HEY THERE.
THE CORRECT ANSWER IS 36/63 = 4/7
Hope this helps you
Answer:
y = 11x
Step-by-step explanation:
We have two points so we can find the slope
(1,11) and (2,22)
m = (y2-y1)/ (x2-x1)
= (22-11)/(2-1)
= 11/1
The slope is 11
We can use the point slope form to get an equation
y-y1 = m(x-x1)
y-11 = 11(x-1)
Distribute the 11
y-11=11x -11
Add 11 to each side
y-11+11 = 11x-11+11
y = 11x
So we have 5x+15y=45
simplify and undistribute 5 from both sides
5(x+3y)=5(9)
divide both sides by 5
x+3y=9
multiply both sides by 6
6x+18y=54
if it was 6x+18y then the answer is 54
if it was 6x-18y, then I don't know the answer
Answer:
Step-by-step explanation:
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
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
