1: \(5^{x+4}-3\cdot5^{x+3}=2\cdot5^{11}\)

=>\(5^{x+3}\cdot5-3\cdot5^{x+3}=2\cdot5^{11}\)

=>\(2\cdot5^{x+3}=2\cdot5^{11}\)

=>x+3=11

=>x=8

2: \(\dfrac{1}{2}\cdot2^x+4\cdot2^x=9\cdot2^5\)

=>\(2^x\cdot\left(\dfrac{1}{2}+4\right)=9\cdot2^5\)

=>\(2^x\cdot\dfrac{9}{2}=9\cdot2^5\)

=>\(2^x=2^6\)

=>x=6

3: \(9^{2x+1}=27^3\)

=>\(3^{4x+2}=3^9\)

=>4x+2=9

=>4x=7

=>\(x=\dfrac{7}{4}\)

4: \(2^{-1}\cdot2^x+4\cdot2^x=9\cdot2^5\)

=>\(2^x\left(4+\dfrac{1}{2}\right)=9\cdot2^5\)

=>\(2^x\cdot\dfrac{9}{2}=9\cdot2^5\)

=>\(2^x=9\cdot2^5:\dfrac{9}{2}=2^6\)

=>x=6

5: \(\left(2x-1\right)^3=\dfrac{8}{27}\)

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

=>\(2x-1=\dfrac{2}{3}\)

=>\(2x=\dfrac{2}{3}+1=\dfrac{5}{3}\)

=>\(x=\dfrac{5}{3}:2=\dfrac{5}{6}\)

Bài 6: Oz là phân giác của góc xOy

=>\(\widehat{xOz}=\dfrac{\widehat{xOy}}{2}=\dfrac{142^0}{2}=71^0\)

Ta có: \(\widehat{xOz}+\widehat{x'Oz}=180^0\)(hai góc kề bù)

=>\(\widehat{x'Oz}+71^0=180^0\)

=>\(\widehat{x'Oz}=109^0\)

Bài 7:

Ta có: Oz là phân giác của góc xOy

=>\(\widehat{xOz}=\widehat{yOz}=\dfrac{\widehat{xOy}}{2}=\dfrac{180^0}{2}=90^0\)

Ot là phân giác của góc xOz

=>\(\widehat{zOt}=\dfrac{\widehat{xOz}}{2}=\dfrac{90^0}{2}=45^0\)

Ov là phân giác của góc yOz

=>\(\widehat{vOz}=\dfrac{90^0}{2}=45^0\)

\(\widehat{vOt}=\widehat{zOv}+\widehat{zOt}=45^0+45^0=90^0\)

sửa đề chia hết 31 nhé 

\(S=5+5^2+5^3+...+5^{2019}=5\left(1+5+5^2+5^3\right)+...+5^{2016}\left(1+5+5^2+5^3\right)\)

\(=31\left(5+...+5^{2016}\right)⋮31\)

Vậy ta có đpcm 

Bài 2:

a) \(\dfrac{-7}{-13}=\dfrac{7}{13}\) là số hưu tỉ dương

b) \(\dfrac{2}{-17}=-\dfrac{2}{17}\) là số hưu tỉ âm

c) \(-\dfrac{-6}{5}=\dfrac{6}{5}\) là số hưu tỉ dương

Bài 3:

a) \(-2\dfrac{1}{4}=-\left(2+\dfrac{1}{4}\right)=-\dfrac{9}{4}\)

b) \(6\dfrac{2}{3}=6+\dfrac{2}{3}=\dfrac{20}{3}\)

c) \(-3\dfrac{1}{4}=-\left(3+\dfrac{1}{4}\right)=-\dfrac{13}{4}\)

She doesn't study on Saturday.

doesn't study

-> Có "saturday" -> lịch trình có sẵn -> Thì HTĐ

(+) S + V(s/es) + O

(-) S + don't / doesn't + V (inf) + O

- Ở đây She là chủ ngữ số it nên đi với doesn't + V

 I like Math and she (like)…likes….Literature.

cho mình hỏi là vì sao là likes

have already read nhé

Staying healthy is now a very important topic around the world, especially in modern life. So how can we do that? Firstly, going to bed early will help you to recover enough energy for the next effective day. Advoid staying up late if you don't want harm your eyes and mental health. Secondly, doing morning exercise or going to the gym everyday will help you improve your physical health. It will make you feel stronger, better and more energetic when doing hard work. Finally, you must have a balanced diet, eat combination of meat and fresh vegetable everyday. Also you can eat variety of fruit especially apple because "An apple a day keeps the doctor away". 

Health is an important part our life so keeping it at a healthy rate is everyone's duty for their own goodness. Build a suitable routine, do excercises and try out new experiences whenever opportunities come. Along with physical upgrades, we also need to improve our minds, read more books, journal, and last but not least, remember to love yourself, improve mental health daily with music and self-care. Health is life, and self-love brings what happiness really is. 

        Bài 6:

\(\dfrac{9^5.9^7}{3^{22}}\) = \(\dfrac{3^{15}.3^{21}}{3^{22}}\) = \(\dfrac{3^{36}}{3^{22}}\)  = 3¹⁴

  Bài 7:

\(\dfrac{9^{16}.8^{11}}{6^{33}}\) =  \(\dfrac{3^{32}.2^{33}}{3^{33}.2^{33}}\) = \(\dfrac{1}{3}\)