How do u see the picture
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Using the rules of exponents
⇔
and
= 1
Substitute the values of x into ![4^{-x}](https://tex.z-dn.net/?f=4%5E%7B-x%7D)
x = 0 →
= 1 ⇒ a = 1
x = 2 →
=
=
, hence
b = ![\frac{1}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D)
x = 4 →
=
=
, hence
c = ![\frac{1}{256}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B256%7D)
the parabola has maximum at 9, meaning is a vertical parabola and it opens downwards.
it has a symmetry at x = -5, namely its vertex's x-coordinate is -5.
check the picture below.
so then, we can pretty much tell its vertex is at (-5 , 9), and we also know it passes through (-7, 1)
![\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Bparabola%20vertex%20form%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cleftarrow%20%5Ctextit%7Busing%20this%20one%7D%5C%5C%5C%5C%20x%3Da%28y-%20k%29%5E2%2B%20h%20%5Cend%7Barray%7D%20%5Cqquad%5Cqquad%20vertex~~%28%5Cstackrel%7B%7D%7B%20h%7D%2C%5Cstackrel%7B%7D%7B%20k%7D%29%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20h%3D-5%5C%5C%20k%3D9%20%5Cend%7Bcases%7D%5Cimplies%20y%3Da%5Bx-%28-5%29%5D%5E2%2B9%5Cimplies%20y%3Da%28x%2B5%29%5E2%2B9)
![\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bwe%20also%20know%20that%20%7D%20%5Cbegin%7Bcases%7D%20x%3D-7%5C%5C%20y%3D1%20%5Cend%7Bcases%7D%5Cimplies%201%3Da%28-7%2B5%29%5E2%2B9%20%5C%5C%5C%5C%5C%5C%20-8%3Da%28-2%29%5E2%5Cimplies%20-8%3D4a%5Cimplies%20%5Ccfrac%7B-8%7D%7B4%7D%3Da%5Cimplies%20-2%3Da%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20y%3D-2%28x%2B5%29%5E2%2B9~%5Chfill)
Answer:
23 days
Step-by-step explanation:
We are told that the stadium holds 7500 individuals.
Now, if 600 seats have already been made, It means the number of seats left to be made to complete the stadium = 7500 - 600 = 6900 seats
We are told that 300 seats can be made in a day. Thus, number of days to be used to finish the remaining seats = 6900/300 = 23 days
Thus, it will take 23 days to complete all the 7500 seats.
![f(x)=mx+b\to y=mx+b](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb%5Cto%20y%3Dmx%2Bb)
We have two points:
![(-3,\ 0);\ (-4,\ 7)](https://tex.z-dn.net/?f=%28-3%2C%5C%200%29%3B%5C%20%28-4%2C%5C%207%29)
The point slope form of the line:
![y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5C%5C%5C%5Cm%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substitute
![m=\dfrac{7-0}{-4-(-3)}=\dfrac{7}{-1}=-7](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B7-0%7D%7B-4-%28-3%29%7D%3D%5Cdfrac%7B7%7D%7B-1%7D%3D-7)
![y-0=-7(x-(-3))\\\\y=-7(x+3)\\\\y=-7x-21](https://tex.z-dn.net/?f=y-0%3D-7%28x-%28-3%29%29%5C%5C%5C%5Cy%3D-7%28x%2B3%29%5C%5C%5C%5Cy%3D-7x-21)
Answer:
![f(x)=-7x-21](https://tex.z-dn.net/?f=f%28x%29%3D-7x-21)