Answer:
55
Step-by-step explanation:
This is 55 because you need to make a sum of 180 when making a line and 125+55=180
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
initial value of 3, namely when x = 0, y = 3, so we have the point (0 , 3) and it has a rate or slope of 3/4.
![(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{3}{4}}(x-\stackrel{x_1}{0})\implies y=\cfrac{3}{4}x+3](https://tex.z-dn.net/?f=%28%5Cstackrel%7Bx_1%7D%7B0%7D~%2C~%5Cstackrel%7By_1%7D%7B3%7D%29%5Cqquad%20%5Cqquad%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B4%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%5Cstackrel%7By_1%7D%7B3%7D%3D%5Cstackrel%7Bm%7D%7B%5Ccfrac%7B3%7D%7B4%7D%7D%28x-%5Cstackrel%7Bx_1%7D%7B0%7D%29%5Cimplies%20y%3D%5Ccfrac%7B3%7D%7B4%7Dx%2B3)
Given:
A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5.
To find:
The coordinates of that point.
Solution:
Section formula: If point divides a line segment in m:n, then the coordinates of that point are
![Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)](https://tex.z-dn.net/?f=Point%3D%5Cleft%28%5Cdfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%5Cdfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5Cright%29)
A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5. Using section formula, we get
![Point=\left(\dfrac{6(5)+5(-6)}{6+5},\dfrac{6(8)+5(-3)}{6+5}\right)](https://tex.z-dn.net/?f=Point%3D%5Cleft%28%5Cdfrac%7B6%285%29%2B5%28-6%29%7D%7B6%2B5%7D%2C%5Cdfrac%7B6%288%29%2B5%28-3%29%7D%7B6%2B5%7D%5Cright%29)
![Point=\left(\dfrac{30-30}{11},\dfrac{48-15}{11}\right)](https://tex.z-dn.net/?f=Point%3D%5Cleft%28%5Cdfrac%7B30-30%7D%7B11%7D%2C%5Cdfrac%7B48-15%7D%7B11%7D%5Cright%29)
![Point=\left(\dfrac{0}{11},\dfrac{33}{11}\right)](https://tex.z-dn.net/?f=Point%3D%5Cleft%28%5Cdfrac%7B0%7D%7B11%7D%2C%5Cdfrac%7B33%7D%7B11%7D%5Cright%29)
![Point=\left(0,3\right)](https://tex.z-dn.net/?f=Point%3D%5Cleft%280%2C3%5Cright%29)
Therefore, the coordinates of the required point are (0,3).
Answer:
Bryan Lively Professional Records Browse Bryan's professional profiles below to see current job title, work email address, place of employment and phone number. Showing 11 of 11 Results i think
For this case we have the following solution.
x = gallons of water to be added
For the 10% solution we have:
0.1 * 8 = 0.8
Then, for 5% we have:
(0.8 / x + 8) = 0.05
Rewriting:
(0.8 / x + 8) = (5/100)
Answer:
An equation can be used to find x, the humber of gallons of water he should add is:
(0.8 / x + 8) = (5/100)