Answer:
The 9 would be pointing at 45 and 45 + 10 = 55 + 5 equals 60 thus making the answer 15 minutes until the next hour
Step-by-step explanation:
1 km = 1000 m
(hence the term "kilo" which means 1000).
so. he runs 1000 m at the rate of 3 minutes per km, that means 3 minutes per 1000 m.
now, we can see the solution already with our eyes.
but let's do it formally :
the rate or ratio between time and distance must be the same for the same speed.
so,
3 min / 1000 m = x min / 500 m
500 m × 3 min / 1000 m = x min
1/2 × 3 min = x min
3/2 = 1.5 min = x min
so, it takes him 1.5 minutes (90 seconds) to run 500 m.
The given expression :
![y=(\frac{1}{2})^x](https://tex.z-dn.net/?f=y%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5Ex)
For coordinates:
put x = 0 then :
![\begin{gathered} y=(\frac{1}{2})^0 \\ y=1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E0%20%5C%5C%20y%3D1%20%5Cend%7Bgathered%7D)
Coordinate : (x, y) = (0, 1)
Put x= 1 and simplify :
![\begin{gathered} y=(\frac{1}{2})^1 \\ y=\frac{1}{2} \\ y=0.5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E1%20%5C%5C%20y%3D%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20y%3D0.5%20%5Cend%7Bgathered%7D)
Coordinate : (x, y) = ( 1, 0.5)
Put x = (-2) and simplify :
![\begin{gathered} y=(\frac{1}{2})^{-2} \\ y=\frac{1^{-2}}{2^{-2}} \\ y=\frac{2^2}{1^2} \\ y=2^2 \\ y=4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-2%7D%20%5C%5C%20y%3D%5Cfrac%7B1%5E%7B-2%7D%7D%7B2%5E%7B-2%7D%7D%20%5C%5C%20y%3D%5Cfrac%7B2%5E2%7D%7B1%5E2%7D%20%5C%5C%20y%3D2%5E2%20%5C%5C%20y%3D4%20%5Cend%7Bgathered%7D)
Coordinate : (x, y) = ( -2, 4)
Put x = (-3) and simplify :
![\begin{gathered} y=(\frac{1}{2})^{-3} \\ y=\frac{1^{-3}}{2^{-3}} \\ y=\frac{2^3}{1^3} \\ y=2^3 \\ y=8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-3%7D%20%5C%5C%20y%3D%5Cfrac%7B1%5E%7B-3%7D%7D%7B2%5E%7B-3%7D%7D%20%5C%5C%20y%3D%5Cfrac%7B2%5E3%7D%7B1%5E3%7D%20%5C%5C%20y%3D2%5E3%20%5C%5C%20y%3D8%20%5Cend%7Bgathered%7D)
Coordinate : (x, y) = (-3, 8)
Substitute x = (-1) and simplify :
![\begin{gathered} y=(\frac{1}{2})^x \\ y=(\frac{1}{2})^{-1} \\ y=\frac{1^{-1}}{2^{-1}} \\ y=\frac{2}{1} \\ y=2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5Ex%20%5C%5C%20y%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-1%7D%20%5C%5C%20y%3D%5Cfrac%7B1%5E%7B-1%7D%7D%7B2%5E%7B-1%7D%7D%20%5C%5C%20y%3D%5Cfrac%7B2%7D%7B1%7D%20%5C%5C%20y%3D2%20%5Cend%7Bgathered%7D)
Coordinate : (x, y) = ( -1, 2)
So, the coordinates are :
The graph is :