Answer: Option C - Construction Y because point E is the circumcentre of triangle LMN.
Point E is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.
Step-by-step explanation:
Before solving an algebra problem, it sometimes helps to get a geometric picture of what's happening. Geometry says that three points determine a circle - in other words, given three points that are not
all on the same line, there is exactly one circle which passes through all 3. Finding the point equidistant from the 3 points is the same thing as finding the center of the circle that passes through all of them (since all points on a circle are equidistant from the center).
Our points are L, M and N. Draw the lines LM, LN and MN to form a triangle. Now construct the perpendicular bisectors of any two of the lines, and their intersection, point E, will be the center of this circle.
As shown in the Construction Y because E is the circumcentre of triangle LMN.
This is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.
QED!
Answer:
y = x^2 - 4
Step-by-step explanation:
The vertex of a parabola is exactly halfway between the focus and the directrix. If the focus is at (0, -6) and the directrix is the line y = -2, then we do this to locate the vertex: Draw a vertical line through (0, -6) also crossing the line y = -2. The y value halfway between y = -6 and y = -2 is y = -4, and the vertex is thus (0, -4).
Using the vertex method, write out the equation of this parabola, starting with the general form y - k = (x-h)^2, where (h, k) is the vertex. Here h = 0 and k = -4
We get: y + 4 = (x - 0)^2, or y + 4 = x^2, or y = x^2 - 4. As a check, let x = 0; y = -4, which is the y-coordinate of the vertex.
PROBLEM 9:
0.25
PROBLEM 8:
3/14
PROBLEM 7:
1 1/12 or 13/12
Answer:
1
Step-by-step explanation:
One-half two times is equal to 2/2, or 1.