Yearly Archives: 2023

Topic Solution domain of the system of inequalities \(\left\{ {\begin{array}{*{20}{c}}{2x – 5y > 1}\\{2x + y > – 5}\\{x + y < – 1}\end{array}} \right.\) is the plane part containing…

Topic The solution domain of the inequality \(2x – 3y > 5\) is a semi-plane (excluding the line \(d:2x – 3y = 5\)) that does not contain any of the…

Topic Which of the following pairs of numbers is the solution of the system of inequalities \(\left\{ {\begin{array}{*{20}{c}}{x – 2y < 0}\\{x + 3y > – 2} \\{ – x…

Topic Make a negative statement of each of the following statements and consider the truth or falsehood of each of them. a) \(\forall n \in \mathbb{N},n(n + 1)\) is divisible…

Topic Given the equation \(a{x^2} + bx + c = 0\). a) Consider the proposition "If \(a + b + c = 0\) then the equation \(a{x^2} + bx +…

Topic Find \(D = E \cap G\), knowing that E and G are the set of solutions of the two inequalities in each of the following cases: a) \(5x –…