Answer:
If
or
, there is only one solution to the given quadratic equation.
Step-by-step explanation:
Given a second order polynomial expressed by the following equation:
![ax^{2} + bx + c, a\neq0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2B%20bx%20%2B%20c%2C%20a%5Cneq0)
This polynomial has roots
such that
, given by the following formulas:
![x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D)
![x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20%5Cfrac%7B-b%20-%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D)
![\bigtriangleup = b^{2} - 4ac](https://tex.z-dn.net/?f=%5Cbigtriangleup%20%3D%20b%5E%7B2%7D%20-%204ac)
The signal of
determines how many real roots an equation has:
: Two real and different solutions
: One real solution
: No real solutions
In this problem, we have the following second order polynomial:
.
This means that ![a = k+1; b = 4k; c = 2](https://tex.z-dn.net/?f=a%20%3D%20k%2B1%3B%20b%20%3D%204k%3B%20c%20%3D%202)
It has one solution if
![\bigtriangleup = 0](https://tex.z-dn.net/?f=%5Cbigtriangleup%20%3D%200)
![b^{2} - 4ac = 0](https://tex.z-dn.net/?f=b%5E%7B2%7D%20-%204ac%20%3D%200)
![16k^{2} -8(k+1) = 0](https://tex.z-dn.net/?f=16k%5E%7B2%7D%20-8%28k%2B1%29%20%3D%200)
![16k^{2} - 8k - 8 = 0](https://tex.z-dn.net/?f=16k%5E%7B2%7D%20-%208k%20-%208%20%3D%200)
We can simplify by 8
![2k^{2} - k - 1 = 0](https://tex.z-dn.net/?f=2k%5E%7B2%7D%20-%20k%20-%201%20%3D%200)
The solution is:
or ![k = -\frac{1}{2}](https://tex.z-dn.net/?f=k%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
So, if
or
, there is only one solution to the given quadratic equation.
The answer is 1.6
How I figured it out:
I divided 8 by 5, which gave me 1.6
To make sure this was right, I multiplied 1.6 by 5, which gave me an answer of 8 or other known as 8 inches.
In conclusion, the number of inces per hour is 1.6
Answer:
Divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle to determine the scale factor for the smaller triangle to the bigger triangle.
Hello,
Five sixths of forty two is = 35.