Check the picture.
since the choices all have rotation about the origin, we must shift the original triangle in a suitable position. This is done by connecting any of the points of A'B'C' to the origin, and extend this line segment, as shown in the picture.
The most appropriate point is C', and we draw C" such that C'O=OC", and C', O and C" are collinear.
We see that the distance CC'' is 5.
So
Answer is:
"<span>A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin</span>"
37* 4.75 =175.75
no overtime since there are no hours over 50
Answer: $175.75
Answer:
Step-by-step explanation:
The vertices lie on the x-axis, as is determined by their coordinates. This makes the center of this hyperbola (0, 0) because the center is directly between the vertices. The fact that the foci also lie on the x-axis tells us that this is the main axis. What this also tells us is which way the hyperbola "opens". This one opens to the left and the right as opposed to up and down. The standard form for this hyperbola is:
and so far we have that h = 0 and k = 0.
By definition, a is the distance between the center and the vertices. So a = 5, and a-squared is 25. So we're getting there. Now here's the tricky part.
The expressions for the foci are (h-c, k) and (h+c, k). Since we know the foci lie at +/-13, we can use that to solve for c:
If h+c = 13 and h = 0, then
0 + c = 13 and c = 13.
We need that c value to help us find b:
and
and
and
so
b = 12. Now we're ready to fill in the equation:
and there you go!
7x+4 is the correct awnser(i think)
Yes 678.05 is greater than 67.805 (because obviously 678 is greater than 67 right? ^ - ^)