Maximize \( z=3 x_{1}-x_{2} \) \( 2 x_{1}+x_{2} \leq 2 \) \( x_{1}+3 x_{2} \geq 3 \) \( x_{2} \leq 4 \)

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

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

aa \( |2 x+3|=|7 x-5| \)

(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 \( x=2 \)

Esefcizio 10.7 Sia dato \( S \) il sottoinsieme di \( \mathbb{R}[x] \) definito da \[ S=\{f(x) \in \mathbb{R}[x] \mid f(-1)=f(1)=0, \operatorname{deg} f(x) \leqslant 4\} \cup\{0\} \] sottospazio vettoriale di \( \mathbb{R}[x] \). Determinare la dimensione, la codimensione, una base, equazioni cartesiane, equazioni parametriche ed un complemento per \( S \).