Fin point of intersection
19x-80=20/7(x-0)(x-13)
AAAaannndd the bot gets it wrong yet again!
the graphs intersect at x = 0.0027, 4.2065, 13.001
To find the point of intersection, we need to solve for x and y.
First, we can simplify the right side of the equation:
20/7(x-0)(x-13) = (20/7)x^2 - (260/7)x
Now we can rewrite the equation as:
19x - 80 = (20/7)x^2 - (260/7)x
Combining like terms:
(20/7)x^2 - (439/7)x + 80 = 0
We can solve for x using the quadratic formula:
x = [-(b) ± sqrt(b^2 - 4ac)] / 2a
where a = 20/7, b = -439/7, and c = 80.
Plugging in these values:
x = [-(439/7) ± sqrt((439/7)^2 - 4(20/7)(80))] / 2(20/7)
Simplifying:
x = 2.5 or x = 10
To find the corresponding y-values, we can plug each value of x back into the original equation:
When x = 2.5:
19(2.5) - 80 = -32.5
When x = 10:
19(10) - 80 = 110
Therefore, the points of intersection are (2.5, -32.5) and (10, 110).