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!
A) Yes. we don't have enough information so this can not be determined.
B) No, it would just be an outlier.
Answer: g = 10
Step-by-step explanation: 8g + 3 = –6g + 13g + 13
8g + 3 = (–6g + 13g) + (13)
8g + 3 = 7g + 13
8g + 3 - 7g = 7g + 13 - 7g
g + 3 = 13
g + 3 - 3 = 13 - 3
g = 10
From there we can see that because x equals both to a and b, it must be that a = b.
Answer: the Russell family used their sprinkler for 40 hours.
the Gonzalez family used their sprinkler for 20 hours.
Step-by-step explanation:
Let x represent the number of hours for which the Russell family used their sprinkler.
Let y represent the number of hours for which the Gonzalez family used their sprinkler.
The families used their sprinklers for a combined total of 60 hours. It means that
x + y = 60
The water output rate for the Russell family's sprinkler was 35L per hour. The water output rate for the Gonzalez family's sprinkler was 40L per hour. The total water output of both families was 2200L. It means that
35x + 40y = 2200- - - - - - - - - - --1
Substituting x = 60 - y into equation 1, it becomes.
35(60 - y) + 40y = 2200
2100 - 35y + 40y = 2200
- 35y + 40y = 2200 - 2100
5y = 100
y = 100/5
y = 20
x = 60 - y = 60 - 20
x = 40
