Kiyoshi paints 1/3 of the fence each hour.
When the friends work together, they paint 1/2 of the fence each hour.
So Red must be painting (1/2 - 1/3) = 1/6 of the fence each hour.
The rate of 1/6 fence per hour means 1 fence per <em>6 hours</em> for Red alone.
For this case we have the following quadratic equation:
![x ^ 2-4x + 23 = 0](https://tex.z-dn.net/?f=x%20%5E%202-4x%20%2B%2023%20%3D%200)
The solutions will be given by:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2a%7D)
Where:
![a = 1\\b = -4\\c = 23](https://tex.z-dn.net/?f=a%20%3D%201%5C%5Cb%20%3D%20-4%5C%5Cc%20%3D%2023)
Substituting the values we have:
![x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (23)}} {2 (1)}\\x = \frac {4 \pm \sqrt {16-92}} {2}\\x = \frac {4 \pm \sqrt {-76}} {2}\\x = \frac {4 \pm \sqrt {76i ^ 2}} {2}\\x = \frac {4 \pmi \sqrt {76}} {2}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 19}} {2}\\x = \frac {4 \pm2i \sqrt {19}} {2}\\x = 2 \pm i\sqrt {19}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-%20%28-%204%29%20%5Cpm%20%5Csqrt%20%7B%28-%204%29%20%5E%202-4%20%281%29%20%2823%29%7D%7D%20%7B2%20%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpm%20%5Csqrt%20%7B16-92%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpm%20%5Csqrt%20%7B-76%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpm%20%5Csqrt%20%7B76i%20%5E%202%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpmi%20%5Csqrt%20%7B76%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpmi%20%5Csqrt%20%7B2%20%5E%202%20%2A%2019%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpm2i%20%5Csqrt%20%7B19%7D%7D%20%7B2%7D%5C%5Cx%20%3D%202%20%5Cpm%20i%5Csqrt%20%7B19%7D)
We have two roots:
![x_ {1} = 2-i \sqrt {19}\\x_ {2} = 2 + i \sqrt {19}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%202-i%20%5Csqrt%20%7B19%7D%5C%5Cx_%20%7B2%7D%20%3D%202%20%2B%20i%20%5Csqrt%20%7B19%7D)
ANswer:
![x_ {1} = 2-i\sqrt {19}\\x_ {2} = 2 + i\sqrt {19}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%202-i%5Csqrt%20%7B19%7D%5C%5Cx_%20%7B2%7D%20%3D%202%20%2B%20i%5Csqrt%20%7B19%7D)
Answer:
A = 5
ft²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A =
bh ( b is the base and h the height ) , then
A =
× 5 × 2
← convert to improper fraction
=
× ![\frac{7}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B3%7D)
= ![\frac{5(7)}{2(3)}](https://tex.z-dn.net/?f=%5Cfrac%7B5%287%29%7D%7B2%283%29%7D)
= ![\frac{35}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B35%7D%7B6%7D)
= 5
ft²
First you subtract 5 from each side. so its 6x+5=29 -5 -5which then you get 6x=24. You then divide 6 from 24 and you get x=4