Answer:
See below for graphs
- (2, -3), r = 2 (blue)
- (-3, -1), r = 1 (green)
- (3, -1), r = 3 (purple)
- (4, 1), r = 3 (red)
Step-by-step explanation:
I like to solve a set of problems like this once, then use a calculator or spreadsheet to crunch the numbers.
We can start with the general form of the equation for a circle:
x^2 +y^2 +ax +by +c = 0
Completing the square gives ...
(x^2 +ax +(a/2)^2) +(y^2 +by +(b/2)^2) = (a/2)^2 +(b/2)^2 -c
(x +(a/2))^2 +(y +(b/2))^2 = (a/2)^2 +(b/2)^2 -c
Comparing this to the standard form formula ...
(x -h)^2 + (y -k)^2 = r^2
we see the relations are ...
- h = -a/2
- k = -b/2
- r = √((a/2)² +(b/2)² -c)
where (h, k) is the center and r is the radius.
Then your circle centers and radii are ...
- (h, k) = (-(-4)/2, -6/2) = (2, -3); r = √(4+9-9) = 2
- (h, k) = (-6/2, -2/2) = (-3, -1); r = √(9+1-9) = 1
- (h, k) = (-(-6)/2, -2/2) = (3, -1); r = √(9+1-1) = 3
- (h, k) = (-(-8)/2, -(-2)/2) = (4, 1); r = √(16+1-8) = 3
Answer: 6
Step-by-step explanation: DE is 4+2 so EF would be the same if it is equal.
Answer:
$150
Step-by-step explanation:
→ Find 3/5 of 1500
( 1500 ÷ 5 ) × 3 = 900
→ Find 6/20 of 1500
( 1500 ÷ 20 ) × 6 = 450
→ Find the sum of the 2 numbers
900 + 450 = 1350
→ Minus it from the original 1500
1500 - 1350 = $150