Answer:
- circumscribed circle
- The center of a circle circumscribing the triangle connecting the 3 cities will be equidistant from all three cities.
Step-by-step explanation:
The circumscribed circle or <em>circumcircle</em> of a polygon is a circle that passes through all the vertices of the polygon. The center of the circle, the circumcenter, is equidistant from all of the polygon's vertices.
The center is found at the point of intersection between the perpendicular bisectors of any two (non-parallel) chords of the circle. That is, <em>the perpendicular bisectors of any two of the sides of the triangle joining the cities will intersect at the circumcenter</em>.
The method of locating the center of the circle this way is simple and effective.
Answer:
3rd option
Step-by-step explanation:
So we are given the following points:
(1,5)
(2,15)
(3,45)
(4,135)
This is a geometric sequence because there is a common ratio, 3. That is you can keep multiply 3 to a previous y-coordinate to get the next y-coordinate.
The formula for a geometric sequence is 
where 
is the first term and r is the common ration.
So we have
.
If you want to know the fifth term, just plug in 5:
Simplifying:
To solve this we use trigonometric functions that would relate the hypotenuse y and the given values. For this case we use cosine function which is expressed as:
cosine theta = adjacent side / hypotenuse
cosine 52 = 35 / y
y = 35 / cos 52
y = 56.85
Y = 0.213x – 352.0 <span> represents this linear model shown in the data table.
Plug in the values of x into the equation for a double check.
Let's try 1980.
</span><span>y = 0.213(1980) – 352.0
</span>y = 69.74
which is closest to the 70.1 whereas other options do not satisfy the condition.
