1. Ans: Option (B) ![-6x^4](https://tex.z-dn.net/?f=-6x%5E4)
Explanation:
Given:
![2x^4 - 8x^4](https://tex.z-dn.net/?f=2x%5E4%20-%208x%5E4)
Take the common out:
=>
![x^4(2 - 8)](https://tex.z-dn.net/?f=x%5E4%282%20-%208%29)
Hence: =>
![[tex]-6x^4](https://tex.z-dn.net/?f=%5Btex%5D-6x%5E4)
[/tex] (Option B)
2. Ans: Option (D) ![-3y^5](https://tex.z-dn.net/?f=-3y%5E5)
Explanation:
Given:
![6y^5 - 9y^5](https://tex.z-dn.net/?f=6y%5E5%20-%209y%5E5)
Take the common term(s) out:
=>
![y^5(6-9)](https://tex.z-dn.net/?f=y%5E5%286-9%29)
Hence: =>
![-3y^5](https://tex.z-dn.net/?f=-3y%5E5)
(Option D)
3. Ans: Option (B) ![9x^2 - 12x + 6](https://tex.z-dn.net/?f=9x%5E2%20-%2012x%20%2B%206)
<span>
quadratic trinomial
Explanation:
</span>Given:
![6 - 12x + 13x^2 - 4x^2](https://tex.z-dn.net/?f=6%20-%2012x%20%2B%2013x%5E2%20-%204x%5E2)
The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.
=> ![13x^2 - 4x^2 - 12x + 6](https://tex.z-dn.net/?f=13x%5E2%20-%204x%5E2%20-%2012x%20%2B%206)
=>
![9x^2 - 12x + 6](https://tex.z-dn.net/?f=9x%5E2%20-%2012x%20%2B%206)
(Option B)
4. Ans: Option (C) ![7.3x^2 + 0.8x + 1.3](https://tex.z-dn.net/?f=7.3x%5E2%20%2B%200.8x%20%2B%201.3)
Explanation:
In order to find the total number of C<span>ommon and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:
</span>Common guppies:
![3.1x^2 +6.0x + 0.3](https://tex.z-dn.net/?f=3.1x%5E2%20%2B6.0x%20%2B%200.3)
<span>
Endler's guppies: </span>
![4.2x^2 - 5.2x + 1.0](https://tex.z-dn.net/?f=4.2x%5E2%20-%205.2x%20%2B%201.0%20)
(add both)
-----------------------------------------------------------------
Total number:
![7.3x^2 +0.8x + 1.3](https://tex.z-dn.net/?f=7.3x%5E2%20%2B0.8x%20%2B%201.3)
-----------------------------------------------------------------
Hence the ans is Option(C)
5. Ans: Option (D) ![2x^2(133 - 18 \pi )](https://tex.z-dn.net/?f=2x%5E2%28133%20-%2018%20%5Cpi%20%29)
Explanation:
First let's find the total area of the yard:
Total Area of the
Yard = 14x * 19x =
![266x^2](https://tex.z-dn.net/?f=266x%5E2)
Now the area of the circular fountain:
Area of the Circular Fountain =
![\pi r^2](https://tex.z-dn.net/?f=%20%5Cpi%20r%5E2)
Since, r=6x
Therefore,
Area of the Circular Fountain =
![\pi (6x)^2 = 36 \pi x^2](https://tex.z-dn.net/?f=%20%5Cpi%20%286x%29%5E2%20%3D%2036%20%5Cpi%20x%5E2)
Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard =
![266x^2](https://tex.z-dn.net/?f=266x%5E2)
-
![36 \pi x^2](https://tex.z-dn.net/?f=36%20%5Cpi%20x%5E2)
=> Final area of the Yard =
![2x^2(133 - 18 \pi)](https://tex.z-dn.net/?f=2x%5E2%28133%20-%2018%20%5Cpi%29)
(Option D)
6. Ans: Option (A) ![56x^2](https://tex.z-dn.net/?f=56x%5E2)
Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x =
![60x^2](https://tex.z-dn.net/?f=60x%5E2)
Now the area of the stadium:
Area of the stadium = 1x * 4x =
![4x^2](https://tex.z-dn.net/?f=4x%5E2)
Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot=
![60x^2](https://tex.z-dn.net/?f=60x%5E2)
-
![4x^2](https://tex.z-dn.net/?f=4x%5E2)
=> Final area of the lot =
![56x^2](https://tex.z-dn.net/?f=56x%5E2)
(Option A)
-i