We need to find the base x in the following equation:
First, lets convert 365 from base 7 to base 10. This is given by
where the upperindex denotes the position of eah number. This gives
that is, 365 based 7 is equal to 194 bases 10.
Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:
where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives
Now, we have all number in base 10. Then, our first equation can be written in base 10 as
For simplicity, we can omit the 10 and get
so, we can solve this equation for x. By combining similar terms. we have
and by moving 197 to the right hand side, we obtain
Finally, we get
Therefore, the solution is x=5
Answer:
because they are both in the circle
Step-by-step explanation:
Melanie said:
Every angle bisector in a triangle bisects the opposite side perpendicularly.
A 'counterexample' would show an angle bisector in a triangle that DOESN'T
bisect the opposite side perpendicularly.
See my attached drawing of a counterexample.
Both of the triangles that Melanie examined have
equal sides on both sides
of the angle bisector. That's the only way that the angle bisector can bisect
the opposite side perpendicularly. Melanie didn't examine enough different
triangles.
Well, we know that y=1/2x+5 from the first equation. if we substitute that into the second equation, it becomes 2x + 1/2x +5 =1. solve for x. 2x+1/2x= -4, 2 1/2x=-4, x=-1.6. plug that in to one of the equations. 2(-1.6)+y=1, -3.2+y=1, y=-2.2. the solution is (-1.6, -2.2)
