Radical equations and inequalities

2010007802

Level: 
A
Find the domain of the following expression. \[ \sqrt{\left (3x - 2 \right ) \left (4+5x\right )} \]
\(\left(-\infty ;-\frac{4} {5}\right] \cup \left[ \frac{2} {3};\infty \right )\)
\(\left[ -\frac{4} {5}; \frac{2} {3}\right] \)
\(\left (-\infty ;-\frac{4} {5}\right) \cup \left( \frac{2} {3};\infty \right)\)
\(\left( -\frac{4} {5}; \frac{2} {3}\right) \)

2010007801

Level: 
A
Identify a true statement which concerns to the following equation. \[ 2\sqrt{x+5} = x+2 \]
The solution is in the set \(\left \{x\in \mathbb{R} : -1 < x\leq - 5 \right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : 5 < x\leq 7 \right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : -4 < x\leq - 1 \right \}\).
The solution is in the set \(\left \{x\in \mathbb{R} : -1 < x\leq 2 \right \}\).

2010007710

Level: 
A
Identify a true statement which concerns the following pair of equations. \[ \begin{aligned} \sqrt{x+3} & = 5 &\text{(1)} \\ \sqrt{11-x} & = 3 &\text{(2)} \end{aligned} \]
The solution of (1) is bigger than the solution of (2).
The solution of (1) is smaller than the solution of (2).
The solutions of both equations are prime numbers.
The solution of (1) equals to the solution of (2).