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9000026010

Level:

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} x & \leq 3 \\ 5 x & < 9 - 3 y \end{aligned}

\begin{aligned} x & < 3 \\ 5 x & < 9 - 3 y \end{aligned}

\begin{aligned} x & > 3 \\ 5 x & < 9 - 3 y \end{aligned}

\begin{aligned} x & \leq 3 \\ 5 x & > 9 - 3 y \end{aligned}

9000025808

Level:

In the following list identify a true statement on the function

f

f (x) = \frac{(x - 1) (x + 2)}{(2 x + 1) (3 - 2 x)}

f (x) > 0 ⟺ x \in (- 2; - \frac{1}{2}) \cup (1; \frac{3}{2})

f (x) > 0 ⟺ x \in (- \infty; - 2) \cup (- \frac{1}{2}; 1) \cup (\frac{3}{2}; \infty)

f (x) > 0 ⟺ x \in (- \infty; - 2) \cup (1; \infty)

f (x) > 0 ⟺ x \in (- 2; \frac{3}{2})

9000025809

Level:

In the following list identify a true statement on the function

f

f (x) = \frac{(6 x - 1)}{(x - 2) (3 x + 1)}

f (x) \geq 0 ⟺ x \in (- \frac{1}{3}; \frac{1}{6}] \cup (2; \infty)

f (x) \geq 0 ⟺ x \in (- \frac{1}{3}; \frac{1}{6}) \cup (2; \infty)

f (x) \geq 0 ⟺ x \in (- \infty; - \frac{1}{3}) \cup [\frac{1}{6}; 2)

f (x) \geq 0 ⟺ x \in [- \frac{1}{3}; \frac{1}{6}] \cup (2; \infty)

9000025810

Level:

In the following list identify a true statement on the function

f

f (x) = \frac{(x - 2) (3 - x)}{(2 x - 1) (3 x - 1)}

f (x) \geq 0 ⟺ x \in (\frac{1}{3}; \frac{1}{2}) \cup [2; 3]

f (x) \geq 0 ⟺ x \in [\frac{1}{3}; \frac{1}{2}] \cup [2; 3]

f (x) \geq 0 ⟺ x \in (- \infty; \frac{1}{3}) \cup [\frac{1}{2}; 2] \cup [3; \infty)

f (x) \geq 0 ⟺ x \in (\frac{1}{3}; \frac{1}{2}) \cup (2; 3)

9000028304

Level:

The following equation has solutions

x_{1} = 1

and

x_{2} = 3

. Find the sum of the remaining real solutions.

x^{4} - 12 x^{3} + 47 x^{2} - 72 x + 36 = 0

8

- 1

3

5

9000028305

Level:

The following equation has solution

x_{1} = 2

and

x_{2} = 4

. Find the sum of the remaining real solutions.

x^{4} - 6 x^{3} - x^{2} + 54 x - 72 = 0

0

- 1

1

2

9000025807

Level:

In the following list identify a true statement on the function

f

f (x) = \frac{- 2 (3 x + 1)}{(2 x + 3) (2 - x)}

f (x) > 0 ⟺ x \in (- \frac{3}{2}; - \frac{1}{3}) \cup (2; \infty)

f (x) > 0 ⟺ x \in (- \infty; - \frac{3}{2}) \cup (- \frac{1}{3}; 2)

f (x) > 0 ⟺ x \in (- \frac{3}{2}; 2)

f (x) > 0 ⟺ x \in (- \infty; - \frac{3}{2}) \cup (2; \infty)

9000026001

Level:

Which part of the plane describes the solution of the following system of inequalities?

\begin{aligned} x + y \leq & 3 \\ y - 2 x < & - 1 \end{aligned}

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green

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9000026002

Level:

Which part of the plane describes the solution of the following system of inequalities?

\begin{aligned} x + y > & 2 + x \\ y + 1 \leq & x + 1 \end{aligned}

green

red

yellow

blue

9000026003

Level:

Which part of the plane describes the solution of the following system of inequalities?

\begin{aligned} 2 x - y \geq & 2 \\ 2 x + y \geq & - 2 \end{aligned}

yellow

red

green

blue

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