6.75
-2.25
----------
4.50
-2.25
----------
2.25
-2.25
----------
0.00
you could bowl 3 times (it starts off at 6.75 because I took away the cost of the shoes)
Answer:
Step-by-step explanation:
Here's the game plan. In order to find a point on the x-axis that makes AC = BC, we need to find the midpoint of AB and the slope of AB. From there, we can find the equation of the line that is perpendicular to AB so we can then fit a 0 in for y and solve for x. This final coordinate will be the answer you're looking for. First and foremost, the midpoint of AB:
and
Now for the slope of AB:
and
So if the slope of AB is 1/3, then the slope of a line perpendicular to that line is -3. What we are finding now is the equation of the line perpendicular to AB and going through (0, 3):
and filling in:
y - 3 = -3(x - 0) and
y - 3 = -3x + 0 and
y - 3 = -3x so
y = -3x + 3. Filling in a 0 for y will give us the coordinate we want for the x-intercept (the point where this line goes through the x-axis):
0 = -3x + 3 and
-3 = -3x so
x = 1
The coordinate on the x-axis such that AC = BC is (1, 0)
Income of the first account after x years:
Income of the second account after x years:
Equating the above tw values we get the equation:
Solving the above equation for x:
Answer 8 years.
