2010015701
Level:
A
\( S \) is the midpoint of \( AB \). \( B = [3; -5] \), \( S = [0; -7] \). Find the coordinates of \( A \).
\( A = [-3; -9] \)
\( A = [1.5; -6] \)
\( A = [3; -12] \)
\( A = [-3; -2] \)
A
2010015607
Level:
A
The rectangular box \( ABCDA'B'C'D' \) has edges of lengths \( |AB|=5\,\mathrm{cm} \) and \( |BC|=6\,\mathrm{cm} \). The distance between the center of the top face \(A'B'C'D'\) and the center of the bottom face \(ABCD\) is \(12\,\mathrm{cm}\). Find the length of the diagonal \(DC'\).
\( 13\,\mathrm{cm} \)
\( 6\sqrt5 \,\mathrm{cm} \)
\( \sqrt{119}\,\mathrm{cm} \)
\(6 \sqrt{3}\,\mathrm{cm} \)
2010015606
Level:
A
The rectangular box \( ABCDA'B'C'D' \) has edges of lengths \( |AB|=4\sqrt3\,\mathrm{cm} \) and \( |BC|=8\,\mathrm{cm} \). The point \(S\) is the center of the lateral face \(ADD'A'\) (see the picture) and the length of the line segment \(B'S\) is \(10\,\mathrm{cm}\). Find the distance between the points \(A\) and \(A'\).
\( 12\,\mathrm{cm} \)
\( 6\,\mathrm{cm} \)
\( \sqrt{164}\,\mathrm{cm} \)
\( \sqrt{272}\,\mathrm{cm} \)
2010015605
Level:
A
The rectangular box \( ABCDA'B'C'D' \) has edges of lengths \( |AB|=6\,\mathrm{cm} \) and \( |BC|=8\,\mathrm{cm} \). The point \(S\) is the center of the base \(ABCD\) (see the picture) and the length of the line segment \(A'S\) is \(13\,\mathrm{cm}\). Find the distance between the points \(A\) and \(A'\).
\( 12\,\mathrm{cm} \)
\( \sqrt{194}\,\mathrm{cm} \)
\( \sqrt{69}\,\mathrm{cm} \)
\( 4\sqrt{10}\,\mathrm{cm} \)
2010015407
Level:
A
Find the solution set of the following equation.
\[x\sqrt5 -2\sqrt{10}x=-35\]
\( \left\{ \sqrt5+2\sqrt{10}\right\}\)
\( \left\{ \sqrt5-2\sqrt{10}\right\}\)
\( \left\{ -\sqrt5+\sqrt{10}\right\}\)
\( \left\{ \sqrt5-\sqrt{10}\right\}\)
2010015406
Level:
A
Find the solution set of the following equation.
\[2\sqrt2 x-5 =x\sqrt3\]
\( \left\{ 2\sqrt2+\sqrt3\right\}\)
\( \left\{ 2\sqrt2-\sqrt3\right\}\)
\( \left\{ \sqrt2+\sqrt3\right\}\)
\( \left\{ \sqrt2-\sqrt3\right\}\)
2010015403
Level:
A
Choose the equation whose graphical solution is in the picture.
\( -\frac49x+1=\frac29x-2\)
\( -\frac94x+1=\frac29x-2\)
\( -\frac49x+1=\frac92x-2\)
\( -\frac94x+1=\frac92x-2\)
2010015402
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac25x-2=-4x+4\)
\( \frac52x-2=-4x+4\)
\( \frac12x-2=-x+4\)
\( \frac25x-2=-x+4\)
2010015401
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac12x+2=5-x\)
\( x+2=-x+5 \)
\( \frac14x+2=5-x \)
\( -x+2=5-\frac12x \)
2010015209
Level:
A
What is the measure of the angle \( \alpha \)? (See the picture.)
\( 72^{\circ} \)
\(44^{\circ}\)
\(88^{\circ}\)
\(108^{\circ}\)