Question

The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answerJanet and Michelle begin walking at the same time from the same point. Janet walks directly north, and Michellewalks directly east. At the point they are 10 km apart, Michelle has walked 2 km farther than Janet has walked. Howfar has Michelle walked? A:6 kmB:10 kmC:8 kmD: 12 km

Answer 1

From the Pythagorean theorem, we can relate the values:

$\begin{gathered} A^2+B^2=C^2 \\ \\ \mleft(x-2\mright)^2+x^2=10^2 \\ \\ x^2-4x+4+x^2=100 \\ \\ 2x^2-4x-96=0 \\ \\ x^2-2x-48=0 \end{gathered}$

We can rewrite the expression as it follows:

$\begin{gathered} x^2-2x-48=(x+6)\times(x-8) \\ \\ (x+6)\times(x-8)=0 \end{gathered}$

If we name this expression as: A: (x + 6) and B: (x - 8)

We now have:

$A\times B=0$

The only way for this expression to be zero is if A of B, or both equal zero. From this, we have:

$\begin{gathered} x+6=0\rightarrow x=-6 \\ \\ x-8=0\rightarrow x=8 \end{gathered}$

The first answer, x = - 6, has no real meaning because there no sense someone waked a negative amount of kilometers. From this, we know that Michelle walked 8 km.

The answer, as explained, is C: 8km.