The ratio between the sum of the fifth, sixth and seventh terms of a geometric series and the sum of the first three terms of the same series is \( 81: 16 \). Determine the sum of the first ten terms, if the first term is 1024 .

Solve \( 8 n-11<5 n+4 \)

(a) Verify that \( A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \) satisfies the equation \( x^{2}-(a+d) x+(a d-b c) I=0 \) where \( I \) is the \( 2 \times 2 \) matrix.

Resuelve \( 9-8 y=27-2 y \)

Bài 1. (1,5 điểm) Cho biểu thức \( P=\left(\frac{1}{x \sqrt{x}-1}-\frac{\sqrt{x}+1}{x-1}\right) \cdot \frac{x+\sqrt{x}+1}{\sqrt{x}+1}(x \geq 0 ; x \neq 1) \) a. Chửng minh \( P=\frac{\sqrt{x}}{1-\sqrt{x}} \) với \( x \geq 0 ; x \neq 1 \). b. Tîm tất cả các giá trị của \( x \) đề \( P>-1 \). Bài 2. \( \left(0,75\right. \) điểm) 1. Giải phương trình \( \quad \frac{-x^{2}+12 x+4}{x^{2}+3 x-4}=\frac{12}{x+4}+\frac{12}{3 x-3} \)

Find the slope of the straight line \( \frac{x}{2}+\frac{y}{3}=1 \), then find the length of \( y \) intercept,