The answer is b, tell me if you don't understand.
Answer:
a.![V(x)=x(10-2x)(6-2x)](https://tex.z-dn.net/?f=V%28x%29%3Dx%2810-2x%29%286-2x%29)
b.![S(x)=4(15-x^2)](https://tex.z-dn.net/?f=S%28x%29%3D4%2815-x%5E2%29)
Step-by-step explanation:
Dimensions of rectangular piece of cardboard=![10\times 6](https://tex.z-dn.net/?f=10%5Ctimes%206)
According to question
Length of box,l=10-2x
Breadth of box,b=6-2x
Height of box,h=x
a.
Volume of box=![l\times b\times h](https://tex.z-dn.net/?f=l%5Ctimes%20b%5Ctimes%20h)
Substitute the values in the formula
Volume of box=![x(10-2x)(6-2x)](https://tex.z-dn.net/?f=x%2810-2x%29%286-2x%29)
![V(x)=x(10-2x)(6-2x)](https://tex.z-dn.net/?f=V%28x%29%3Dx%2810-2x%29%286-2x%29)
b.Surface area of box=![2(b+l)h+lb](https://tex.z-dn.net/?f=2%28b%2Bl%29h%2Blb)
Because the box has no lid
Substitute the values in the formula
Surface area of box=![2(10-2x+6-2x)x+(10-2x)(6-2x)](https://tex.z-dn.net/?f=2%2810-2x%2B6-2x%29x%2B%2810-2x%29%286-2x%29)
Surface area of box=![2(16-4x)x+60-20x-12x+4x^2](https://tex.z-dn.net/?f=2%2816-4x%29x%2B60-20x-12x%2B4x%5E2)
Surface area of box=![32x-8x^2+60-32x+4x^2](https://tex.z-dn.net/?f=32x-8x%5E2%2B60-32x%2B4x%5E2)
Surface area of box=![60-4x^2=4(15-x^2)](https://tex.z-dn.net/?f=60-4x%5E2%3D4%2815-x%5E2%29)
Surface area of box, S(x)=![4(15-x^2)](https://tex.z-dn.net/?f=4%2815-x%5E2%29)
Answer:
79853709 with the exponent of 94
Step-by-step explanation:
For this case we have the following polynomial:
7x2 + 68xy - 20y2
Factoring we have:
(7x-2y) (x + 10y)
We verify the factorization:
7x2 + 70xy - 2xy - 20y2
Rewriting we have:
7x2 + 68xy - 20y2
Therefore, the factorization is correct.
Answer:
A) (7x - 2y) (x + 10y)
5*3^0 = 5,
5*3^1 = 15,
5*3^2 = 45,
5*3^3 = 135,
5*3^4 = 405
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