At least they admitted this is algebra not geometry. You'll get the same question next year but they'll call it geometry.
The area is the product of the sides:
![A=(x-6)(3x^2-4x+6)](https://tex.z-dn.net/?f=A%3D%28x-6%29%283x%5E2-4x%2B6%29)
We just distribute and collect terms:
![A=x(3x^2-4x+6) - 6(3x^2-4x+6)](https://tex.z-dn.net/?f=A%3Dx%283x%5E2-4x%2B6%29%20-%206%283x%5E2-4x%2B6%29%20)
![A=3x^3-4x^2+6x - 18x^2 +24x -36](https://tex.z-dn.net/?f=A%3D3x%5E3-4x%5E2%2B6x%20-%2018x%5E2%20%2B24x%20-36)
![A=3x^3- 22x^2+30x-36](https://tex.z-dn.net/?f=A%3D3x%5E3-%2022x%5E2%2B30x-36)
Answer: 3rd choice
Answer:
-4/9
Step-by-step explanation:
Given:
The bases of triangular prism are right triangles with a base of 12 inches and height of 9 inches.
The height of the prism is 11 inches.
To find:
The surface area of the triangular prism.
Solution:
Using the Pythagoras theorem, the hypotenuse of the bases of the triangular prism is:
![Hypotenuse^2=Base^2+Height^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DBase%5E2%2BHeight%5E2)
![Hypotenuse^2=12^2+9^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D12%5E2%2B9%5E2)
![Hypotenuse^2=144+81](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D144%2B81)
![Hypotenuse^2=225](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D225)
Taking square root on both sides.
![Hypotenuse=15](https://tex.z-dn.net/?f=Hypotenuse%3D15)
The surface after of the triangular prism contains 3 rectangles of dimensions 12 inches by 11 inches, 9 inches by 11 inches, 15 inches by 11 inches and two triangles with base 12 inches and height 9 inches.
Area of the rectangle:
![Area=Length \times Width](https://tex.z-dn.net/?f=Area%3DLength%20%5Ctimes%20Width)
So, the area of three rectangles are:
![A_1=12 \times 11](https://tex.z-dn.net/?f=A_1%3D12%20%5Ctimes%2011)
![A_1=132](https://tex.z-dn.net/?f=A_1%3D132)
![A_2=9 \times 11](https://tex.z-dn.net/?f=A_2%3D9%20%5Ctimes%2011)
![A_2=99](https://tex.z-dn.net/?f=A_2%3D99)
![A_3=15 \times 11](https://tex.z-dn.net/?f=A_3%3D15%20%5Ctimes%2011)
![A_3=165](https://tex.z-dn.net/?f=A_3%3D165)
Area of a triangle is:
![Area=\dfrac{1}{2}\times base \times height](https://tex.z-dn.net/?f=Area%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20base%20%5Ctimes%20height)
So, the area of the triangles is:
![A_4=\dfrac{1}{2}\times 12 \times 9](https://tex.z-dn.net/?f=A_4%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2012%20%5Ctimes%209)
![A_4=6 \times 9](https://tex.z-dn.net/?f=A_4%3D6%20%5Ctimes%209)
![A_4=54](https://tex.z-dn.net/?f=A_4%3D54)
And, the triangles have same dimensions so their areas are equal.
![A_4=A_5=54](https://tex.z-dn.net/?f=A_4%3DA_5%3D54)
Now,
![Area=A_1+A_2+A_3+A_4+A_5](https://tex.z-dn.net/?f=Area%3DA_1%2BA_2%2BA_3%2BA_4%2BA_5)
![Area=132+99+165+54+54](https://tex.z-dn.net/?f=Area%3D132%2B99%2B165%2B54%2B54)
![Area=504](https://tex.z-dn.net/?f=Area%3D504)
Therefore, the surface area of the triangular prism is 504 sq. inches.
Answer:
275
Step-by-step explanation:
x + x + 50 = 600
2x = 550
x = 275
The customer gave me:
-- a ticket worth $5
-- a ticket worth $2
-- a bill worth $100
Total. . . . . . .$107
I gave him:
-- some gas worth $17.01
-- a ticket worth $ 5
-- two $1 tickets $ 2
-- a ticket worth $ 3
Total. . . . . . . .$27.01
The total value of everything we trade has to be equal.
I owe him ( $107.00 - $27.01 ) = $79.99 in change