PART A :OK so here is the table for the health inspector; all you are really doing is 7+7+7, and so on:
PART A: health inspector: 7,14,21,28,35,42,49,56,63,70,77,84..........
PART A:same thing for the fire inspector, except this time your adding 12+12+12, and so on:
PART A: fire inspector: 12,24,36,48,60,72,84,96.......
PART B: and to figure out what day they will both come is you have to find the LCM (least common multiple)
PART B: which in this case is Day 84
hopes this helps!!!!!
Write the equation of the lines in slope-intercept form (y=mx+b)
First equation: It is already in slope-intercept form
![y=\frac{2}{5}x-4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%7D%7B5%7Dx-4)
Second equation: solve y:
![\begin{gathered} 4x-10y=-7 \\ 4x-4x-10y=-4x-7 \\ -10y=-4x-7 \\ \frac{-10}{-10}y=\frac{-4}{-10}x-\frac{7}{-10} \\ \\ y=\frac{4}{10}x+\frac{7}{10} \\ \\ y=\frac{2}{5}x+\frac{7}{10} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%204x-10y%3D-7%20%5C%5C%204x-4x-10y%3D-4x-7%20%5C%5C%20-10y%3D-4x-7%20%5C%5C%20%5Cfrac%7B-10%7D%7B-10%7Dy%3D%5Cfrac%7B-4%7D%7B-10%7Dx-%5Cfrac%7B7%7D%7B-10%7D%20%5C%5C%20%20%5C%5C%20y%3D%5Cfrac%7B4%7D%7B10%7Dx%2B%5Cfrac%7B7%7D%7B10%7D%20%5C%5C%20%20%5C%5C%20y%3D%5Cfrac%7B2%7D%7B5%7Dx%2B%5Cfrac%7B7%7D%7B10%7D%20%5Cend%7Bgathered%7D)
Identify the slope of each line:
If two or more lines have the same slope then the lines are parallel
If two lines have slopes that are negative reciprocals then the lines are perpendicular
The two given lines have the same slope: 2/5. Then, they are parallel lines
First subtract 4 from both sides
![13 - 4 - 5m = - 6m](https://tex.z-dn.net/?f=13%20-%204%20-%205m%20%3D%20-%206m)
then simplify
![9 - 5m = - 6m](https://tex.z-dn.net/?f=9%20-%205m%20%3D%20-%206m)
add -5 to both sides
![9 = - m](https://tex.z-dn.net/?f=9%20%3D%20-%20m)
since a variable shouldn't be negative the answer should be
![m = - 9](https://tex.z-dn.net/?f=m%20%3D%20-%209)
(I prefer having the variable on the left side)
It’s c. Where the two planes intersect
X= tennis balls Noah has
x<8