16x³ - 54
= 2(8x³ - 27)
= 2(2x - 3)(4x² + 6x + 9) ← answer
Answer:
The length of the pig pen for fencing the plans is 28 feet .
Step-by-step explanation:
Given as :
The measure of the fencing = 186 feet
The width of the pig pen = w = 15 feet
Let the length of the pig pen = l = x feet
Now, To find the measure of the fencing , we calculate the perimeter of the plans .
So, <u>From perimeter method</u>
I.e Perimeter = 2 × Length + 2 × Width
or, 186 feet = 2 × l + 2 × w
Or, 186 feet = 2 × l + 2 × 15
Or, 186 - 2 × 15 = 2 × l
or, 186 - 30 = 2 × l
Or, 2 × l = 156
∴ l =
= 78 feet
So, The length of pig pen = l = 28 feet
Hence The length of the pig pen for fencing the plans is 28 feet . Answer
Answer:
Pigeonhole Principle
Step-by-step explanation:
From series {1,2......2n} ; we need to select 'n + 1' integers.
Even integers series from above series = {2,4,6..........2(n-1), 2n}
Odd integers series from above series = {1,3,5........2(n-2), 2n-1}
So, we can choose only n odd integers from the series. Hence, if we choose n+1 integers, atleast one of them have to be even integer.
- Eg : n = 5, Series = (1,2,3,4,5,6,7,8,9,10}, Odd series = {1,3,5,7,9}, Even series = {2,4,6,8,10}. If we choose 5 +1 ie 6 integers, there must be one even integer, as there are only 5 total odd integers in series.
Answer:
<u>The volume of a mound of salt-sand mixture is 589.05 feet ³ or 589.05 cubic feet.</u>
Step-by-step explanation:
1. Let's check the information given to resolve the question:
Diameter of a mound of the mixture = 15 feet
Height (h) of the mound of the mixture = 10 feet
How much salt-sand mixture is there?
2. Let's find the volume of a mound of mixture with a conical shape:
For doing that, we need to use the volume formula of a cone.
It's: 1/3 * π * r² * h
Replacing with real values, we have:
1/3 * 3.1416 * 7.5 ² * 10 (Diameter = 15, so radius = Diameter/2 = 15/2 = 7.5)
Volume = 1/3 * 3.1416 * 56.25 * 10
Volume = 1/3 * 3.1416 * 562.5 (56.25 * 10 = 562.5)
<u>Volume = 187.5 * 3.1416 = 589.05 feet ³ or 589.05 cubic feet.</u>
Answer: I think the answer is 0 because there isn't an orange color on the diagram
Step-by-step explanation:
I'm so sorry if its wrong!