The answer is x2 + 2xy + y2.
Answer:
=0.3 per km²
Step-by-step explanation:
Population density is the population per uni area.
Area=πr² Where A is area and r is the radius of the circle.
A=3.14×34
=106.76km²
Population density = Population/Area
=32 antelopes/106.76 km²
=0.3 per km²
The population of antelopes within the given radius is 0.3 per km²
The factorization of 12a^3b^2 +18a²b^2 – 12ab^2 is ![6 a b^{2}(a+2)(2 a-1)](https://tex.z-dn.net/?f=6%20a%20b%5E%7B2%7D%28a%2B2%29%282%20a-1%29)
<u>Solution:</u>
Given, expression is ![12 a^{3} b^{2}+18 a^{2} b^{2}-12 a b^{2}](https://tex.z-dn.net/?f=12%20a%5E%7B3%7D%20b%5E%7B2%7D%2B18%20a%5E%7B2%7D%20b%5E%7B2%7D-12%20a%20b%5E%7B2%7D)
We have to factorize the given expression completely.
Now, take the expression
![12 a^{3} b^{2}+18 a^{2} b^{2}-12 a b^{2}](https://tex.z-dn.net/?f=12%20a%5E%7B3%7D%20b%5E%7B2%7D%2B18%20a%5E%7B2%7D%20b%5E%7B2%7D-12%20a%20b%5E%7B2%7D)
Taking
as common term,
![b^{2}\left(12 a^{3}+18 a^{2}-12 a\right)](https://tex.z-dn.net/?f=b%5E%7B2%7D%5Cleft%2812%20a%5E%7B3%7D%2B18%20a%5E%7B2%7D-12%20a%5Cright%29)
Taking "a" as common term,
![b^{2}\left(a\left(12 a^{2}+18 a-12\right)\right)](https://tex.z-dn.net/?f=b%5E%7B2%7D%5Cleft%28a%5Cleft%2812%20a%5E%7B2%7D%2B18%20a-12%5Cright%29%5Cright%29)
Taking "6" as common term,
![b^{2}\left(a\left(6\left(2 a^{2}+3 a-2\right)\right)\right)](https://tex.z-dn.net/?f=b%5E%7B2%7D%5Cleft%28a%5Cleft%286%5Cleft%282%20a%5E%7B2%7D%2B3%20a-2%5Cright%29%5Cright%29%5Cright%29)
Splitting "3a" as "4a - a" we get,
![b^{2}\left(a\left(6\left(2 a^{2}+4 a-a-2\right)\right)\right)](https://tex.z-dn.net/?f=b%5E%7B2%7D%5Cleft%28a%5Cleft%286%5Cleft%282%20a%5E%7B2%7D%2B4%20a-a-2%5Cright%29%5Cright%29%5Cright%29)
![\begin{array}{l}{b^{2}(a(6(2 a(a+2)-1(a+2))))} \\\\ {b^{2}(a(6((a+2) \times(2 a-1))))} \\\\ {6 a b^{2}(a+2)(2 a-1)}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Bb%5E%7B2%7D%28a%286%282%20a%28a%2B2%29-1%28a%2B2%29%29%29%29%7D%20%5C%5C%5C%5C%20%7Bb%5E%7B2%7D%28a%286%28%28a%2B2%29%20%5Ctimes%282%20a-1%29%29%29%29%7D%20%5C%5C%5C%5C%20%7B6%20a%20b%5E%7B2%7D%28a%2B2%29%282%20a-1%29%7D%5Cend%7Barray%7D)
Hence, the factored form of given expression is ![6 a b^{2}(a+2)(2 a-1)](https://tex.z-dn.net/?f=6%20a%20b%5E%7B2%7D%28a%2B2%29%282%20a-1%29)
Answer:
QUESTION 1
The given system of equation,
We simplify to get.
The correct answer is option A.
1.
A.) (4, −2)
2.
x = -7
y = 2
3.
x = 5
y = 14
QUESTION 2
The given system of equations is
and
We make y the subject in equation (2) to get,
We put equation (3) into equation (1) to obtain,
We group like terms to get,
This implies that,
we divide through by to get,
Hence the x-coordinate is
QUESTION 3
The given system is
and
We make the subject in equation (2)
We put equation (3) into equation (1) to obtain,
We expand the bracket to get,
Group like terms to get,
We simplify to get;
This implies that,
Therefore the y-coordinate is 14.
Step-by-step explanation:
No, the number of sitcker in each row and coumn is 3;
6 faces------------------54 colored stickers
1 face-------------------- x
x=(1 face * 54 colored stickers) / 6 faces=9 colored stickers.
1 face is a square,therefore the number of rows is equal the number of columns.
number of stickers=number of rows * number of columns
number of rows=x
number of columns=x
9=x²
x=+√9=3
Answer: the number of stickers in each row and column is 9.