2010007704
Level:
A
Find the domain of the expression.
\[
\sqrt{-x^2-7x+30}
\]
\([ -10;3] \)
\(\left(-\infty;-10 ] \cup[ 3;\infty\right)\)
\([ -3;10] \)
\(\emptyset\)
Radical equations and inequalities
2010007706
Level:
A
If \( \sqrt{x^2-x-12}=x+3 \), then the number \( x \) can be equal to:
\( -3\)
\( -4\)
\( -5\)
\( -6\)
2010007707
Level:
A
Find the domain of the following equation.
\[
\sqrt{7 - x} = 13
\]
\((-\infty ;7 ] \)
\( [ -7;\infty )\)
\((-\infty ;6 ) \)
\( (6;\infty )\)
2010007708
Level:
A
Find the domain of the following equation.
\[
\sqrt{9-3x} + \sqrt{2x+8} = 13
\]
\( [ -4;3 ] \)
\((-\infty ;-4] \)
\( [ -4;\infty )\)
\( [ 3;\infty )\)
2010007709
Level:
A
Identify a true statement referring to the solution of the following equation.
\[
\sqrt{3x - 6} = 3
\]
The solution is an odd number.
The solution is a number divisible by the number
\(3\).
The solution is an irrational number.
The solution is not a prime number.
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).
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 \(\left \{x\in \mathbb{R} : -1 < x\leq 2 \right \}\).
2010007802
Level:
A
Find the domain of the following expression.
\[
\sqrt{\left (3x - 2 \right ) \left (4+5x\right )}
\]
\(\left(-\infty ;-\frac{4}
{5}\right] \cup \left[ \frac{2}
{3};\infty \right )\)
\(\left[ -\frac{4}
{5}; \frac{2}
{3}\right] \)
\(\left (-\infty ;-\frac{4}
{5}\right) \cup \left( \frac{2}
{3};\infty \right)\)
\(\left( -\frac{4}
{5}; \frac{2}
{3}\right) \)
9000020001
Level:
A
Find the domain of the following equation.
\[
\sqrt{2x - 5} = 3
\]
\(\left [ \frac{5}
{2};\infty \right )\)
\(\left (\frac{2}
{5};\infty \right )\)
\(\left [ -\frac{5}
{2};\infty \right )\)
\(\left (\infty ; \frac{2}
{5}\right )\)
9000020002
Level:
A
Find the domain of the following equation.
\[
\sqrt{6 - x} = 11
\]
\((-\infty ;6] \)
\((5;\infty )\)
\((-\infty ;5)\)
\([ - 6;\infty )\)