Answer:
The corresponding change is 3
Step-by-step explanation:
3 is the slope and corresponds to the relative change when incresing in 1 unit
//I'll use the discriminant rule for this.
b^2 - 4ac = 0 when one real root
Therefore, k^2 - 4*3*4= 0
k^2 = 48
k= +-4√3
The perimeter of rectangle is 25.13 feet
<em><u>Solution:</u></em>
Given that,
width of a rectangle = ![4\frac{1}{6} \text{ feet }](https://tex.z-dn.net/?f=4%5Cfrac%7B1%7D%7B6%7D%20%5Ctext%7B%20feet%20%7D)
Convert the mixed fraction to improper fraction
![\rightarrow 4\frac{1}{6} = \frac{6 \times 4 + 1}{6} = \frac{25}{6}](https://tex.z-dn.net/?f=%5Crightarrow%204%5Cfrac%7B1%7D%7B6%7D%20%3D%20%5Cfrac%7B6%20%5Ctimes%204%20%2B%201%7D%7B6%7D%20%3D%20%5Cfrac%7B25%7D%7B6%7D)
Therefore,
![\text{width of rectangle } = \frac{25}{6} \text{ feet }](https://tex.z-dn.net/?f=%5Ctext%7Bwidth%20of%20rectangle%20%7D%20%3D%20%5Cfrac%7B25%7D%7B6%7D%20%5Ctext%7B%20feet%20%7D)
Area of rectangle = 35 feet
<em><u>The area of rectangle is given by formula:</u></em>
![area = length \times width](https://tex.z-dn.net/?f=area%20%3D%20length%20%5Ctimes%20width)
Substituting the given values, we get
![35 = length \times \frac{25}{6}\\\\length = 35 \times \frac{6}{25} = \frac{42}{5}](https://tex.z-dn.net/?f=35%20%3D%20length%20%5Ctimes%20%5Cfrac%7B25%7D%7B6%7D%5C%5C%5C%5Clength%20%3D%2035%20%5Ctimes%20%5Cfrac%7B6%7D%7B25%7D%20%3D%20%5Cfrac%7B42%7D%7B5%7D)
Thus we get,
![\text{length of rectangle } = \frac{42}{5} \text{ feet }](https://tex.z-dn.net/?f=%5Ctext%7Blength%20of%20rectangle%20%7D%20%3D%20%5Cfrac%7B42%7D%7B5%7D%20%5Ctext%7B%20feet%20%7D)
<em><u>The perimeter of rectangle is given as:</u></em>
perimeter = 2(length + width)
![perimeter = 2(\frac{42}{5} + \frac{25}{6})\\\\perimeter =2(8.4+4.167)\\\\perimeter = 2(12.567)\\\\perimeter = 25.13](https://tex.z-dn.net/?f=perimeter%20%3D%202%28%5Cfrac%7B42%7D%7B5%7D%20%2B%20%5Cfrac%7B25%7D%7B6%7D%29%5C%5C%5C%5Cperimeter%20%3D2%288.4%2B4.167%29%5C%5C%5C%5Cperimeter%20%3D%202%2812.567%29%5C%5C%5C%5Cperimeter%20%3D%2025.13)
Thus perimeter of rectangle is 25.13 feet
its b as the slope of the line is constant so it's 2.