Since real numbers are closed with respect to division (i.e. the division between two real numbers is again a real number), the fraction 
is a real number everytime both m and n are real numbers.
In other words, you can choose any real number m and any real number n, and their ratio will still be a real number.
Of course, you have to follow the only rule that you can't divide by zero, so the answer is more precisely
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
You're pretty much screwed
Answer:
Step-by-step explanation:
(x - h) {}^{2} + (y - k) {}^{2} = {r}^{2}(x−h)
2
+(y−k)
2
=r
2
here
r = 7. (the circle is symmetrical with y - axis )
h = 0. and k = 1
Thus equation of circle is,
(x - 0) {}^{2} + (y - ( - 1)) {}^{2} = {7}^{2}(x−0)
2
+(y−(−1))
2
=7
2
x^2 + (y+1)^2 = 49
Given:
x = candy selling at 6 per pound
y = candy selling at 9 per pound
x + y = 15
6x + 9y = 15(7)
6x + 9y = 105
x = 15 - y
6(15-y) + 9y = 105
90 - 6y + 9y = 105
3y = 105 - 90
3y = 15
3y/3 = 15/3
y = 5
There should be 5 pounds of more expensive candy.
x = 15 - y
x = 15 - 5
x =10
There should be 10 pounds of less expensive candy.
