Do năm 2024 là năm nhuận.

\(\rightarrow\) 30/7/2023 là chủ nhật

Mỗi năm trừ đi 1 ngày

\(\rightarrow\) 30/7/2022 là thứ bảy.

\(\rightarrow\) 30/7/2021 là thứ sáu

\(a,\left(-45\right)+123+45-23\\ =\left(-45+45\right)+\left(123-23\right)\\ =0+100\\ =100\)

\(17\cdot85+15\cdot17-2^3\cdot14\\ =17\cdot\left(85+15\right)-8\cdot14\\ =17\cdot100-112\\ =1700-112\\ =1588\)

\(\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}+\dfrac{2}{143}+\dfrac{2}{195}\\ =\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}+\dfrac{2}{11\times13}+\dfrac{2}{13\times15}\\ =1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}\\ =1-\dfrac{1}{15}\\ =\dfrac{15}{15}-\dfrac{1}{15}\\ =\dfrac{14}{15}\)

Sửa:

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

\(-\dfrac{2}{3}-\dfrac{1}{3}\left(2x-5\right)=\dfrac{3}{2}\\\)

\(\Rightarrow\dfrac{1}{3}\cdot2x-\dfrac{1}{3}\cdot5=-\dfrac{2}{3}-\dfrac{3}{2}\)

\(\Rightarrow\dfrac{2}{3}x-\dfrac{5}{3}=-\dfrac{13}{6}\)

\(\Rightarrow\dfrac{2}{3}x=\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{1}{2}:\dfrac{2}{3}\\ \Rightarrow x=\dfrac{1}{2}\cdot\dfrac{3}{2}\\ \Rightarrow x=\dfrac{3}{4}\)

\(x^3=x^2\\ \Rightarrow x^3-x^2=0\\ \Rightarrow x^2\left(x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x^2=0\\x-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

Ta có:

\(35+b+74=56\times3\\ \left(35+74\right)+b=168\\ 109+b=168\\ b=168-109\\ b=59\)

Vậy: \(b=59\)

\(\left(x+1\right)\left(2x-2\right)-\left(x+3\right)\left(x+1\right)\\ =\left(x+1\right)\left(2x-2-x-3\right)\\ =\left(x+1\right)\left(x-5\right)\)

Sửa:

\(10^6:1000=10^6:10^3=10^{6-3}=10^3\)