A

9000020910

Level: 
A
The perimeter of a rectangle is \(28\, \mathrm{cm}\). The diagonal of this rectangle is \(10\, \mathrm{cm}\). Find the sides of the rectangle.
\(8\, \mathrm{cm}\) and \(6\, \mathrm{cm}\)
\(7\, \mathrm{cm}\) and \(7\, \mathrm{cm}\)
\(9\, \mathrm{cm}\) and \(5\, \mathrm{cm}\)
\(7\, \mathrm{cm}\) and \(3\, \mathrm{cm}\)

9000020906

Level: 
A
Identify an equation which can be obtained from the following system by eliminating one of the variables. \[ \begin{alignedat}{80} &y^{2} & - &2 &x & + &3 & = 0 & & & & & & & & \\ &x & - & &y & - &1 & = 0 & & & & & & & & \\\end{alignedat}\]
\((y - 1)^{2} = 0\)
\((y + 1)^{2} = 0\)
\((x - 4)^{2} = 0\)
\((x + 2)^{2} = 0\)

9000020408

Level: 
A
Which of the given equations have at least one root the same? \[ \begin{aligned} x^{2} + 8x + 15 & = 0 &\text{(1)} \\x^{2} - 8x + 15 & = 0 &\text{(2)} \\x^{2} +\phantom{ 8}x - 12 & = 0 &\text{(3)} \\x^{2} - 2x -\phantom{ 1}8 & = 0 &\text{(4)} \\\end{aligned}\]
equations (2) and (3)
equations (1) and (3)
equations (2) and (4)
Such a pair does not exist.