Answer:
(6, 9 ) and r = 3
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 12x - 18y + 108 = 0
Rearrange the x- terms and the y- terms together and subtract 108 from both sides, that is
x² - 12x + y² - 18y = - 108
To obtain standard form use the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(- 9)y + 81 = - 108 + 36 + 81
(x - 6)² + (y - 9)² = 9 ← in standard form
with centre = (6, 9 ) and r = 
= 3
Given at you have an equilateral triangle, all sides have the same length.
Therefore,
First side 2x-7 = Second side x+y-9 = Third side y+5
Let us look at the second and third sides for now:
x+y-9 = y+5
x = y+5 - (y-9)
x = y-y+5+9
x = 14
Then we look at equating the first and third sides:
2x-7 = y+5
y = 2x-7-5
Substitute x =14 in the equation above:
y = 2(14)-7-5
= 28-7-5
= 21-5
= 16
The length of the third side is:
y+5 = 16 +5 = 21
Given that the length of each sides are the same in an equilateral triangle, all sides have the length 21cm.
Make it a fraction
7/25 * 4/4 = 28/100
0.28 = 28 percent
There is a 28 percent chance the next marble will be red
Answer:
h = V/y^2
Step-by-step explanation:
The volume of a right pyramid is given by the expression = Area of base × height.
Area of base = Area of square at the base
= y × y = y^2.
Now, we substitute these values:
V = y^2 × height
height = V/y^2
Answer: w = 12
Step-by-step explanation: In this problem, we want to get <em>w</em> by itself on one side of the equation. Since we have <em>14 + W</em>, in order to get <em>w</em> by itself, we must subtract 14 from the left side of the equation.
If we subtract 14 from the left side of the equation, we must also subtract 14 from the right side of the equation. So on the left, +14 and -14 cancel each other and on the right, 26 - 14 simplifies to 12 so <em>w = 12</em>.
To check our answer, we substitute a 12 back in for <em>w </em>in the original equation and we have 14 + (12) = 26 or 26 = 26 which is a true statement so the answer checks.
