Answer:
The volume of the prism is ![1,299\ in^{3}](https://tex.z-dn.net/?f=1%2C299%5C%20in%5E%7B3%7D)
Step-by-step explanation:
we know that
The volume of the prism is equal to
![V=BL](https://tex.z-dn.net/?f=V%3DBL)
where
B is the area of the triangular base
L is the length of the prism
we have
![L=30\ in](https://tex.z-dn.net/?f=L%3D30%5C%20in)
<em>Find the area of the base B</em>
The area of a equilateral triangle is equal to
![B=\frac{1}{2}(10)^{2} sin(60\°)](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B1%7D%7B2%7D%2810%29%5E%7B2%7D%20sin%2860%5C%C2%B0%29)
![B=25\sqrt{3}\ in^{2}](https://tex.z-dn.net/?f=B%3D25%5Csqrt%7B3%7D%5C%20in%5E%7B2%7D)
substitute
![V=(25\sqrt{3})(30)=1,299\ in^{3}](https://tex.z-dn.net/?f=V%3D%2825%5Csqrt%7B3%7D%29%2830%29%3D1%2C299%5C%20in%5E%7B3%7D)
I think it might be a sphere sorry if I got it wrong
correct Option is B i.e,
whose simplified form is: ![360x^2-216x](https://tex.z-dn.net/?f=360x%5E2-216x)
Step-by-step explanation:
We need to solve the expression:
![2[(6x)(6x)]+4[(12x - 9)(6x)]](https://tex.z-dn.net/?f=2%5B%286x%29%286x%29%5D%2B4%5B%2812x%20-%209%29%286x%29%5D)
Solving:
![2[(6x)(6x)]+4[(12x - 9)(6x)]\\=2[36x^2]+4[(12x*6x)-(9*6x)]\\=72x^2+4[72x^2-54x]\\=72x^2+288x^2-216x\\=360x^2-216x](https://tex.z-dn.net/?f=2%5B%286x%29%286x%29%5D%2B4%5B%2812x%20-%209%29%286x%29%5D%5C%5C%3D2%5B36x%5E2%5D%2B4%5B%2812x%2A6x%29-%289%2A6x%29%5D%5C%5C%3D72x%5E2%2B4%5B72x%5E2-54x%5D%5C%5C%3D72x%5E2%2B288x%5E2-216x%5C%5C%3D360x%5E2-216x)
So, correct Option is B i.e,
whose simplified form is: ![360x^2-216x](https://tex.z-dn.net/?f=360x%5E2-216x)
Keywords: Surface area of the rectangular prism
Learn more about surface area of the rectangular prism at:
#learnwithBrainly
Answer: The answer is 6n+7y
Step-by-step explanation: All you have to do is add like terms