Bài 1:

a; A = 31.17 + 41.29 

   A = \(\overline{..7}\) + \(\overline{..9}\)

A = \(\overline{..6}\) 

2 < A ⋮ 2 

Vậy A là hợp số.

b; B = 12.14.16.18 + 90

    12 ⋮ 3; 90 ⋮ 3 ⇒ 3 < B ⋮ 3 

Vậy B là hợp số

c; C = 10⁸ - 1

    10 \(\equiv\) 1 (mod 3)

    10⁸ \(\equiv\) 1 (mod 3)

    1     \(\equiv\) 1 (mod 3)

    10⁸ - 1 \(\equiv\) 1 - 1 (mod 3)

    10⁸ - 1 \(\equiv\) 0 (mod 3)

   3< 10⁸ - 1 ⋮ 3

   10⁸ - 1 là hợp số.

d; D = 1.2.3.4.5 + 5²⁰ + 5³⁰

    D = 5.(1.2.3.4  + 5¹⁹ + 5²⁹)

    5 < D  \(⋮\) 5

D là hợp số

Bài 1:

a) A= \(31\cdot17+41\cdot29\) 

Tích 31.17 có kết quả là số lẻ 

Tích 41.29 có kết quả là số lẻ 

=> 31.17 + 41.29 có kết quả là số chẵn 

=> A = 31.17 + 41.29 chia hết cho 2 

Nên A sẽ là hợp số

b) \(B=12\cdot14\cdot16\cdot18+90\)

Có tích 12.14.16.18 là một số chẵn 

=> B=12.14.16.18 + 90 có kết quả là một số chẵn 

=> B chia hết cho 2

=> B là hợp số 

c) \(C=10^8-1\) 

\(10^8=\overline{10...0}\Rightarrow10^8-1=\overline{10...0}-1=\overline{99...9}\) 

Mà: \(\overline{99...9}\) ⋮ 9

=> C chia hết cho 9

=> C là hợp số 

d) \(D=1.2.3.4.5+5^{20}+5^{30}=5\cdot\left(1.2.3.4+5^{19}+5^{30}\right)\)

=> D chia hết 5

=> D là hợp số

Số phần tử của tập hợp X là:

(81 - 1) : 1 + 1 = 81 (phần tử)

Số phần tử của tập hợp T là:

(81 - 0) : 1 + 1 = 82 (phần tử) 

ko biết chịu khó lắm

chiều rộng mảnh vườn là: 12 x 3/4 = 9

a) chu vi mảnh vườn là: (12 + 9) x 2 = 42

b) diện tích mảnh vườn là: 12 x 9 = 108

c) diện tích trồng rau là: 108 x 2/3 = 72

a) Chiều rộng mảnh vườn là:

`3/4 xx 12 = 9` 

Chu vi mảnh vườn là:

(12 + 9) x 2 = 42

b) Diện tích mành vườn là:

12 x 9 = 108 

c) Diện tích trồng rau là:

`2/3 xx 108 = 72` '

ĐS: ... 

\(\dfrac{3}{8}-\dfrac{1}{2}:\left(\dfrac{2x}{5}-\dfrac{2}{3}\right)=\dfrac{-8}{5}\\ \dfrac{3}{8}-\dfrac{1}{2}:\left(\dfrac{6x}{15}-\dfrac{10}{15}\right)=-\dfrac{8}{5}\\ \dfrac{3}{8}-\dfrac{1}{2}:\dfrac{6x-10}{15}=-\dfrac{8}{5}\\ \dfrac{1}{2}:\dfrac{6x-10}{15}=\dfrac{3}{8}+\dfrac{8}{5}\\ \dfrac{1}{2}\cdot\dfrac{15}{6x-10}=\dfrac{79}{40}\\ \dfrac{15}{6x-10}=\dfrac{79}{20}\\ 6x-10=15:\dfrac{79}{20}\\ 6x-10=\dfrac{300}{79}\\ 6x=\dfrac{300}{79}+10\\ 6x=\dfrac{1090}{79}\\ x=\dfrac{1090}{79}:6\\x =\dfrac{545}{237}\)

\(\dfrac{3}{8}-\dfrac{1}{2}:\left(\dfrac{2x}{5}-\dfrac{2}{3}\right)=-\dfrac{8}{5}\\ \dfrac{1}{2}:\left(\dfrac{2x}{5}-\dfrac{2}{3}\right)=\dfrac{79}{40}\\ \dfrac{2x}{5}-\dfrac{2}{3}=\dfrac{20}{79}\\ \dfrac{2x}{5}=\dfrac{218}{237}\\ 2x=\dfrac{1090}{237}\\ x=\dfrac{545}{237}\)

