The slope is 2/3 because it rises 2 and moves right 3
Answer:
f^-1(x) = 4x-3
Step-by-step explanation:
f(x) = (x+3)/4
y = (x+3)/4
Exchange x and y
x = (y+3)/4
Solve for y
4x = y+3
Subtract 3
4x-3 = y
The inverse
f^-1(x) = 4x-3
Hello from MrBillDoesMath!
Answer: The other side has a length of 8
Discussion:
Area of a rectangle = l * w ( length times width). In our case
Area = 144 = l * w = 18 * w =>
18 w = 144 =>
w = 144/18 = 8
Thank you,
MrB
Answer:
![3x^2-5x=-8](https://tex.z-dn.net/?f=3x%5E2-5x%3D-8)
![2x^2=6x-5](https://tex.z-dn.net/?f=2x%5E2%3D6x-5)
![-x^2-10x=34](https://tex.z-dn.net/?f=-x%5E2-10x%3D34)
Step-by-step explanation:
The equations are:
![3x^2-5x=-8](https://tex.z-dn.net/?f=3x%5E2-5x%3D-8)
![2x^2=6x-5](https://tex.z-dn.net/?f=2x%5E2%3D6x-5)
![-x^2-10x=34](https://tex.z-dn.net/?f=-x%5E2-10x%3D34)
(a) ![3x^2-5x=-8](https://tex.z-dn.net/?f=3x%5E2-5x%3D-8)
Add 8 to both sides
![3x^2 - 5x + 8 =0](https://tex.z-dn.net/?f=3x%5E2%20-%205x%20%2B%208%20%3D0)
To do this, we simply calculate the discriminant (d) using:
![d =b^2 - 4ac](https://tex.z-dn.net/?f=d%20%3Db%5E2%20-%204ac)
If ![d < 0](https://tex.z-dn.net/?f=d%20%3C%200)
Then it has complex roots
Where: ![a = 3; b = -5; c = 8](https://tex.z-dn.net/?f=a%20%3D%203%3B%20b%20%3D%20-5%3B%20c%20%3D%208)
![d = (-5)^2 - 4 * 3 * 8](https://tex.z-dn.net/?f=d%20%3D%20%28-5%29%5E2%20-%204%20%2A%203%20%2A%208)
![d = 25 - 96](https://tex.z-dn.net/?f=d%20%3D%2025%20-%2096)
![d = -71](https://tex.z-dn.net/?f=d%20%3D%20-71)
--- complex root
(b) ![2x^2=6x-5](https://tex.z-dn.net/?f=2x%5E2%3D6x-5)
Equate to 0
![2x^2 - 6x + 5 = 0](https://tex.z-dn.net/?f=2x%5E2%20-%206x%20%2B%205%20%3D%200)
![d =b^2 - 4ac](https://tex.z-dn.net/?f=d%20%3Db%5E2%20-%204ac)
![d = (-6)^2 - 4 * 2 * 5](https://tex.z-dn.net/?f=d%20%3D%20%28-6%29%5E2%20-%204%20%2A%202%20%2A%205)
![d = 36 - 40](https://tex.z-dn.net/?f=d%20%3D%2036%20-%2040)
![d =-4](https://tex.z-dn.net/?f=d%20%3D-4)
--- complex root
(c)
Equate to 0
![9x^2 - 12x + 4 = 0](https://tex.z-dn.net/?f=9x%5E2%20-%2012x%20%2B%204%20%3D%200)
![d =b^2 - 4ac](https://tex.z-dn.net/?f=d%20%3Db%5E2%20-%204ac)
![d = (-12)^2 - 4 * 9 * 4](https://tex.z-dn.net/?f=d%20%3D%20%28-12%29%5E2%20-%204%20%2A%209%20%2A%204)
![d = 144 - 144](https://tex.z-dn.net/?f=d%20%3D%20144%20-%20144)
---- real roots
(d) ![-x^2-10x=34](https://tex.z-dn.net/?f=-x%5E2-10x%3D34)
Equate to 0
![-x^2 - 10x - 34 = 0](https://tex.z-dn.net/?f=-x%5E2%20-%2010x%20-%2034%20%3D%200)
![d =b^2 - 4ac](https://tex.z-dn.net/?f=d%20%3Db%5E2%20-%204ac)
![d = (-10)^2 - 4 * (-1) * (-34)](https://tex.z-dn.net/?f=d%20%3D%20%28-10%29%5E2%20-%204%20%2A%20%28-1%29%20%2A%20%28-34%29)
![d = 100 - 136](https://tex.z-dn.net/?f=d%20%3D%20100%20-%20136)
![d = - 36](https://tex.z-dn.net/?f=d%20%3D%20-%2036)
---- complex root
Answer:
160
Step-by-step explanation:
This is the answer because:
1) Whenever there are two negative factors, the answer will be a positive
- x - = +
Hope this helps!