Answer:Yes, it is
Step-by-step explanation:
2^2+4(2)-12=0
4+8-12=0
12-12=0
0=0
No graph, so cannot be precise.
But you can apply rotation 270 CCW = rotation -90 CCW
r_[90] : (x,y) -> (y,-x)
Answer:
yah if all your grades are A's and B's
Step-by-step explanation:
Answer: Choice B (31, 52)
--------------------------------------
Explanation:
To go from the point (1,2) to (4,7) we do two things:
A) Move 3 units to the right
B) Move 5 units up
Applying the scale factor will multiply those movement steps by 10. So instead of "3 units to the right" we'll go "30 units to the right" since 3*10 = 30. Similarly, we'll move 50 units up instead of 5 (5*10 = 50)
So if we start at (1,2) and move 30 units to the right and 50 units up, then we'll land on (31, 52) which is the image point for the preimage (4,7)
This is why the answer is choice B
-------------
Note: We can alternatively shift both initial points to the left 1 and down 2 so that (1,2) lands on the origin (0,0). That means (4,7) turns into (3,5). Apply the scale factor through multiplying both coordinates by 10. This works only because the reference point is the origin. We end up with (30,50). Now undo the "left 1 and down 2" to "move right 1, up 2" and we arrive at (31,52) which is the same answer as before. So this is further confirmation that the answer is choice B
Direct variation: y=kx where k is some number thats not 0
that means if x is 2, y is 2k. if x is 1, y is k. if x is 0, y is 0.
notice: no matter what k is, when you put 0 in for x, y will always be 0. that means that a direct variation always goes through the origin, a.k.a. (0,0).
do all lines go through the origin? nah. a line is y=mx+b, where m and b are some numbers. a line is only a direct variation if b is 0. this makes sense because if b is 0, then the y-intercept is 0, so the line goes through the origin.
in conclusion, no, not all linear relationships are direct varations, but all direct variations are linear relationships.