\(\dfrac{-13}{15}=\dfrac{-13}{5}\cdot\dfrac{1}{3}=\dfrac{-13}{5}:3\)

\(\dfrac{-2}{11}=-2\cdot\dfrac{1}{11}=-2:11\)

\(a.\dfrac{3}{4}:x=-\dfrac{1}{2}\\ x=\dfrac{3}{4}:\left(-\dfrac{1}{2}\right)\\ x=-\dfrac{3}{2}\\ b.x:\left(-\dfrac{2}{3}\right)=-\dfrac{5}{6}\\ x=\left(-\dfrac{5}{6}\right)\cdot\left(-\dfrac{2}{3}\right)\\ x=\dfrac{5}{9}\\ c.\dfrac{1}{2}:x-\dfrac{1}{2}=-\dfrac{3}{4}\\ \dfrac{1}{2}:x=-\dfrac{1}{4}\\ x=\dfrac{1}{2}:\left(-\dfrac{1}{4}\right)\\ x=-2\\ d.\dfrac{1}{2}\cdot x+\dfrac{3}{4}=-\dfrac{5}{6}\\ \dfrac{1}{2}\cdot x=-\dfrac{19}{12}\\ x=\dfrac{-19}{12}:\dfrac{1}{2}=-\dfrac{19}{12}\cdot2\\ x=-\dfrac{19}{6}\)

\(e.x:\dfrac{1}{2}+\dfrac{1}{2}=-\dfrac{5}{6}\\ x:\dfrac{1}{2}=-\dfrac{4}{3}\\ x=-\dfrac{4}{3}\cdot\dfrac{1}{2}\\ x=-\dfrac{2}{3}\\ g.\dfrac{4}{3}-\dfrac{1}{2}\cdot x=\dfrac{1}{2}\\ \dfrac{1}{2}\cdot x=\dfrac{5}{6}\\ x=\dfrac{5}{6}:\dfrac{1}{2}=\dfrac{5}{6}\cdot2\\ x=\dfrac{5}{3}\\ h.\dfrac{3}{8}\cdot x-\dfrac{1}{2}=\dfrac{3}{4}\\ \dfrac{3}{8}\cdot x=\dfrac{1}{4}\\ x=\dfrac{1}{4}:\dfrac{3}{8}=\dfrac{1}{4}\cdot\dfrac{8}{3}\\ x=\dfrac{2}{3}\)

mình làm lại câu h xíu

\(\dfrac{3}{8}\cdot x-\dfrac{1}{2}=\dfrac{3}{4}\\ \dfrac{3}{8}\cdot x=\dfrac{5}{4}\\ x=\dfrac{5}{4}:\dfrac{3}{8}=\dfrac{5}{4}\cdot\dfrac{8}{3}\\ x=\dfrac{10}{3}\)

\(a.\dfrac{3}{2}-4\cdot\left(\dfrac{1}{2}+\dfrac{3}{4}\right)\\ =\dfrac{3}{2}-4\cdot\dfrac{5}{4}\\ =\dfrac{3}{2}-5=-\dfrac{7}{2}\\ b.\left(-\dfrac{1}{3}+\dfrac{5}{6}\right)\cdot11-7\\ =\dfrac{1}{2}\cdot11-7\\ =\dfrac{11}{2}-7=-\dfrac{3}{2}\\ c.\left(\dfrac{5}{8}+\dfrac{-2}{7}\right):\dfrac{3}{4}+\left(\dfrac{3}{8}-\dfrac{5}{7}\right):\dfrac{3}{4}\\ =\left(\dfrac{5}{8}+\dfrac{-2}{7}\right)\cdot\dfrac{4}{3}+\left(\dfrac{3}{8}-\dfrac{5}{7}\right)\cdot\dfrac{4}{3}\\ =\dfrac{4}{3}\cdot\left(\dfrac{5}{8}-\dfrac{2}{7}+\dfrac{3}{8}-\dfrac{5}{7}\right)\)

\(\dfrac{4}{3}\cdot\left[\left(\dfrac{5}{8}+\dfrac{3}{8}\right)-\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\right]\\ =\dfrac{4}{3}\cdot\left(1-1\right)=\dfrac{4}{3}\cdot0=0\)

\(d.\dfrac{\dfrac{3}{4}-\dfrac{3}{5}+\dfrac{3}{7}+\dfrac{3}{11}}{\dfrac{13}{4}-\dfrac{13}{5}+\dfrac{13}{7}+\dfrac{13}{11}}\\ =\dfrac{3\cdot\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{11}\right)}{13\cdot\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{11}\right)}=\dfrac{3}{13}\)

a) 

