a: \(\dfrac{1}{2}< \dfrac{12}{a}< \dfrac{4}{3}\)

=>\(\dfrac{12}{24}< \dfrac{12}{a}< \dfrac{12}{9}\)

=>9<a<24

mà a nguyên

nên \(a\in\left\{10;11;...;23\right\}\)

b: \(\dfrac{7}{4}< \dfrac{a}{8}< 3\)

=>\(\dfrac{14}{8}< \dfrac{a}{8}< \dfrac{24}{8}\)

=>14<a<24

mà a nguyên

nên \(a\in\left\{15;16;...;23\right\}\)

\(\dfrac{7}{2x+2}=\dfrac{3}{2y-4}=\dfrac{5}{z+4}\) và \(x+y+z=17\) (1)

ĐK: \(x\ne-1;y\ne2;z\ne-4\)

Áp dụng tính chất của dãy tỉ số bằng nhau và (1), ta được:

\(\dfrac{7}{2x+2}=\dfrac{3}{2y-4}=\dfrac{5}{z+4}=\dfrac{10}{2z+8}\)

\(=\dfrac{7+3+10}{2x+2+2y-4+2z+8}\)

\(=\dfrac{20}{2\left(x+y+z\right)+6}=\dfrac{20}{2.17+6}=\dfrac{1}{2}\)

\(\Rightarrow\left\{{}\begin{matrix}2x+2=2.7=14\\2y-4=2.3=6\\z+4=5.2=10\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=12\\2y=10\\z=6\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=6\left(tm\right)\\y=5\left(tm\right)\\z=6\left(tm\right)\end{matrix}\right.\)

a: \(\dfrac{7}{5}>\dfrac{7}{9}\)

=>\(-\dfrac{7}{5}< -\dfrac{7}{9}\)

\(\dfrac{3}{2}=1,5;\dfrac{4}{5}=0,8;\dfrac{9}{11}=0,\left(9\right);-\dfrac{3}{-4}=0,75\)

mà 0<0,75<0,8<0,(9)<1,5

nên \(0< \dfrac{3}{4}< \dfrac{4}{5}< \dfrac{9}{11}< \dfrac{3}{2}\)

=>\(-\dfrac{7}{5}< -\dfrac{7}{9}< 0< \dfrac{-3}{-4}< \dfrac{4}{5}< \dfrac{9}{11}< \dfrac{3}{2}\)

b: \(-\dfrac{11}{12}=-1+\dfrac{1}{12};\dfrac{-3}{4}=-1+\dfrac{1}{4};\dfrac{-18}{19}=-1+\dfrac{1}{19};\dfrac{-4}{5}=-1+\dfrac{1}{5};-\dfrac{25}{26}=-1+\dfrac{1}{26}\) 

=>

Vì 4<5<12<19<26

nên \(\dfrac{1}{4}>\dfrac{1}{5}>\dfrac{1}{12}>\dfrac{1}{19}>\dfrac{1}{26}\)

=>\(\dfrac{1}{4}-1>\dfrac{1}{5}-1>\dfrac{1}{12}-1>\dfrac{1}{19}-1>\dfrac{1}{26}-1\)

=>\(\dfrac{-3}{4}>-\dfrac{4}{5}>\dfrac{-11}{12}>\dfrac{-18}{19}>\dfrac{-25}{26}\)

=>

\(\dfrac{-25}{26}< \dfrac{-18}{19}< \dfrac{-11}{12}< \dfrac{-4}{5}< -\dfrac{3}{4}\)

mà \(\dfrac{-3}{4}< 0< \dfrac{-4}{-5}\)

nên \(-\dfrac{25}{26}< -\dfrac{18}{19}< \dfrac{-11}{12}< -\dfrac{4}{5}< -\dfrac{3}{4}< \dfrac{-4}{-5}\)

a) \(\dfrac{1}{2};0;-\dfrac{2}{9};-\dfrac{4}{9};-\dfrac{5}{9};-\dfrac{7}{9};-\dfrac{10}{9}\)

b) \(\dfrac{7}{15};\dfrac{3}{10};0;\dfrac{2}{-5};-\dfrac{3}{4};-\dfrac{5}{6}\)

Giải thích:

b) \(\dfrac{7}{15}=\dfrac{14}{30}>\dfrac{3}{10}=\dfrac{9}{30}\)

