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.
Answer:
C
Step-by-step explanation:
Answer:
3.8
Step-by-step explanation:
A train averages a speed of 90 miles per hour across the plains and 37.5 miles per hour through the mountains.
If a trip of 300 miles took 3 hour and 48 minutes, how much of it was through the mountains?
Let d = distance traveled at 37.5 (thru the mountains)
then
(300-d) = distance traveled at 90 mph
Write a time equation, time = dist/speed
change 3 hr 48 min to hrs: 3 + 48/60 = 3.8 hrs
plain time + mountain time = 3.8 hrs
%28300-d%29%2F90 + d%2F37.5 = 3.8
Multiply 90*37.5
3375*%28300-d%29%2F90 + 3375*d%2F37.5 = 3.8(3375)
cancel the denominator
37.5(300-d) + 90d = 12825
11250 - 37.5d + 90d = 12825
52.5d = 1575
d = 1575/52.5
d = 30 mi thru the mountains
Check this, find the distance on the plain
300-30 = 270 mi
Find the actual time at each speed
270/90 = 3 hrs
30/37.5 = .8 hrs
-----------------
total time: 3.8 hrs
The answer is 3 ft
The surface area (SA) of a cylinder with radius r and height h is:
SA = 2πr² + 2πrh = π(2r² + 2rh)
We have:
SA = 126π ft²
h = 3 * d
d = 2r
h = 3 * 2r = 6r
126π = π(2r² + 2rh)
126 = 2r² + 2rh
126 = 2r² + 2r * 6r
126 = 2r² + 12r²
126 = 14r²
r² = 126/14
r² = 9
r = √9
r = 3
Answer: 30 degrees
Step-by-step explanation:
Corresponding angles of similar triangles are congruent.
