To find out if they are parallel we need to see if the gradient is the same, to do this we need to get y in terms of x:
assuming the first equation is x+y+7=0
y=-x-7
and
y=x-3
The gradient is the coefficient of x (the number infront of x)
For equation 1 the gradient is -1, and for number 2 it is 1, therefore they are not parallel.
However to check if they are perpendicular we need to see if their gradients multiply to equal -1.
-1*1=-1 therefore they are perpendicular
X^4=256
x^4-256=0
(x^2)^2-(16)^2=0
(x^2+16)(x^2-16)=0
either x^2+16=0
it gives complex roots.
or x^2-16=0
or x^2-4^2=0
(x+4)(x-4)=0
either x+4=0,x=-4
or x-4=0
x=4
7 red, 8 yellow, 9 white......total = 24 roses
probability first pick is white : 9/24
probability second pick is yellow : 8/23
probability of both : 9/24 * 8/23 = 72/552 reduces 3/23 <====
Domain: all reals, (-∝, ∝)
All inputs for x result in a solution.
