9000023801
Level:
A
Find the sum of the solutions of the following equation.
\[
\sqrt{x - 2} = \frac{x}
{3}
\]
\(9\)
\(3\)
\(6\)
\(12\)
A
9000023707
Level:
A
Identify a true statement which concerns the following equation.
\[
\sqrt{3x - 5} = 4
\]
The solution is a prime number.
The solution is from the interval \([ - 5;5] \).
The solution is from the set \(A = \left \{x\in \mathbb{R} : -4 < x\leq 3\right \}\).
The solution is a multiple of \(4\).
9000023802
Level:
A
Find the product of the solutions of the following equation.
\[
\sqrt{3x - 8} = \frac{x}
{2}
\]
\(32\)
\(4\)
\(8\)
\(16\)
9000023708
Level:
A
Identify a true statement which concerns the following equation.
\[
\sqrt{x + 5} = x - 1
\]
The solution is an even number.
The solution is from the interval \([ - 2;2)\).
The solution is from the set \(A = \left \{x\in \mathbb{R} : -1\leq x < 3\right \}\).
The solution is a divisor of \(6\).
9000023810
Level:
A
Denote by \(x_{1}\)
the solution of the equation
\[
\sqrt{6 - 2x} = -x - 1
\]
and by \(x_{2}\)
the solution of the equation
\[
\sqrt{2x + 6} = 9 - x.
\]
Identify a correct statement about \(x_{1}\)
and \(x_{2}\).
\(|x_{1}| = |x_{2}|\)
\(|x_{1}| < |x_{2}|\)
\(|x_{1}| > |x_{2}|\)
\(5|x_{1}| = |x_{2}|\)
9000023710
Level:
A
Identify a true statement which concerns the following pair of equations.
\[
\begin{aligned}
\sqrt{
2x + 17} & = 3 &\text{(1)}
\\
\sqrt{8 - 4x} & = 4 &\text{(2)}
\end{aligned}
\]
The product of the solutions of (1) and (2) is
\(8\).
The sum of the solutions of (1) and (2) is
\(- 2\).
The quotient of the solution of (1) divided by the solution of (2) is
\(- 2\).
The quotient of the solution of (2) divided by the solution of (1) is
\(- 0.5\).
9000023901
Level:
A
Solve the following system and write the solution as the ordered pair
\([x,y]\).
\[\begin{aligned}
x + y & = -1 & &
\\x - y & = 5 & &
\end{aligned}\]
\([2;-3]\)
\([-2;1]\)
\([3;-2]\)
\([-3;2]\)
9000023803
Level:
A
In the following list identify a true statement referring to the solution of the
following equation.
\[
\sqrt{x + 3} = 3 + x
\]
The difference of the bigger and smaller solutions is
\(1\).
The difference of the bigger and smaller solutions is
\(- 1\).
The difference of the smaller and the bigger solutions is
\(1\).
The difference of the smaller and twice the bigger solutions is
\(- 1\).
9000023902
Level:
A
Solve the following system and write the solution as the ordered pair
\([x,y]\).
\[\begin{aligned}
2x + y & = 2 & &
\\x + 2y & = 7 & &
\end{aligned}\]
\([-1;4]\)
\([2;-2]\)
\([1;3]\)
\([3;-4]\)
9000023804
Level:
A
Identify a true statement which concerns to the following equation.
\[
\sqrt{x + 3} = x - 3
\]
The solution is in the interval \((5;8)\).
The solution is in the interval \([ - 2;2] \).
The solution is in the interval \([ - 3;1)\).
The solution is in the interval \([ 3;5)\).