Answer:
(x-1)^2+(y+19/8)^2=2665/64
Step-by-step explanation:
The general equation of a circle is
(x - h)^2 + (y - k)^2 = r^2
Substituting the values of the 3 given points:
(-5 - h)^2 + (0 - k)^2 = r^2
(0 - h)^2 + (4 - k)^2 = r^2
(2 - h)^2 + (4 -k)^2 = r^2
Subtracting the second equation from the first:
(-5-h)^2 - h^2 + k^2 - (4 - k)^2 = 0
25 + 10h + h^2 - h^2 + k^2 - 16 + 8k - k^2 = 0
10h + 8k = -9 ------------ (A).
Subtract the third equation for the second:
h^2 - (2 - h)^2 + 0 = 0
h^2 - 4 + 4h - h^2 = 0
4h = 4
h = 1.
Substituting for h in equation A:
10 + 8k = -9
8k = -19
k = -19/8
So r^2 = (-5-1)^2 + (0 + 19/8)^2 =
36 + 361/ 64
= 2665/64
Move the -4 to the right (+4 on both sides). now you have 4y=20. divide both sides by 4. y=5
Answer:
- length: 14 feet , width: 43 feet, or
- length: 86 feet, width: 7 feet
Both solutions are valid.
Explanation:
1. First assumption is that the shape of the fence is <u>rectangular</u>.
2. Second, assum the length parallel to the wall measure y feet, so the other two lengths, y, together with x will add up 100 feet
3. The, the area of the fence will be:
- length × width = xy = 600
4. Now you have two equation with two variables which you can solveL
- Solve for y in the first equation: y = 100 - 2x
- Substitute the value of y into the second equation: x (100 - 2x) = 600
5. Solve the last equation by completing squares:
- Distributive property: 100x - 2x² = 600
- Divide both sides by - 1: 2x² - 100x = - 600
- Divide both sides by 2: x² - 50x = -300
- Add the sequare of the half of 50 to both sides: x² - 50x + 625 = 325
- Factor the left side: (x - 25)² = 325
- Square root both sides: x - 25 = ± 18.028
- Clear x: x = 25 ± 18.028
- x = 43.028 ≈ 43 or x = 6.972 ≈ 7
Both values are valid,
If x = 43 , then y = 600/43 = 14
If x = 7, then y = 600/7 = 86
Thus, the lenght and width of the fence may be:
- 43 feet (width) and 14 feet (length), or
- 7 feet (width) and 86 feet (length).
Answer:
6 and 11/25
Step-by-step explanation:
Turn demical number into an unreduced fraction, or 6 and 44/100. Then, reduce the fraction to simplest terms via dividing by a common factor. In this case, 11.
