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Answer:
x=40 and y= 60
Step-by-step explanation:
<u>step:1</u>
Let 'x' and 'y' are two numbers
given data the sum of two numbers is 100
x+y = 100......(1)
Given difference of two numbers are
x - y = -20 ......(2)
<u>Step :2</u>
solving the equation (1) and (2)
adding the equations (1) and (2)
x+y+x-y=100-20
cancelling 'y' terms are
2 x = 80
dividing "2" on both sides, we get
x = 40
<u>Step :3</u>
substitute x = 40 in equation (1)
x + y =100
40 + y = 100
subtracting "40" on both sides, we get
40 + y - 40 = 100 -40
y = 60
Final answer:-
The two numbers are x = 40 and y= 60
Answer:
Step-by-step explanation:
The equation for a circle is
This should tell you that in order to write the equation for a circle, you need either the center and a point and then solve for the radius, or you need 2 points ON the circle that will help you find the center (it would be exactly between those 2 points so you could use the midpoint formula to find the center and then you would have the h and the k and can take it from there.)
The definition of a circle is the locus of all points that is equidistant from a point in space. That point in space is the center and all the points equidistance from it are ON the circle, not inside the circle.
Hope that helps.
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
Each lion has 1 head. The number of lion heads is L .
Each bird has 1 head. The number of bird heads is B.
The total number of heads of all species is (L + B) = 30
Each lion has 4 feet. The number of lion feet is 4L .
Each bird has 2 feet. The number of bird feet is 2B .
The total number of feet of all species is (4L + 2B) = 100
The system of linear equations is:
L + B = 30
4L + 2B = 100 .