I believe it's A. Hope it helps :)
Answer:
C
Step-by-step explanation:
ley y = f(x) and rearrange making x the subject
y =
- 1 ( add 1 to both sides )
y + 1 =
( multiply both sides by (x + 5)
(y + 1)(x + 5) = 1 ← expand factors using FOIL
xy + 5y + x + 5 = 1 , that is
xy + x + 5y + 5 = 1 ( factor first/second and third/fourth terms on left side )
x(y + 1) + 5(y + 1) = 1 ← factor out (y + 1) from each term on left side
(y + 1)(x + 5) = 1 ( divide both sides by (y + 1) )
x + 5 =
( subtract 5 from both sides )
x =
- 5
Change y back into terms of x with x =
(x) , then
(x) =
- 5 where x ≠ - 1
6.974 rounded to the nearest tenth is 7.0, because 7 is more than 5, and since 9's there, we make that 6 to a 7.
Given:
A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.
To find:
The total surface area of the prism.
Solution:
We have,
Height of prism = 7½ = 7.5
Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because
![5^2+12^2=13^2](https://tex.z-dn.net/?f=5%5E2%2B12%5E2%3D13%5E2)
![25+144=169](https://tex.z-dn.net/?f=25%2B144%3D169)
![169=169](https://tex.z-dn.net/?f=169%3D169)
So, the base of the prism is a right triangle.
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)
![A_1=\dfrac{1}{2}\times 5\times 12](https://tex.z-dn.net/?f=A_1%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%205%5Ctimes%2012)
![A_1=30](https://tex.z-dn.net/?f=A_1%3D30)
The area of the base is equal to the area of the top, i.e.,
sq units.
Perimeter of the base is
![P=5+12+13](https://tex.z-dn.net/?f=P%3D5%2B12%2B13)
![P=30](https://tex.z-dn.net/?f=P%3D30)
The curved surface area of the prism is
![CSA=\text{Perimeter of the base}\times \text{Height of the prism}](https://tex.z-dn.net/?f=CSA%3D%5Ctext%7BPerimeter%20of%20the%20base%7D%5Ctimes%20%5Ctext%7BHeight%20of%20the%20prism%7D)
![CSA=30\times 7.5](https://tex.z-dn.net/?f=CSA%3D30%5Ctimes%207.5)
![CSA=225](https://tex.z-dn.net/?f=CSA%3D225)
Now, the total area of the prism is
![A=A_1+A_2+CSA](https://tex.z-dn.net/?f=A%3DA_1%2BA_2%2BCSA)
![A=30+30+225](https://tex.z-dn.net/?f=A%3D30%2B30%2B225)
![A=285](https://tex.z-dn.net/?f=A%3D285)
Therefore, the total surface area of the triangular prism is 285 square units.
Answer:
580
Step-by-step explanation: