Answer:
Step-by-step explanation:
To solve this problem, you must:
- Subtract 7 from both sides of the equation:
- Now, you can factor it. Choose two numbers whose sum -14 and whose product is 45. These numbers would be -9 and -5. Therefore, you obtain the following solution:
Answer:
Step-by-step explanation:
The expression is for the interior angle of the hexagon; one interior angle is equal to 
.
Since an interior angle of a hexagon measures 120°, we have the equality
.
Now it is just a matter of solving for 
Answer:
y = - 2(x - 1)² + 18
Step-by-step explanation:
- 2x² + 4x + 16 ← factor out - 2 from the first 2 terms
= - 2(x² - 2x) + 16
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 2x
= - 2(x² + 2(- 1)x + 1 - 1) + 16
= - 2(x - 1)² + 2 + 16
= - 2(x - 1)² + 18 ← in vertex form
Answer:
C 1055 04 cm
Step-by-step explanation:
We don't need to see the figure, since we know for sure the cone fits into the cylinder (smaller diameter and height).
So, we first need to calculate the volume of the cylinder, which is given by the formula:
VT = π * r² * h
VT = 3.14 * 5² * 16 = 3.14 * 400 = 1,256 cubic cm
Then we calculate the volume of the cone, which is given by:
VC = (π * r² * h)/3
VC = (3.14 * 4² * 12)/3 = (3.14 * 192)/3 = 200.96 cu cm
Then we calculate the void space left inside the cylinder by subtracting the volume of the cone from the volume of the cylinder:
NV = VT - VC = 1,256 - 200.96 = 1,055.04 cu cm
Arc length (L) = 83.7758 ft
