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 :
Answer:
x = 147/5 and y = 78
Step-by-step explanation:
First solve by substitution and put 78 into y in -5x + 2y = 9 so you get 147/5
then plug 147/5 into x and find y
Answer:
([-3], [0]), ([3], [0])
Step-by-step explanation:
The given equation of the hyperbola is presented as follows;
![\dfrac{x^2}{9} - \dfrac{y^2}{49} = 1](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%7D%7B9%7D%20-%20%5Cdfrac%7By%5E2%7D%7B49%7D%20%3D%201)
The vertices of an hyperbola (of the form)
are (± a, 0)
The given hyperbola can we presented in a similar form as follows;
![\dfrac{x^2}{9} - \dfrac{y^2}{49} = \dfrac{x^2}{3^2} - \dfrac{y^2}{7^2} = 1](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%7D%7B9%7D%20-%20%5Cdfrac%7By%5E2%7D%7B49%7D%20%3D%20%5Cdfrac%7Bx%5E2%7D%7B3%5E2%7D%20-%20%5Cdfrac%7By%5E2%7D%7B7%5E2%7D%20%3D%201)
Therefore, by comparison, the vertices of the parabola are (± 3, 0), which gives;
The vertices of the parabola are ([-3], [0]), ([3], [0]).