=>\(S_{MBC}=\dfrac{1}{2}\cdot MB\cdot BC=\dfrac{1}{2}\cdot2\cdot4=4\left(cm^2\right)\)

ΔCBM vuông tại B

=>\(CM^2=CB^2+BM^2=4^2+2^2=20\)

=>\(CM=\sqrt{20}=2\sqrt{5}\left(cm\right)\)

Xét ΔCON vuông tại O và ΔCBM vuông tại B có

\(\widehat{MCB}\) chung

Do đó: ΔCON~ΔCBM

=>\(\dfrac{S_{CON}}{S_{CBM}}=\left(\dfrac{CN}{CM}\right)^2=\left(\dfrac{2}{2\sqrt{5}}\right)^2=\dfrac{1}{5}\)

=>\(S_{CON}=\dfrac{S_{MBC}}{5}=\dfrac{4}{5}\left(cm^2\right)\)