C

2000017703

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?
\(\begin{aligned} 3x-4y &>6\\ -1.5x+2y &< 5 \end{aligned}\)
\(\begin{aligned} 3x-4y &< 6\\ -1.5x+2y& < 5 \end{aligned}\)
\(\begin{aligned} 3x-4y &< 6\\ -1.5x+2y &> 5 \end{aligned}\)
\(\begin{aligned} 3x-4y &> 6\\ -1.5x+2y& > 5 \end{aligned}\)

2000017702

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?
\(\begin{aligned} 5x+8y& \leq 27 \\ 9x+2y &< -15 \end{aligned}\)
\(\begin{aligned} 5x+8y &< 27 \\ 9x+2y &\leq -15 \end{aligned}\)
\(\begin{aligned} 5x+8y &\geq 27\\ 9x+2y &> -15 \end{aligned}\)
\(\begin{aligned} 5x+8y &> 27 \\ 9x+2y &\geq -15 \end{aligned}\)

2000017606

Level: 
C
Determine the set of all real numbers \(b\) for which the determinant of the following matrix equals to \(5\). \[ \left (\array{ 4 & b & -1\cr 3 &0& 2\cr b & 0 & -1\cr } \right ) \]
\( \left\{1;-\frac52\right\}\)
\( \left\{-\frac52\right\}\)
\( \left\{1\right\}\)
\( \emptyset\)

2000017604

Level: 
C
Which of the given matrices \(A\), \(B\), \(C\) and \(D\) has a different determinant than the others? \[ A=\left (\array{ 6 & 11 \cr 2 & 2\cr } \right ) \] \[ B=\left (\array{ 1 & 3 \cr 5 & 2\cr } \right ) \] \[ C=\left (\array{ 5 & -2 \cr 10 & -6\cr } \right ) \] \[ D=\left (\array{ 10 & 0 \cr -7 & -1\cr } \right ) \]
\( B\)
\( D\)
All given matrices have the same determinant.
Each matrix has a different determinant.