The diagram shows that FG = IJ are congruent segments due to the double tickmarks. These are the hypotenuses of the right triangles.
So that takes care of the "H" in "HL".
The L stands for "leg", so we need to have a congruent pair of corresponding legs.
Due to the orientation of the triangles, it's not clear how the corresponding legs match up, but if any of the following is true
- EF = IK
- EF = JK
- EG = IK
- EG = JK
then we'd have enough to use HL.
Answer:
They are not congruent because the lines aren't parallel.
Step-by-step explanation:
For all of those angle relation theorems to be valid, PARALLEL lines need to be split by a transversal.
I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,
One possible answer is 
Another possible answer is 
There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)
So in the first example above, we would have
In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.
Similar steps will happen with the second example as well (when g(x) = x^2)
The easiest way is to try the point (-4,1), that is, x=-4, y=1,
to see which equation works.
b works.
The usual way to do it is to find the equation of the circle
standard form of a circle is (x-h)²+(y-k)²=r², (h,k) are the coordinates of the center, r is the radius.
in this case, the center is (-2,1), so (x+2)²+(y-1)²=r²
the given point (-4,1) is for you to find r: (-4+2)²+(1-1)²=r², r=2
so the equation is (x+2)²+(y-1)²=2²
expand it: x²+4x+4+y²-2y+1=4
x²+y²+4x-2y+1=0, which is answer b.
