Answer:
5X + 8Y >= 300; intersection at (-20, 50)
Step-by-step explanation:
let t = work hours
0 < t < 30
X = time lawn mowing
Y = time babysitting.
X + Y < 30
5X + 8Y >= 300
We could solve...
X < 30 - Y
5(30 - Y) + 8Y >=300
150 - 5Y + 8Y >= 300
3Y >=150
Y >=50
then X < -20
intersection at (-20, 50)
We know that C is dependent on how many hours of service was done. We also know that C is linearly dependent on how many hours of service was done because it's a constant $50 per hour.
So, the equation would be a linear equation in the form C = 50h + L where h is the number of hours and L is the y-intercept.
Since there is an initial charge of $25, when h = 0, C = $25 -> L = $25.
So, the equation is C = 50h + 25.
Answer:
x≤ -3/8
Step-by-step explanation:
![4x\le \:-\frac{2}{5}\left(6x+6\right)\\](https://tex.z-dn.net/?f=4x%5Cle%20%5C%3A-%5Cfrac%7B2%7D%7B5%7D%5Cleft%286x%2B6%5Cright%29%5C%5C)
Expand ;
![\mathrm{Expand\:}-\frac{2}{5}\left(6x+6\right):\quad -\frac{12}{5}x-\frac{12}{5}](https://tex.z-dn.net/?f=%5Cmathrm%7BExpand%5C%3A%7D-%5Cfrac%7B2%7D%7B5%7D%5Cleft%286x%2B6%5Cright%29%3A%5Cquad%20-%5Cfrac%7B12%7D%7B5%7Dx-%5Cfrac%7B12%7D%7B5%7D)
![4x\le \:-\frac{12}{5}x-\frac{12}{5}\\\\\mathrm{Add\:}\frac{12}{5}x\mathrm{\:to\:both\:sides}\\\\4x+\frac{12}{5}x\le \:-\frac{12}{5}x-\frac{12}{5}+\frac{12}{5}x](https://tex.z-dn.net/?f=4x%5Cle%20%5C%3A-%5Cfrac%7B12%7D%7B5%7Dx-%5Cfrac%7B12%7D%7B5%7D%5C%5C%5C%5C%5Cmathrm%7BAdd%5C%3A%7D%5Cfrac%7B12%7D%7B5%7Dx%5Cmathrm%7B%5C%3Ato%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C4x%2B%5Cfrac%7B12%7D%7B5%7Dx%5Cle%20%5C%3A-%5Cfrac%7B12%7D%7B5%7Dx-%5Cfrac%7B12%7D%7B5%7D%2B%5Cfrac%7B12%7D%7B5%7Dx)
Simplify
![\frac{32}{5}x\le \:-\frac{12}{5}\\\\Multiply \:both\:sides\:by\:5\\5\times\frac{32}{5}x\le \:5\left(-\frac{12}{5}\right)\\\\Simplify\\32x\le \:-12\\\\Divide \:both\:sides\:by\:32\\\frac{32x}{32}\le \frac{-12}{32}\\\\Simplify\\x\le \:-\frac{3}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B5%7Dx%5Cle%20%5C%3A-%5Cfrac%7B12%7D%7B5%7D%5C%5C%5C%5CMultiply%20%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A5%5C%5C5%5Ctimes%5Cfrac%7B32%7D%7B5%7Dx%5Cle%20%5C%3A5%5Cleft%28-%5Cfrac%7B12%7D%7B5%7D%5Cright%29%5C%5C%5C%5CSimplify%5C%5C32x%5Cle%20%5C%3A-12%5C%5C%5C%5CDivide%20%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A32%5C%5C%5Cfrac%7B32x%7D%7B32%7D%5Cle%20%5Cfrac%7B-12%7D%7B32%7D%5C%5C%5C%5CSimplify%5C%5Cx%5Cle%20%5C%3A-%5Cfrac%7B3%7D%7B8%7D)
M = (y2-y1)/(x2-x1) so for your question (2--8)/(4--3) = (2+8)/(4+3) = 10/7
Now to find the slope-intercept form (y=mx+b) plug in the slope and a point to find b. I'm going to use point T. So 2 = (10/7)*4 +b => b = 2 - (40/7) = -26/7. So the answer would be y = (10/7)x - (26/7).
Hope this helps!