The equation representing the circle centered at (-27, 120) that passes through the origin is:
Solution:
The general equation of a circle is expressed as:
Where,
(a, b) denotes the center of the circle
r signifies the radius
Given the center as (-27, 120)
Thus;
a = -27
b = 120
Considering it intersects the origin, meaning (x, y) = (0, 0)
Substituting (a, b) = (-27, 120) and (x, y) = (0, 0) into the equation
Input 
= 15129 and (a, b) = (-27, 120) into the equation
Hence, the equation characterizing the circle is determined
No, mixed numbers must include both a whole number and a fraction to qualify as such. If a fraction were present, it wouldn’t sum to two due to the presence of the 1's ❤️.
Answer: The correct formulation is option A.)A = x(x − 4) − 0.5(8)(x − 4) − 4(8)
Step-by-step explanation:
To calculate the area that needs painting in the theater room in square feet, follow these steps:
1. Calculate the area of the theater room
Length: x
Width: x-4
A (area of theater room) = x (x-4)
2. Calculate the area of the right triangle
Height: x-4
Base: 8
A (area of right triangle) = 0.5 (8) (x-4)
3. Calculate the area of the rectangle designated as a closet
Length: 8
Width: 4
A (closet) = 8 (4)
4. The painted area is calculated by subtracting the areas of the right triangle and the closet from the total area of the theater room:
A= A(theater room) - A(right triangle) - A (closet)
A = x (x-4) -0.5 (8) (x - 4) - 4 (8)
Thus, the proper equation to compute the area is option A.
Solution:
30% of the workforce consists of managers.
Explanation:
Given that there are 80 employees, out of which 24 are managers, we need to determine what percentage this represents.
This percentage can be calculated using the formula below:
By plugging in the known values, we have:
Thus, 30% of the employees are managers.
Answer:
StartFraction negative 1 Over k cubed EndFraction
Detailed breakdown:
3k / (k + 1) × (k² - 1) / 3k³
= 3k(k² - 1) / (k + 1)(3k³)
= 3k³ - 3k / 3k⁴ + 3k³
= -3k / 3k⁴
= -1/k³
StartFraction k + 1 Over k squared EndFraction
(k + 1) / k²
StartFraction k minus 1 Over k squared EndFraction
(k - 1)/k²
StartFraction negative 1 Over k cubed EndFraction
= -1/k³
StartFraction 1 Over k EndFraction
= 1/k
