You need to find points where the line g(x) intercepts the quadratic function f(x) in one and only one point.
Then 3x^2 + 4x -2 = mx - 5
solve 3x^2 + 4x - mx -2 + 5 = 0
3x^2 + (4 - m)x + 3 = 0
In order to there be only one solution (one intersection point) the radicand of the quadratic formula must be 0 =>
b^2 - 4ac = (4 - m)^2 - 4(3)(3) = 0
(4 - m)^2 = 24
4 - m = +/- √(24)
m = 4 +/- √(24) = 4 +/- 2√(6)
Then m, the slope of the line, may be 4 + 2√6 and 4 - 2√6
If it is a rhombus then you know each side is the same length, so only have to work out one side. To do this you have to use Pythagoras' theorem (a^2 + b^2 = c^2)
So take two sets of coordinates, for example, (0,3) and (5,3), a and b represent the height difference and the length difference. Therefore (5-0)^2 + (3-3)^2 = c^2
c^2 = 25
c = 5 , which would be the side of the rhombus
Hm..I'm pretty sure the answer is 34
To find this you multiply the 2 numbers together. 3*3/4=2.25.
2.25 in fraction form is
