Answer: hope this helps
simplified:
14w^3 + 2w^2
Step-by-step explanation:
Answer:
The area of triangle is 48.
Step-by-step explanation:
Given:
The vertices of triangle are (0,0),(12,0),(2,8).
Now, to find the area of triangle.
So, the coordinates of triangle are:
.
Now, to get the area of triangle we put formula:
![Area\,of\,triangle\,=\,\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|](https://tex.z-dn.net/?f=Area%5C%2Cof%5C%2Ctriangle%5C%2C%3D%5C%2C%5Cfrac%7B1%7D%7B2%7D%5Cleft%7Cx_1%28y_2-y_3%29%2Bx_2%28y_3-y_1%29%2Bx_3%28y_1-y_2%29%5Cright%7C)
![Area\,of\,triangle\,=\,\frac{1}{2}\left|0(0-8)+(12)(8-0)+2(0-0)\right|](https://tex.z-dn.net/?f=Area%5C%2Cof%5C%2Ctriangle%5C%2C%3D%5C%2C%5Cfrac%7B1%7D%7B2%7D%5Cleft%7C0%280-8%29%2B%2812%29%288-0%29%2B2%280-0%29%5Cright%7C)
![Area\,of\,triangle\,=\,\frac{1}{2}\left|0\times -8+12\times 8+2\times 0\right|](https://tex.z-dn.net/?f=Area%5C%2Cof%5C%2Ctriangle%5C%2C%3D%5C%2C%5Cfrac%7B1%7D%7B2%7D%5Cleft%7C0%5Ctimes%20-8%2B12%5Ctimes%208%2B2%5Ctimes%200%5Cright%7C)
![Area\,of\,triangle\,=\,\frac{1}{2}\left|0+96+0\right|](https://tex.z-dn.net/?f=Area%5C%2Cof%5C%2Ctriangle%5C%2C%3D%5C%2C%5Cfrac%7B1%7D%7B2%7D%5Cleft%7C0%2B96%2B0%5Cright%7C)
![Area\,of\,triangle\,=\,\frac{1}{2}\left|96\right|](https://tex.z-dn.net/?f=Area%5C%2Cof%5C%2Ctriangle%5C%2C%3D%5C%2C%5Cfrac%7B1%7D%7B2%7D%5Cleft%7C96%5Cright%7C)
![Area\,of\,triangle\,=\,\frac{1}{2}\times 96](https://tex.z-dn.net/?f=Area%5C%2Cof%5C%2Ctriangle%5C%2C%3D%5C%2C%5Cfrac%7B1%7D%7B2%7D%5Ctimes%2096)
![Area\,of\,triangle\,=\,\frac{96}{2}](https://tex.z-dn.net/?f=Area%5C%2Cof%5C%2Ctriangle%5C%2C%3D%5C%2C%5Cfrac%7B96%7D%7B2%7D)
![Area\,of\,triangle\,=\,48.](https://tex.z-dn.net/?f=Area%5C%2Cof%5C%2Ctriangle%5C%2C%3D%5C%2C48.)
Therefore, the area of triangle is 48.
Answer:
![sin(\theta)=\frac{5}{13}](https://tex.z-dn.net/?f=sin%28%5Ctheta%29%3D%5Cfrac%7B5%7D%7B13%7D)
Step-by-step explanation:
step 1
Find the hypotenuse of the right triangle with legs of 5 ft and 12 ft
Applying the Pythagoras Theorem
Let
d ----> the length of the hypotenuse
![d^{2}=12^2+5^2](https://tex.z-dn.net/?f=d%5E%7B2%7D%3D12%5E2%2B5%5E2)
![d^{2}=169](https://tex.z-dn.net/?f=d%5E%7B2%7D%3D169)
![d=13\ ft](https://tex.z-dn.net/?f=d%3D13%5C%20ft)
step 2
Find the sine of angle theta
Remember that
The sine of angle theta is equal to divide the opposite side of angle theta (5 feet) by the hypotenuse (13 feet)
![sin(\theta)=\frac{5}{13}](https://tex.z-dn.net/?f=sin%28%5Ctheta%29%3D%5Cfrac%7B5%7D%7B13%7D)
Answer:
x = 7 and x = 5
Step-by-step explanation:
12x - 35 = x²
x² - 12x + 35 = 0
(x - 7)(x - 5) = 0
x = 7 and x = 5
Answer:
Step-by-step explanation:
e^ lnx = x
e^ ln5 = 5
e^ ln 3x = 3x
I think you get the idea... e is an inverse operation to ln :o