\(\dfrac{3}{2}-4\left(\dfrac{1}{2}+\dfrac{3}{4}\right)\\ =\dfrac{3}{4}-4\left(\dfrac{2}{4}+\dfrac{3}{4}\right)\\ =\dfrac{3}{4}-4\cdot\dfrac{5}{4}\\ =\dfrac{3}{4}-5\\ =-\dfrac{17}{4}\) 

b) 

\(\left(-\dfrac{1}{3}+\dfrac{5}{6}\right)\times11-7\\ =\left(-\dfrac{2}{6}+\dfrac{5}{6}\right)\times11-7\\ =\dfrac{1}{2}\times11-7\\ =\dfrac{11}{2}-7\\ =-\dfrac{3}{2}\)

c) 

\(\left(\dfrac{5}{8}+\dfrac{-2}{7}\right):\dfrac{3}{4}+\left(\dfrac{3}{8}-\dfrac{5}{7}\right):\dfrac{3}{4}\\ =\left(\dfrac{5}{8}+\dfrac{-2}{7}\right)\times\dfrac{4}{3}+\left(\dfrac{3}{8}-\dfrac{5}{7}\right)\times\dfrac{4}{3}\\ =\dfrac{4}{3}\times\left(\dfrac{5}{8}+\dfrac{-2}{7}+\dfrac{3}{8}-\dfrac{5}{7}\right)\times\dfrac{4}{3}\\ =\left(1-1\right)\times\dfrac{4}{3}\\ =0\times\dfrac{4}{3}\\ =0\)

d) 

\(M=\dfrac{\dfrac{3}{4}-\dfrac{3}{5}+\dfrac{3}{7}+\dfrac{3}{11}}{\dfrac{13}{4}-\dfrac{13}{5}+\dfrac{13}{7}+\dfrac{13}{11}}\\ =\dfrac{3\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{11}\right)}{13\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{11}\right)}\\ =\dfrac{3}{13}\)

\(a.\left(-\dfrac{9}{34}\right)\cdot\dfrac{17}{4}=-\dfrac{9}{8}\\ b.\left(-\dfrac{20}{41}\right)\cdot\left(-\dfrac{4}{5}\right)=\dfrac{16}{41}\\ c.1\dfrac{1}{7}\cdot\left(-3\dfrac{1}{2}\right)=\dfrac{8}{7}\cdot\left(-\dfrac{7}{2}\right)=-4\\ d.\left(-\dfrac{5}{2}\right):\dfrac{3}{4}=\left(-\dfrac{5}{2}\right)\cdot\dfrac{4}{3}=-\dfrac{10}{3}\\ e.\left(-\dfrac{3}{4}\right):\left(-1\dfrac{1}{3}\right)=\left(-\dfrac{3}{4}\right)\cdot\left(-\dfrac{3}{4}\right)=\dfrac{9}{16}\\ g.\left(-5\right):\left(-2\dfrac{1}{2}\right)=\left(-5\right)\cdot\left(-\dfrac{2}{5}\right)=2\)

\(a)-\dfrac{9}{34}\times\dfrac{17}{4}\\ =\dfrac{-9}{17\times2}\times\dfrac{17}{4}\\ =\dfrac{-9}{8}\\ b)-\dfrac{20}{41}\times-\dfrac{4}{5}\\ =\dfrac{4\times5}{41}\times\dfrac{-4}{5}\\ =-\dfrac{16}{41}\\ c)1\dfrac{1}{7}\times\left(-3\dfrac{1}{2}\right)\\ =\dfrac{8}{7}\times\dfrac{-7}{2}\\ =-4\\ d)-\dfrac{5}{2}:\dfrac{3}{4}\\ =-\dfrac{5}{2}\times\dfrac{4}{3}\\ =\dfrac{-10}{3}\\ e)-\dfrac{3}{4}:\left(-1\dfrac{1}{3}\right)\\ =-\dfrac{3}{4}:-\dfrac{4}{3}\\ =-\dfrac{3}{4}\times-\dfrac{3}{4}\\ =\dfrac{9}{16}\\ g)-5:\left(-2\dfrac{1}{2}\right)\\ =-5:-\dfrac{5}{2}\\ =-5\times-\dfrac{2}{5}\\ =2\)

Bài 1

1 two pieces of furniture

2 Two plates of pasta

3 four sheets of paper

4 Three glasses of lemonade

5 Two cups of yoghurt

6 Three bottles of oil

7 Two tubes of toothpaste

8 Five steaks of salmon

IV

30 every

31 everyone

32 every

33 nothing

34 somewhere