C

2000017705

Level: 
C
The interval \( \left[ -\frac{12}{11}; \frac6{23}\right)\) is the solution of a system of two linear inequalities with one unknown. Which of the following systems is it?
\(\begin{aligned} \frac{x}3-\frac{x}4 &> 2x-\frac12 \\ 3x+8 &\geq 2-\frac52x \end{aligned}\)
\(\begin{aligned} \frac{x}3-\frac{x}4 &\geq 2x-\frac12\\ 3x+8 &> 2-\frac52x \end{aligned}\)
\(\begin{aligned} \frac{x}3-\frac{x}4& < 2x-\frac12 \\ 3x+8 &\geq 2-\frac52x \end{aligned}\)
\(\begin{aligned} \frac{x}3-\frac{x}4 &> 2x-\frac12 \\ 3x+8 &\leq 2-\frac52x \end{aligned}\)

2000017704

Level: 
C
Assuming \( x \in \mathbb{R}\), find the solution set of the following system of inequalities. \[\begin{aligned} 2x- [x-(2x+1)]\cdot 3 &> (3+x)-2(1-x)-2x+6 \\ x^2-3\cdot [x-2x(1-x)] &< 5(10-x^2)-2x \end{aligned}\]
\( (1;10)\)
\( \emptyset \)
\( (-10;1)\)
\( \{1;10\}\)

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 \(5\). \[ \left (\array{ 4 & b & -1\cr 3 &0& 2\cr b & 0 & -1\cr } \right ) \]
\( \left\{1;-\frac52\right\}\)
\( \left\{-\frac52\right\}\)
\( \left\{1\right\}\)
\( \emptyset\)