Chiều rộng đám ruộng là:

100 x 3/4 = 75 (m)

a) Chu vi đám ruộng là:

(100 + 75) x 2 = 350 (m)

Diện tích đám ruộng là:

100 x 75 = 7500 (m²)

b) 7500 m² = 0,75 ha

Số tạ lúa đám ruộng đó thu hoạch được là:

0,75 x 60 = 45 (kg) = 0,45 tạ

a)

\(B=1+3+3^2+3^3+...+3^{100}\\ \Rightarrow3B=3+3^2+3^3+3^4+...+3^{101}\\ \Rightarrow3B-B=\left(3+3^2+3^3+3^4+...+3^{101}\right)-\left(1+3+3^2+3^3+...+3^{100}\right)\\ \Rightarrow2B=3^{101}-1\\ \Rightarrow B=\dfrac{3^{101}-1}{2}\)

b)

\(C=1+5+5^2+...+5^{50}\\ \Rightarrow5C=5+5^2+5^3+...+5^{51}\\ \Rightarrow5C-C=\left(5+5^2+5^3+...+5^{51}\right)-\left(1+5+5^2+...+5^{50}\right)\\ \Rightarrow4C=5^{51}-1\\ \Rightarrow C=\dfrac{5^{51}-1}{4}\)

c)

\(A=2^1+2^3+2^5+...+2^{99}\\ \Rightarrow4A=2^3+2^5+2^7+...+2^{101}\\ \Rightarrow4A-A=\left(2^3+2^5+2^7+...+2^{101}\right)-\left(2^1+2^3+2^5+...+2^{99}\right)\\ \Rightarrow3A=2^{101}-2\\ \Rightarrow A=\dfrac{2^{101}-1}{3}\)

1/8 + 1/6 + 1/3

= 3/24 + 4/24 + 8/24

= 15/24

= 5/8

12 x 4 - X : 5 + 156 : 13 = 56

48 - X : 5 + 12 = 56

48 - X : 5 = 56 - 12

48 - X : 5 = 44

X : 5 = 48 - 44

X : 5 = 4

X = 4 x 5

X = 20

a) 

\(2\times3^2-24:\left(3^{100}:3^{99}\right)\\ =2\times9-24:3\\ =18-8\\ =10\)

b)

\(9\times2^2:\left(14^0+1^{2022}\right)\\ =9\times4:\left(1+1\right)\\ =36:2\\ =18\)

c)

\(3\times\left\{9+3\times\left[30-\left(5^2-22\right)\right]\right\}\\ =3\times\left\{9+3\times\left[30-\left(25-22\right)\right]\right\}\\ =3\times\left\{9+3\times\left[30-3\right]\right\}\\ =3\times\left\{9+3\times27\right\}\\ =3\times\left\{9+81\right\}\\ =3\times90\\ =270\)

Để 32ab chia hết cho 2 và 5 ⇒ b = 0

Để 32a0 ⋮ 3

⇒ (3 + 2 + a + 0) ⋮ 3

⇒ (5 + a) ⋮ 3

⇒ a ϵ {1 ; 4 ; 7}

Vậy a ϵ {1 ; 4 ; 7} ; b = 0

\(A=\dfrac{2}{5.8}+\dfrac{2}{8.11}+\dfrac{2}{11.14}+\dfrac{2}{14.17}+...+\dfrac{2}{26.29}\\ =\dfrac{2}{3}.\left(\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17}+...+\dfrac{3}{26.29}\right)\\ =\dfrac{2}{3}.\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}+...+\dfrac{1}{26}-\dfrac{1}{29}\right)\\ =\dfrac{2}{3}.\left(\dfrac{1}{5}-\dfrac{1}{29}\right)\\ =\dfrac{2}{3}.\left(\dfrac{29}{145}-\dfrac{5}{245}\right)\\ =\dfrac{2}{3}.\dfrac{24}{145}\\ =\dfrac{16}{145}\)

\(B=-137.\left(136-417\right)-136.\left(417-137\right)\\ =-137.136-\left(-137\right).417-\left(136.417-136.137\right)\\ =-137.136+137.417-136.417+136.137\\ =\left(-137.136+136.137\right)+\left(137.417-136.417\right)\\ =0+417.\left(137-136\right)\\ =417.1\\ =417\)

7⁶ + 7⁵ - 7⁴

= 7 . (7⁵ + 7⁴ - 7³)
7 ⋮ 7 ⇒ [7 . (7⁵ + 7⁴ - 7³)] ⋮ 7

Vậy (7⁶ + 7⁵ - 7⁴) ⋮ 7

a) Ta có:

B(12) = {0; 12 ; 24 ; 36 ; 48 ; 60 ; ...}

Mà x ϵ B(12) và 20 ≤ x ≤ 50

⇒ x ϵ {24 ; 36 ; 48}

b) Ta có: 

x ⋮ 15 ⇒ x ϵ B(15) = {0 ; 15 ; 30 ; 45 ; 60 ; ...}

Mà 0 < x ≤ 40

⇒ x ϵ {15 ; 30}

c) Ta có:

Ư(20) = {1 ; 2 ; 4 ; 5 ; 10 ; 20}

Mà x ϵ Ư(20) và x > 8

⇒ x ϵ {10 ; 20}

d) Ta có:

16 ⋮ x ⇒ x ϵ Ư(16) = {1 ; 2 ; 4 ; 8 ; 16}

Vậy x ϵ {1 ; 2 ; 4 ; 8 ; 16}

\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+99\right)=5000\\ \Rightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+99\right)=5000\\ \Rightarrow99x+\dfrac{99\times\left(99+1\right)}{2}=5000\\ \Rightarrow99x+\dfrac{99\times100}{2}=5000\\ \Rightarrow99x+4950=5000\\ \Rightarrow99x=5000-4950\\ \Rightarrow99x=50\\ \Rightarrow x=\dfrac{50}{99}\)