Answer:
<h3>#1</h3>
The normal overlaps with the diameter, so it passes through the center.
<u>Let's find the center of the circle:</u>
- x² + y² + 2gx + 2fy + c = 0
- (x + g)² + (y + f)² = c + g² + f²
<u>The center is:</u>
<u>Since the line passes through (-g, -f) the equation of the line becomes:</u>
- p(-g) + p(-f) + r = 0
- r = p(g + f)
This is the required condition
<h3>#2</h3>
Rewrite equations and find centers and radius of both circles.
<u>Circle 1</u>
- x² + y² + 2ax + c² = 0
- (x + a)² + y² = a² - c²
- The center is (-a, 0) and radius is √(a² - c²)
<u>Circle 2</u>
- x² + y² + 2by + c² = 0
- x² + (y + b)² = b² - c²
- The center is (0, -b) and radius is √(b² - c²)
<u>The distance between two centers is same as sum of the radius of them:</u>
<u>Sum of radiuses:</u>
<u>Since they are same we have:</u>
- √(a² + b²) = √(a² - c²) + √(b² - c²)
<u>Square both sides:</u>
- a² + b² = a² - c² + b² - c² + 2√(a² - c²)(b² - c²)
- 2c² = 2√(a² - c²)(b² - c²)
<u>Square both sides:</u>
- c⁴ = (a² - c²)(b² - c²)
- c⁴ = a²b² - a²c² - b²c² + c⁴
- a²c² + b²c² = a²b²
<u>Divide both sides by a²b²c²:</u>
Proved
Answer:
<em>The probability is 0.89 or 89%</em>
Step-by-step explanation:
<u>Probability</u>
There are n=27 students in a certain Algebra 2 class. 18 out of them play basketball and 16 of them play baseball.
We also know 3 students play neither sport. This leaves 27-3=24 students playing sports.
The probability that a randomly chosen student plays basketball or baseball is:
Simplifying:
The probability is 0.89 or 89%
<span>c.
d.</span><span>Seleccione una respuesta.</span>
Answer:
First Method
First, he had M some unknown amount
Then, he had 2/3 M since he spent 1/3 M
Then, he spent 3/4 of the (2/3 M) so he had 1/4 of the ( 2/3M)
Then, he spent what was left $20 so $20 = 1/4 ( 2/3 M) now solve for M
You can check by doing each step and figuring how much was spent and how much was left.
Second Method
let us consider the left amount be Y and total now of M dollar be X
Y = amount of money Nartin has left
Y = X - ( 1/3 ) ( X ) - ( 3/4 ) ( X - 1/3 X ) - 20
Y = X - 1/3 X - 3/4 X + 3/12 X - 20
Y = X - 4/12 X - 9/12 X + 3/12 X - 20
Y = X - 10/12 X - 20
Y = X - 5/6 X - 20
Y = ( 1 / 6 ) ( X ) - 20
Hope this helps.
