I’m pretty sure the answer is 160 because the rectangle on the top has a volume of 64(16 x 4) and the rectangle on the bottom has a volume of 96(2 x 4 x 12). Add those together and you get 160 cubed inches. Hope this helped :)
Answer: 2584
Step-by-step explanation:
We can find N with 2584 and 4181.
4181 - 2584
= 1597
We can also check our answer by adding 1597 and 987
1597 + 987
= 2584
First off, we factor out the expression:

In the bracket, separate 8 out of the expression.
![\displaystyle \large{y = 2[ ( {x}^{2} - 6x + 8)] }\\ \displaystyle \large{y = 2[ ( {x}^{2} - 6x) + 8]}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%28%20%7Bx%7D%5E%7B2%7D%20-%206x%20%2B%208%29%5D%20%7D%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%28%20%7Bx%7D%5E%7B2%7D%20-%206x%29%20%2B%208%5D%7D)
In x^2-6x, find the third term that can make up or convert it to a perfect square form. The third term is 9 because:

So we add +9 in x^2-6x.
![\displaystyle \large{y = 2[ ( {x}^{2} - 6x + 9) + 8]}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%28%20%7Bx%7D%5E%7B2%7D%20-%206x%20%2B%209%29%20%20%2B%208%5D%7D)
Convert the expression in the small bracket to perfect square.
![\displaystyle \large{y = 2[ {(x - 3)}^{2} + 8]}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20%2B%208%5D%7D)
Since we add +9 in the small bracket, we have to subtract 8 with 9 as well.
![\displaystyle \large{y = 2[ {(x - 3)}^{2} + 8 - 9]} \\ \displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20%2B%208%20-%209%5D%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20-%201%5D%7D)
Then we distribute 2 in.
![\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20-%201%5D%7D%20%5C%5C%20)
![\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \displaystyle \large{y = [2 \times {(x - 3)}^{2} ]+[ 2 \times ( - 1)] } \\ \displaystyle \large{y = 2 {(x - 3)}^{2} - 2 }](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20-%201%5D%7D%20%5C%5C%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%20%5B2%20%5Ctimes%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%5D%2B%5B%202%20%5Ctimes%20%28%20-%201%29%5D%20%7D%20%5C%5C%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20-%202%20%7D)
Remember that negative multiply positive = negative.
Hence the vertex form is y = 2(x-3)^2-2 or first choice.
Area of a pyramid is ⅓ * area of Base * height
or ⅓ * 144 * 42 or 2016 cm³