Answer:
idk just google it :)
Step-by-step explanation:
1. google it
Where are the answers?
Step-by-step explanation:
4x + 2y = 8 (1)
8x + 4y = -4y (2)
A) Two lines are parallel if they have the same gradient
- putting both equations into the gradient- intercept form ( y = mx + c where m is the gradient)
(1) 4x + 2y = 8
2y = 8 - 4x
y = -2x + 4
(2) 8x + 4y = -4y
<span> </span>8x = -4y - 4y
y =
y = -x
<span>
Thus the gradient of the two equations are different and as such the two lines are not parallel</span>
B) When two lines are perpendicular, the product of their gradient is -1
p = (-2) * (-1)
p = 2
<span> ∴
the two lines are not perpendicular either.</span>
Thus these lines are SKEWED LINES
R = { (x,y): 3x-y=0 }
The condition is 3x=y so that's not going to be any of these things.
R is reflexive if (x,x)∈R for all x. Let's check.
3x - y = 3x - x = 2x ≠ 0 necessarily. NOT REFLEXIVE
R is symmetric if (x,y)∈R → (y,x)∈R. Let's check.
(x,y)∈R so
3x-y = 0
y = 3x
Is (y,x)∈R. That would be true if 3y-x=0
3y - x = 3(3x) - x = 8x ≠ 0 necessarily NOT SYMMETRIC
R is transitive if (x,y)∈R and (y,z)∈R → (x,z)∈R. Let's check.
3x-y = 0 so y=3x
3y-z = 0 so z=3y = 9x
3x - z = 3x - 9x = -6x ≠ 0 necessarily NOT TRANSITIVE