High school

Answer all the questions below and press submit to see how many you got right.

id: 7924
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We look at a triangle with corners A,B and C. We call the sides opposite of A,B and C a, b and c and the midpoints of a,b,c D,E and F. Select all the statements that are true.

  • AD, BE and CF intersect in a point Z that cuts these line segments in the ratio 2:1.
    If AD and BE cross in X, AD and CF in Y and BE and CF in Z the XYZ is a right triangle.
    If AD, BE and CF intersect in a point Z, ABC is a right triangle.
    AD, BE and CF intersect in a point Z that cuts these line segments in the ratio 1:1.
id: 16899

What does the triangle inequality state for vectors $x,y$ in $\mathbb{R}^{18}?$

  • $\lVert x+y\rVert\leq\lvert x\cdot y\rvert$
    $\lVert x+y\rVert\geq\lVert x\rVert+\lVert y\rVert$
    $\lVert x+y\rVert\geq\lvert x\cdot y\rvert$
    $\lVert x+y\rVert\leq\lVert x\rVert+\lVert y\rVert$
id: 16803

Which of the following is a basis of $\mathbb{R}^3?$

  • $\{\left(\begin{smallmatrix}2\\0\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\1\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\0\\5\\\end{smallmatrix}\right)\}$
    $\{\left(\begin{smallmatrix}2\\0\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\1\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}2\\-5\\0\\\end{smallmatrix}\right)\}$
    $\{\left(\begin{smallmatrix}2\\0\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}5\\4\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}5\\4\\3\\\end{smallmatrix}\right)\}$
    $\{\left(\begin{smallmatrix}1\\5\\5\\\end{smallmatrix}\right),\left(\begin{smallmatrix}5\\2\\-4\\\end{smallmatrix}\right),\left(\begin{smallmatrix}6\\7\\1\\\end{smallmatrix}\right)\}$