\(\dfrac{2}{-5}=-\dfrac{4}{10}=-0,4>-\dfrac{3}{4}=-\dfrac{75}{100}=-0,75\)

\(-\dfrac{3}{4}=-\dfrac{9}{12}>-\dfrac{5}{6}=-\dfrac{10}{12}\)

?

a/

$\frac{97}{100}< \frac{98}{100}< \frac{98}{99}$

b/

$\frac{19}{18}=1+\frac{1}{18}> 1+\frac{1}{2020}=\frac{2021}{2020}$
c/

$\frac{131}{171}=1-\frac{40}{171}> 1-\frac{40}{170}=1-\frac{4}{17}=\frac{13}{17}$
d/

$\frac{51}{61}=1-\frac{10}{61}=1-\frac{100}{610}$

$\frac{515}{616}=1-\frac{101}{616}$

Xét hiệu:

$\frac{100}{610}-\frac{101}{616}=\frac{100.616-101.610}{610.616}$

$=\frac{100(610+6)-101.610}{610.616}$

$=\frac{600-610}{610.616}<0$

$\Rightarrow \frac{100}{610}< \frac{101}{616}$

$\Rightarrow 1-\frac{100}{610}> 1-\frac{101}{616}$

$\Rightarrow \frac{51}{61}> \frac{515}{616}$ 

Lời giải:

ĐKĐB $\Rightarrow \frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}$

Áp dụng TCDTSBN:

$\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}$

$=\frac{4(3x-2y)}{16}=\frac{3(2z-4x)}{9}=\frac{2(4y-3z)}{4}$

$=\frac{4(3x-2y)+3(2z-4x)+2(4y-3z)}{16+9+4}$

$=\frac{0}{29}=0$

$\Rightarrow 3x-2y=2z-4x=4y-3z=0$

$\Rightarrow 3x=2y; 4y=3z\Rightarrow \frac{x}{2}=\frac{y}{3}=\frac{z}{4}$

Áp dụng TCDTSBN:

$\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{x+y-z}{2+3-4}=\frac{-10}{1}=-10$

$\Rightarrow x=(-10).2=-20; y=3(-10)=-30; z=4(-10)=-40$

giả sử : x = 5k; y = 4k; z = 3k (k là N*)

ta có: \(P=\dfrac{5k+2\left(4k\right)-3\left(3k\right)}{5k-2\left(4k\right)+3\left(3k\right)}=\dfrac{5k+8k-9k}{5k-8k+9k}=\dfrac{4k}{6k}=\dfrac{4}{6}=\dfrac{2}{3}\)

vậy P = \(\dfrac{2}{3}\)

giúp mình với mình xin cảm ơn

vì góc A và góc B là 2 góc bù nhau nên

góc A + góc B = 180 độ (1)

mà góc A = 1/6B (2)

từ (1) (2) => 1/6B + B = 180

7/6B = 180

B = 154 độ

A = 180 - 154 = 26

vậy góc A = 26 độ

TASK 2
1 My father's hobby is collecting stamps
2 She often spends hours drawing pictures every Sunday
3 The Japanese live long lives because of their healthy diet
4 We give these clothes to the homeless
5 My mother started working as an English teacher in 1996
TASK 3 + TASK 5
1 We taught English to children in a primary school last summer
2 I love spending time outdoors with my family
3 Acne affects 80% of young people
4 I enjoy listening to classical music in my spare time
5 She often carves eggshells as special gifts for her family

TASK 2. For each question, complete the second sentence so that it means the same as the first one. Use the word in brackets and do not change it. Write NO MORE THAN THREE WORDS.
Example:
0. The bookshop is opposite the library. ______ a bookshop opposite the library. (THERE)
Answer: 0. There is
1. My father often collects stamps in his free time. (HOBBY)
My ______father's hobby is______________ collecting stamps.
2. It often takes her hours to draw pictures every Sunday. (SPENDS)
She often ______spends hours drawing______________ pictures every Sunday.
3. The Japanese have a healthy diet so they live long lives. (OF)
The Japanese live long lives _______because of_____________ healthy diet.
4. We donate these clothes to children who have no home. (HOMELESS)
We give these clothes _______to homeless children_____________.
5. My mother began to teach English in 1996. (WORKING)
My mother started _________working as an___________ English teacher in 1996.
 

