The area of a rectangle is length x width. We can find the 3 areas of the rectangles with this formula:
20 x 5 = 100
100 yd²
15 x (20-14) = 90
90 yd²
14 x 10 = 140
140 yd²
The area of a trapezoid is 1/2(b1+b2)h
In this problem:
b1=25-15-5
b1=5
b2=10
h=20-14
h=6
We can then plug this into the formula:
A = 1/2(5+10)(6)
A = 1/2(15)(6)
A = 45 yd²
We can then get the area of the whole polygon by adding up the areas of the three rectangles and trapezoid:
A = 100+90+140 + 45
A = 375 yd²
Answer:
it does not have a solution
Step-by-step explanation:
4(b + 1) ≤ 2(2b + 1)+1
4b + 4 ≤ 4b + 2 + 1
0 ≤ -1
0 isn't less than or equal to -1
F(1) = 42
f(n) = f(n-1) - 5
f(2) = f(1) - 5
f(2) = 42-5
f(2) = 37
a1 = 42
a2 = 37
r = 5
PA: (42, 37, 32, 27, 22, 17, 12, 7)
The correct option is Option 4: ![2a^2b^3 + 10ab^4](https://tex.z-dn.net/?f=2a%5E2b%5E3%20%2B%2010ab%5E4)
Step-by-step explanation:
Given
Length of box = l = ab
Width of box = w = a+5b
Height of box = h = 2b^2
The volume of a box is given by:
![V = Length*Width*Height\\V = l*w*h](https://tex.z-dn.net/?f=V%20%3D%20Length%2AWidth%2AHeight%5C%5CV%20%3D%20l%2Aw%2Ah)
Putting the values
![V = (ab)(a+5b)(2b^2)\\ = (ab)(2b^2)(a+5b)\\=(2ab^3)(a+5b)\\Distributive property\\=(2ab^3*a) + (2ab^3*5b)\\=2a^2b^3 + 10ab^4](https://tex.z-dn.net/?f=V%20%3D%20%28ab%29%28a%2B5b%29%282b%5E2%29%5C%5C%20%3D%20%28ab%29%282b%5E2%29%28a%2B5b%29%5C%5C%3D%282ab%5E3%29%28a%2B5b%29%5C%5CDistributive%20property%5C%5C%3D%282ab%5E3%2Aa%29%20%2B%20%282ab%5E3%2A5b%29%5C%5C%3D2a%5E2b%5E3%20%2B%2010ab%5E4)
Hence,
The correct option is Option 4: ![2a^2b^3 + 10ab^4](https://tex.z-dn.net/?f=2a%5E2b%5E3%20%2B%2010ab%5E4)
Keywords: Volume, Polynomials
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