9000033304 Level: BFind the solution set of the following inequality. \[ \frac{x + 4} {x + 2}\leq 0 \]\([ - 4;-2)\)\((-\infty ;-4] \cup [ 2;\infty )\)\((-\infty ;-4)\cup (-2;\infty )\)\((-4;-2] \)
9000033305 Level: BFind the solution set of the following inequality. \[ \frac{2} {x + 1}\geq 1 \]\((-1;1] \)\([ - 1;1)\)\((-\infty ;-1)\cup [ 1;\infty )\)\((-\infty ;1] \)
9000033307 Level: BFind the solution set of the following inequality. \[ \frac{4} {x^{2} - x - 6}\leq 0 \]\((-2;3)\)\(\mathbb{R}\)\((-\infty ;-2)\cup (3;\infty )\)\((-3;2)\)
9000033703 Level: BFind the domain of the following function. \[ f\colon y = \frac{x} {\sqrt{4x^{2 } - 9}} \]\(\left (-\infty ;-\frac{3} {2}\right )\cup \left (\frac{3} {2};\infty \right )\)\(\mathbb{R}\)\(\mathbb{R}\setminus \left \{-\frac{3} {2}; \frac{3} {2}\right \}\)\(\left (-\frac{3} {2}; \frac{3} {2}\right )\)\(\left [ -\frac{3} {2}; \frac{3} {2}\right ] \)\(\left (-\infty ;-\frac{3} {2}\right ] \cup \left [ \frac{3} {2};\infty \right )\)
9000033701 Level: BFind out, how many integer solutions the following inequality has. \[ m^{2} + 2m - 4 < 0 \]Five integer solutions.Less than five integer solutions.More than five integer solutions.
9000033803 Level: BIn the following list identify a true statement about the function \(f(x) =\sin x\), where \(x\in \left [ -\frac{\pi }{2}; \frac{\pi } {2}\right ] \).The function \(f\) is increasing.The function \(f\) is decreasing.The function \(f\) is neither increasing nor decreasing.The function \(f\) is non-increasing.
9000031001 Level: BFind the sum of all real roots of the following equation. \[ (3x - 1)(2x + 1)(4x^{2} + 3x - 1) = 0 \]\(-\frac{11} {12}\)\(- \frac{1} {12}\)\(-\frac{1} {6}\)\(\frac{1} {6}\)
9000031102 Level: BSolve the following system of equations and identify a correct statement. \[\begin{aligned} (x - 1)^{2} + y^{2} = 1 & & \\(x - 4)^{2} + y^{2} = 4 & & \end{aligned}\]The system has a unique solution \(\left [x,y\right ]\), where \(y = 0\).The system does not have any solution.The system has a unique solution \(\left [x,y\right ]\), where \(y > 0\).The system has two solutions \(\left [x_{1},y_{1}\right ]\), \(\left [x_{2},y_{2}\right ]\), where \(y_{1} = -y_{2}\).
9000031004 Level: BAssuming \(y\in \mathbb{R}\), find the number of the solutions of the following algebraic equation. \[ y^{4} + 5y^{2} + 6 = 0 \]\(0\)\(4\)\(3\)\(2\)
9000031005 Level: BAssuming \(x\in \mathbb{R}\), solve the following algebraic equation. \[ (x + 1)^{4} - 5(x + 1)^{2} + 4 = 0 \]\( \{ - 3;-2;0;1\}\)\( \{1;4\}\)\( \{ - 2;-1;1;2\}\)\( \{ - 1;3\}\)