TASK 3. Reorder the words and phrases to make meaningful sentences.
1. taught / a primary school / We / last summer / English / in / to children / .

➝ We taught English to children in a primary school last summer.
2. being outdoors / love / with / my family / I / spending time / .

➝ I love spending time being outdoors with my family.
3. young people / affects / of / Acne / 80% / .

➝ Acne affects 80% of young people.
4. classical music / I / enjoy / in / my spare time / listening to /.

➝ I enjoy listening to classical music in my spare time.
5. carves eggshells / She / often / as / for her family / special gifts / .

➝ She often carves eggshells as special gifts for her family.
 

TASK 5. Reorder the words and phrases to make meaningful sentences.
1. taught / a primary school / We / last summer / English / in / to children / .

➝ We taught English to children in a primary school last summer.
2. being outdoors / love / with / my family / I / spending time / .

➝ I love spending time being outdoors with my family.
3. young people / affects / of / Acne / 80% / .

➝ Acne affects 80% of young people.
4. classical music / I / enjoy / in / my spare time / listening to /.

➝ She often carves eggshells as special gifts for her family.
5. carves eggshells / She / often / as / for her family / special gifts / .

➝ She often carves eggshells as special gifts for her family.
 

TASK 5. Reorder the words and phrases to make meaningful sentences.
1. taught / a primary school / We / last summer / English / in / to children / .

➝ We taught English to children in a primary school last summer.
2. being outdoors / love / with / my family / I / spending time / .

➝ I love spending time being outdoors with my family.
3. young people / affects / of / Acne / 80% / .

➝ Acne affects 80% of young people.
4. classical music / I / enjoy / in / my spare time / listening to /.

➝ She often carves eggshells as special gifts for her family.
5. carves eggshells / She / often / as / for her family / special gifts / .

➝ She often carves eggshells as special gifts for her family.
 

TASK 5. Reorder the words and phrases to make meaningful sentences.
1. taught / a primary school / We / last summer / English / in / to children / .

➝ We taught English to children in a primary school last summer.
2. being outdoors / love / with / my family / I / spending time / .

➝ I love spending time being outdoors with my family.
3. young people / affects / of / Acne / 80% / .

➝ Acne affects 80% of young people.
4. classical music / I / enjoy / in / my spare time / listening to /.

➝ She often carves eggshells as special gifts for her family.
5. carves eggshells / She / often / as / for her family / special gifts / .

➝ She often carves eggshells as special gifts for her family.
 

TASK 5. Reorder the words and phrases to make meaningful sentences.
1. taught / a primary school / We / last summer / English / in / to children / .

➝ We taught English to children in a primary school last summer.
2. being outdoors / love / with / my family / I / spending time / .

➝ I love spending time being outdoors with my family.
3. young people / affects / of / Acne / 80% / .

➝ Acne affects 80% of young people.
4. classical music / I / enjoy / in / my spare time / listening to /.

➝ She often carves eggshells as special gifts for her family.
5. carves eggshells / She / often / as / for her family / special gifts / .

➝ She often carves eggshells as special gifts for her family.

a: \(\dfrac{8}{9}=1-\dfrac{1}{9}\)

\(\dfrac{108}{109}=1-\dfrac{1}{109}\)

Vì 9<109 nên \(\dfrac{1}{9}>\dfrac{1}{109}\)

=>\(-\dfrac{1}{9}< -\dfrac{1}{109}\)

=>\(-\dfrac{1}{9}+1< -\dfrac{1}{109}+1\)

=>\(\dfrac{8}{9}< \dfrac{108}{109}\)

b: \(\dfrac{97}{100}=0,97;\dfrac{98}{99}=0,\left(98\right)\)

mà 0,97<0,(98)

nên \(\dfrac{97}{100}< \dfrac{98}{99}\)

c: \(\dfrac{19}{18}=1+\dfrac{1}{18}\)

\(\dfrac{2021}{2020}=1+\dfrac{1}{2020}\)

Vì 18<2020 nên \(\dfrac{1}{18}>\dfrac{1}{2020}\)

=>\(1+\dfrac{1}{18}>1+\dfrac{1}{2020}\)

=>\(\dfrac{19}{18}>\dfrac{2021}{2020}\)

d: \(\dfrac{131}{171}=\dfrac{130+1}{170+1}>\dfrac{130}{170}=\dfrac{13}{17}\)