The value of \( k \) for which the system of equations \( \left\{\begin{array}{l}x+k z=1 \\ y+z=2 \\ 2 x+y=5\end{array}\right. \) is inconsistent equals

\( 1 \frac{3}{2} \leqslant x<5 / 2 \) et \( \frac{2}{3} \leqslant y \leqslant \frac{4}{3} \) exarder \( x+y, x-y, x+y, \frac{x-3 y}{x} \)

2 Find the solution set in \( R:|2 x-3|+3>7 \)

(C) If \( a, b, c \) and \( d \) are proportion quantities, then prove that: \( \frac{a+2 c}{b+2 d}=\frac{c-a}{d-b} \) (a) If \( \frac{a}{x+y}=\frac{b}{y-2 x}=\frac{c}{x+4 y} \), find the value of : \( \frac{b+2 c}{2 a+b} \) (b) If \( y=3+a \) and \( a \propto \frac{1}{x} \) and \( y=5 \) when \( x=1 \), find the relation bet \( x \) and \( y \), then find the value of \( y \) when \( x=2 \)

(a) 2023: If \( y \propto x \) and \( y=5 \) when \( x=15 \), Find the value of \( x \) when \( y=3 \) (b) If \( y \) varies inversely with \( x^{2} \) and \( x=3 \) when \( y=4 \), Find: [1] The relation between \( y \) and \( x \) [2] The value of \( x \) when \( y=9 \) (C) If \( a, b, c \) and \( d \) are proportion quantities, then prove that : \( \frac{a}{b+2 c}=\frac{c-a}{d-b} \)

Вычисли дискриминант квадратного уравнения: \( 5 \mathrm{x}-2+11 \mathrm{x}^{2}=0 \) Запиши в поле ответа верное число. \( \mathrm{D}= \)