The translation that maps triangle ABC to A prime B prime C prime would be a reflection across the y axis. This is because when you reflect something, you are pretty much flipping it. When you reflect across the y axis, you are flipping the triangle across the y axis. Take one point for example. I will use C. Notice how the point C is 3 units away from the y axis. So the same way you would move the point 3 units right from the y axis, and that would be your new point. This sounds kind of complicated, so I will give you a list of rules to make it more simple.
Reflection across y axis: (x,y) would be equal to (-x, y)
Reflection across x axis: (x,y) would be equal to (x, -y)
Reflection across y = x: (x,y) would be equal to (y,x)
Reflection across y = x: (x,y) would be equal to (-y,-x).
A reflection across y = x would be when you have a line that for every 1 it rises, it goes right 1. It is a positive line, as opposed to the y = -x line. It also has a slope of 1. I will try attaching a graph if I can.
Anyway, as I was saying. So pretty much if you don't want to go through the logic, to see whether a figure is reflected, just try each of these rules and if one works then you have your answer. Otherwise it would not be a reflection.
Thanks for being a great mod and hope this helps! :D
Answer:
d/7 = c
Step-by-step explanation:
-5c+d=2c
Add 5c to each side
-5c+5c+d=2c+5c
d = 7c
Divide each side by 7
d/7 = 7c/7
d/7 = c
The three slices are each approximately 1/9 pound in weight, and, since 2/9 is less than 1/4, he can eat 2 whole slices and be okay. If he wants to eat partial slices, then he could eat 2 1/4 slices, as each slice weighs 4/36 pounds, so 2 slices would equal 8/36 pounds, leaving 1/36 pound left over in his diet, which is a quarter of the third slice.
2.25
Answer:
c = -12
Step-by-step explanation:
Quadratic Standard Form: ax² + bx + c
Step 1: Write equation
3x² + 6x = 12
Step 2: Subtract 12 on both sides
3x² + 6x - 12 = 0
Here, we have the standard form of the quadratic. We see that our c = -12
5p-4p-8=-2+3
Combine like terms
p-8= 1
Add 8 to both sides to isolate p
p=9
Final answer: 1 solution only, p=9
