Answer: 6.5
Step-by-step explanation:
13/5 divided by 2/5 so 6.5
Answer:
3 hours
Step-by-step explanation:
You find the LCM between 20 and 15, which is 5. This means that Kim and Tom are both biking at 5 miles per hour, meaning that to determine how much time Tom takes, you would do 15/5, which is 3 hours.
Let the two numbers be x and y
then x+y=9
x-y=3
2x=12
x=6
6+y=9
y=3
so the numbers are 9 and 3
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
![-2x+4y=8\implies 4y=2x+8\implies y=\cfrac{2x+8}{4} \\\\\\ y=\cfrac{2x}{4}+\cfrac{8}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x+2\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}](https://tex.z-dn.net/?f=-2x%2B4y%3D8%5Cimplies%204y%3D2x%2B8%5Cimplies%20y%3D%5Ccfrac%7B2x%2B8%7D%7B4%7D%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7B2x%7D%7B4%7D%2B%5Ccfrac%7B8%7D%7B4%7D%5Cimplies%20y%3D%5Cstackrel%7B%5Cstackrel%7Bm%7D%7B%5Cdownarrow%20%7D%7D%7B%5Ccfrac%7B1%7D%7B2%7D%7Dx%2B2%5Cimpliedby%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20slope-intercept~form%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y%3D%5Cunderset%7By-intercept%7D%7B%5Cstackrel%7Bslope%5Cqquad%20%7D%7B%5Cstackrel%7B%5Cdownarrow%20%7D%7Bm%7Dx%2B%5Cunderset%7B%5Cuparrow%20%7D%7Bb%7D%7D%7D%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D)
since we know that's its slope, then
![\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}](https://tex.z-dn.net/?f=%5Cstackrel%7B~%5Chspace%7B5em%7D%5Ctextit%7Bperpendicular%20lines%20have%20%5Cunderline%7Bnegative%20reciprocal%7D%20slopes%7D~%5Chspace%7B5em%7D%7D%20%7B%5Cstackrel%7Bslope%7D%7B%5Ccfrac%7B1%7D%7B2%7D%7D%20~%5Chfill%20%5Cstackrel%7Breciprocal%7D%7B%5Ccfrac%7B2%7D%7B1%7D%7D%20~%5Chfill%20%5Cstackrel%7Bnegative~reciprocal%7D%7B-%5Ccfrac%7B2%7D%7B1%7D%5Cimplies%20-2%7D%7D)
so then we're really looking for the equation of a line whose slope is -2 and passes through (2 , 1)
![(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad \qquad \stackrel{slope}{m}\implies -2 \\\\\\ \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}{1}=\stackrel{m}{-2}(x-\stackrel{x_1}{2}) \\\\\\ y-1=-2x-4\implies y=-2x-3](https://tex.z-dn.net/?f=%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B1%7D%29%5Cqquad%20%5Cqquad%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20-2%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%7B1%7D%3D%5Cstackrel%7Bm%7D%7B-2%7D%28x-%5Cstackrel%7Bx_1%7D%7B2%7D%29%20%5C%5C%5C%5C%5C%5C%20y-1%3D-2x-4%5Cimplies%20y%3D-2x-3)
Repeating decimals are rational....but they have to be repeating.
The only one that is not repeating is : D .131131113...now if the last 3 digits would have been 131 instead of 113, then it would have been rational.