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)
A. 6 times 1=6 is the answer to which of the following is an example of identical property of multiplication
<span>It must be the same as it was when constructing the arc above P.</span>
You can use the distance formula: d = sqrt((second x value - first x value)^2 + (second y value - first y value)^2):
answer : d = sqrt((3+2)^2+(6+6)^2) = 11.95826074 units
Answer:
![x1 = 2 \\ x2 = - \frac{3}{2}](https://tex.z-dn.net/?f=x1%20%3D%202%20%5C%5C%20x2%20%3D%20%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20)
Step-by-step explanation:
![x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{1 + - \sqrt{ {( - 1)}^{2} - 4(2)( - 6) } }{2(2)} \\ x = \frac{1 + - \sqrt{1 + 48} }{4} \\ x = \frac{1 + - \sqrt{49} }{4} \\ x = \frac{1 + - 7}{4} \\ \\ x1 = \frac{1 + 7}{4} = \frac{8}{4} = 2 \\ x2 = \frac{1 - 7}{4} = - \frac{6 }{4} = - \frac{3}{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20b%20%2B%20%20-%20%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20-%204ac%20%7D%20%7D%7B2a%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B1%20%2B%20%20-%20%20%5Csqrt%7B%20%7B%28%20-%201%29%7D%5E%7B2%7D%20-%204%282%29%28%20-%206%29%20%7D%20%7D%7B2%282%29%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B1%20%2B%20%20-%20%20%5Csqrt%7B1%20%20%2B%2048%7D%20%7D%7B4%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B1%20%2B%20%20-%20%20%5Csqrt%7B49%7D%20%7D%7B4%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B1%20%2B%20%20-%207%7D%7B4%7D%20%20%5C%5C%20%20%5C%5C%20x1%20%3D%20%20%5Cfrac%7B1%20%20%2B%207%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B8%7D%7B4%7D%20%20%3D%202%20%5C%5C%20x2%20%3D%20%20%5Cfrac%7B1%20-%207%7D%7B4%7D%20%20%3D%20%20%20-%20%5Cfrac%7B6%20%7D%7B4%7D%20%20%3D%20%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20)