Answer:
Step-by-step explanation:
Perpendicular bisector of the chord connecting the the points (-1,2) and (2,3) is also passing through the center of the circle.
We'll find the equation of the line and solve the system to find the center.
<u>Midpoint of the chord:</u>
- ((-1 + 2)/2, (2 + 3)/2) = (0.5, 2.5)
<u>Equation of the line through chord (-1,2) and (2,3):</u>
- m = (3 - 2)/(2 + 1) = 1/3
- y - 2 = 1/3(x + 1)
- y = 1/3x + 7/3
<u>Perpendicular bisector is:</u>
- y - 2.5 = -3(x - 0.5)
- y = -3x + 4 >> (1)
<u>And the given line is:</u>
- 2x - 3y + 1 = 0
- y = 2/3x + 1/3 >> (2)
<u>Solve the system:</u>
- -3x + 4 = 2/3x + 1/3
- -9x + 12 = 2x + 1
- 11x = -11
- x = -1
<u>Find y:</u>
- y = -3(-1) + 4 = 3 + 4 = 7
The center is (-1, 7)
<u>Find the radius, the distance from center to one of points on circle </u>
- (-1, 7) and (-1, 2)
- 7 - 2 = 5
<u>The equation of circle is:</u>
- (x + 1)² + (y - 7)² = 5²
- (x + 1)² + (y - 7)² = 25
Answer:
Opposite Angles Theorem
Step-by-step explanation:
All opposite angles are congruent, meaning that two angles created by intersecting lines that oppose eachother are equal in size. The theorem goes by different names, so I don't know exactly what your teacher is asking for, but I hope I could help.
The ordered pairs are (0,4), (1,6), (2,8).
I've helped my sister with this question before and it was similar. :)
C.248,000
to find standard form if the power is positive move the decimal that many places to the right. If the power is negative move the decimal that many times to the left.
Answer:
She will have $2,698.896
Step-by-step explanation:
Principal (P) = $2200
Rate (R) = 5.2% = 0.052
t = 4 years
N = 365 (number of days in a year)
Compound interest (A) = P(1 + r/n)^nt
A = 2,200 * [ 1 + (0.052/365)]^4*365
A = 2200 * [ 1.00014]^1460
A = 2200 * 1.227
A = $2698.896
At the end of four years, she'll have $2698.896 in her account.