-7x - 2y = 14 6x + 6y = 18 x = y =
1 answer:
You might be interested in
Answer: B. x = 40
Step-by-step explanation:
The angles given are supplementary.
Supplementary angles are any two angles that add to 180 degrees, most commonly seen on one side of a straight line.
As these angles are supplementary, we can solve for x by adding both angles to get 180:
This means that the angle on the left is (3*40) + 15, or 135 degrees, while the angle on the right is 45 degrees. These angles add to 180 degrees.
The correct answer choice is B.
Answer:
- p = -3
- v: (4, -1)
- f: (4, -4)
- d: y = 2
Step-by-step explanation:
The equation ...
(x -h)² = 4p(y -k)
is the equation of a parabola with vertex (h, k) and vertex-focus distance of p. When p is negative (as here), it means the focus is below the vertex, and the parabola opens downward. The directrix is p units on the other side of the vertex from the focus.
The vertex for equation ...
(x -4)² = -12(y +1)
is (h, k) = (4, -1). The value of p is (-12/4) = -3, so the focus is (4, -1-3) = (4, -4), and the directrix is y = -1+3 = 2.
_____
<em>Additional comment</em>
As a check on the graph, you can remember that any point on the parabola is equidistant from the focus and directrix. You will notice the vertex is halfway between the focus and directrix, so you know that relationship is true there.
You will also notice that a horizontal line from the focus to the parabola intersects the same distance away from the focus as from the directrix. Thus the parabola distance relation holds at that point as well.
