Answer:
Area = 200x - x², Max area is 10000m² with dimensions 100m × 100m
Step-by-step explanation:
Total fencing = perimeter
Let length of the sides be x and y,
2(x + y) = 400
x + y = 200
y = 200 - x
Area = x × y
= x(200 - x)
Area = 200x - x²
For max area, convert area into the completed square form
-(x² - 200x)
-(x² -2(x)(100) + 100² - 100²)
-[(x - 100)² - 10000]
-(x - 100)² + 10000
Max area is 10000 m²
Because the least value of (x - 100)² is 0.
That too when x = 100
When x = 100,
y = 200 - x = 200 - 100 = 100
Dimensions are 100m × 100m
The product of the given polynomials is:
![2a^4+5a^3-6a^2+19a-2](https://tex.z-dn.net/?f=2a%5E4%2B5a%5E3-6a%5E2%2B19a-2)
Step-by-step explanation:
Given polynomials are:
![a^2+3a-4\\and\\2a^2-a+5](https://tex.z-dn.net/?f=a%5E2%2B3a-4%5C%5Cand%5C%5C2a%5E2-a%2B5)
We will use the distributive property to multiply the polynomials
So,
![(a^2+3a-4)(2a^2-a+5)\\=a^2(2a^2-a+5)+3a(2a^2-a+5)-4(2a^2-a+5)\\=2a^4-a^3+5a^2+6a^3-3a^2+15a-8a^2+4a-20\\Combining\ like\ terms\\=2a^4-a^3+6a^3+5a^2-3a^2-8a^2+15a+4a-20\\= 2a^4+5a^3-6a^2+19a-2](https://tex.z-dn.net/?f=%28a%5E2%2B3a-4%29%282a%5E2-a%2B5%29%5C%5C%3Da%5E2%282a%5E2-a%2B5%29%2B3a%282a%5E2-a%2B5%29-4%282a%5E2-a%2B5%29%5C%5C%3D2a%5E4-a%5E3%2B5a%5E2%2B6a%5E3-3a%5E2%2B15a-8a%5E2%2B4a-20%5C%5CCombining%5C%20like%5C%20terms%5C%5C%3D2a%5E4-a%5E3%2B6a%5E3%2B5a%5E2-3a%5E2-8a%5E2%2B15a%2B4a-20%5C%5C%3D%202a%5E4%2B5a%5E3-6a%5E2%2B19a-2)
Hence,
The product of the given polynomials is:
![2a^4+5a^3-6a^2+19a-2](https://tex.z-dn.net/?f=2a%5E4%2B5a%5E3-6a%5E2%2B19a-2)
Keywords: Polynomials, Expressions
Learn more about polynomials:
#LearnwithBrainly
Answer:
-c-4≥8
Step-by-step explanation:
Just ask!
Hope this helps. :)
The solution is: x >-2/3 or x< -2
Step-by-step explanation:
we will solve the inequalities one by one
So,
First inequality is:
![-3(x-2)](https://tex.z-dn.net/?f=-3%28x-2%29%3C8%5C%5C-3x%2B6%3C8%5C%5C-3x%2B6-6%3C8-6%5C%5C-3x%20%3C%202%5C%5C%5Cfrac%7B-3x%7D%7B3%7D%20%3C%20%5Cfrac%7B2%7D%7B3%7D%5C%5C-x%20%3C%20%5Cfrac%7B2%7D%7B3%7D%5C%5Cx%20%3E%20-%5Cfrac%7B2%7D%7B3%7D)
Second inequality is:
![-3(x-2)>12\\-3x+6>12\\-3x+6-6>12-6\\-3x>6\\\frac{-3x}{3} >\frac{6}{3}\\-x> 2\\x](https://tex.z-dn.net/?f=-3%28x-2%29%3E12%5C%5C-3x%2B6%3E12%5C%5C-3x%2B6-6%3E12-6%5C%5C-3x%3E6%5C%5C%5Cfrac%7B-3x%7D%7B3%7D%20%3E%5Cfrac%7B6%7D%7B3%7D%5C%5C-x%3E%202%5C%5Cx%20%3C-2)
The solution is: x >-2/3 or x< -2
Keywords: Inequalities, compound inequalities
Learn more about inequalities at:
#LearnwithBrainly
Answer:
C, 121
Step-by-step explanation:
Every term is X4 + 1.
For example, term 2. 2 X 4 is 8 + 1 is 9. This rules applies to all terms.