Answer:
Yes
Step-by-step explanation:
1/2 + 6/6
= (1*3)/(2*3) + 6/6
= 3/6 + 6/6
= 9/6
= 3/2
So the fraction 1/2 make the equation true.
Answer:
A. P' = (9, -2)
B. P" = (1, -4)
Step-by-step explanation:
To make it easier to understand, make point C the origin (0 , 0). From that, you will notice point P is 3 units right and 5 units up of point C, meaning the coordinates of point P is (3, 5). A 90° rotation clockwise on point P (3, 5) is (5, -3). Since point C is 4 units right and 1 unit up from the actual origin, we will add that to (5,-3); (5 + 4, -3 + 1) = (9, -2). Therefore, P' = (9, -2).
Knowing the coordinates of P' allows us to figure out the coordinates of P''. Once again, we'll make point C the origin, meaning P' would be at (5, -3). Like we did before, we will perform a 90° rotation clockwise of (5, -3) to get (-3, -5). Lastly, add back the appropriate amount of units to (-3, -5) to make point C the center of rotation in this example; (-3 + 4, -5 + 1) = (1, -4). Therefore, P" = (1, -4).
Please note that this is only my method of solving translations. Please consult more official sources if you want to learn more. Other than that, I hope this helps!
So we have v(w) = 2w - 1
Now we make the following change: w ---> w +3.
So we change every "w" into a "w+3" as follows:
v(w) = 2w - 1 --------> v(w+3) = 2*(w+3) - 1
Let's solve this.
2*(w+3) - 1
2*w + 2*3 - 1
2w + 6 - 1
2w + 5
So
v(w+3) = 2w + 5
