a) 1/3 + 3/10 + 4/15

= 19/30 + 4/15

= 9/10 

b) 5/9 . 19/24 + 5/9 . 5/24

= 5/9 . ( 19/24 + 5/24)

= 5/9 . 1

= 5/9 

c) 5/7 + 4/9 + 2/7 - 4/9 

= 73/63 + ( -10/63)

= 1 

d)  64.6 + 81.4 + 17.6

= 81 . 4 + 6 . ( 64 + 17 )

= 81 . 4 + 6 . 81

= 81 . ( 4 + 6)

= 81 . 10

= 810 

e) 43 . 27 + 93 . 43 + 57 . 61 + 59 . 57 

= 43 . ( 27 + 93 ) + 57. ( 61 + 59 )

= 43 . 120 + 57 . 120

= 120 . ( 43 + 57 )

= 120 . 100

= 12 000

uk

(2003 - 123 x 8 : 4) x ( 3636 : 101 - 36)

= ( 1880 x 2 ) x ( 36 - 36 )

= ( 1880 x 2 ) x 0

= 0 

 2003 - 123 x 8 : 4 ) x ( 36 : 6 - 6 ) 

= ( 2003 - 123 x 8 : 4 ) x ( 6 - 6 )

=  ( 2003 - 123 x 8 : 4 ) x 0

= 0 

\(A\left(x\right)=4x^2-2x-8+5x^3-7x^2+1\)

\(A\left(x\right)=5x^3-3x^2-2x-7\)

\(B\left(x\right)=-3x^3+4x^2+9+x-2x-2x^3\)

\(B\left(x\right)=-5x^3+4x^2-x+9\)

+) \(A\left(x\right)=4x^2-2x-8+5x^3-7x^2+1\)

\(\Leftrightarrow A\left(x\right)=-3x^2-2x-7+5x^3\)

+) \(B\left(x\right)=-3x^3+4x^2+9+x-2x-2x^3\)

\(\Leftrightarrow B\left(x\right)=-5x^3+4x^2-x+9\)

+) \(M\left(x\right)=A\left(x\right)+B\left(x\right)\)

\(\Leftrightarrow M\left(x\right)=-3x^2-2x-7+5x^3-5x^3+4x^2-x+9\)

\(\Leftrightarrow M\left(x\right)=x^2-3x+2\)

+) \(N\left(x\right)=A\left(x\right)-B\left(x\right)\)

\(\Leftrightarrow N\left(x\right)=-3x^2-2x-7+5x^3+5x^3-4x^2+x-9\)

\(\Leftrightarrow N\left(x\right)=-7x^2+10x^3-x-16\)

2⁹ = 512 

2¹¹  = 2048 

\(2^9=2^{10-1}=2^{10}:2^1=1024:2=512\)

\(2^{11}=2^{10+1}=2^{10}.2=1024.2=2048\)

Sửa đề:

\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

\(=\dfrac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.120}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)

\(=\dfrac{2^{12}.3^{10}+2^9.3^9.120}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\dfrac{2^9.3^9\left(2^3.3+120\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)

\(=\dfrac{2^9.3^9.144}{2^{11}.3^{11}.5}=\dfrac{144}{180}=\dfrac{4}{5}\)

4-x^2

4-x^2

Đặt \(S=\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+100\right)\)

Ta có :

Số cặp trong tổng trên là : \(\left(100-1\right):1+1=100\) ( cặp )

\(\Rightarrow S=100x+1+2+3+4+5+....+100\)

\(\Leftrightarrow S=100x+\dfrac{\left(100+1\right)\times100}{2}\)

\(\Leftrightarrow100x+5050=7450\)

\(\Leftrightarrow100x=2400\)

\(\Leftrightarrow x=24\)

(x + 1) + (x +2 ) + ( x + 3 ) + ....... + (x + 100 ) =7450

 =>  100 x + (1+ 100 ) .100 : 2 =77450

=>   100x+5050  =7450

=>    100x  =7450-5050

=>    100x =2400

=>     x  =2400 : 100

=>     x      =24

Số trừ tăng hơn số bị trừ là : 3,2 - 1,5 = 1,7
Hiệu ban đầu là : 8,05 + 1,7 = 9,75
 

Ta có :

Số bị trừ + 1,5 - 3,2 - số trừ = 8,05

Số bị trừ - số từ = 8,05 - 1,5 + 3,2 

Hiệu = 9,75

Vậy...........

( 71 - 59 ) - ( - 83 + 95 )

= 71 - 59 + 83 + 95

= 190

\(\left(71-59\right)-\left(-83+95\right)\)

\(=71-59+83-95\)

\(=0\)

`x . 0,75 + 3/4 . 5 + 2 : 4/3 = 10,5`

`x . 0,75 + 3/4 . 5 + 2 : 4/3 =21/2`

`x. 3/4 + 3/4 . 5 + 2 : 4/3 = 21/2`

`x . 3/4 + 15/4 + 2 xx 3/4 = 21/2`

`x. 3/4 + 21/4=21/2`

`x.3/4 = 21/2 - 21/4`

`x.3/4 = 21/4`

`x=21/4 : 3/4`

`x=21/4 xx 4/3`

`x=21/3`

`x=7`

Vậy `x=7`

\(x\times0,75+\dfrac{3}{4}\times5+2\div\dfrac{4}{3}=10,5\)

\(x\times0,75+\dfrac{15}{4}+2\times\dfrac{3}{4}=10,5\)

\(x\times0,75+\dfrac{15}{4}+\dfrac{6}{4}=10,5\)

\(x\times0,75+\dfrac{21}{4}=10,5\)

\(x\times0,75=\dfrac{21}{4}\)

\(x=7\)