The answer as a decimal is 0.06507705122
Hope this helps!
Answer:
Below
Step-by-step explanation:
● y -(-3) = (1/4) (x-9)
Replace 1/4 by 0.25 to make it easier
● y + 3 = 0.25(x-9)
● y + 3 = 0.25x - 2.25
Add 3 to both sides
● y +3-3 = 0.25x -2.25-3
● y = 0.25x -5.25
To the coordinates of a point from this line replace x by a value.
The easiest one is 0.
● y = 0.25×0 -5.25
● y = 5.25
5.25 is 21/4
So the coordinates are (0, 21/4)
8 would be the constant but in this situation there is a variable next to it so I’m not sure if it would be considered a constant
Answer:
5b
Step-by-step explanation:
<em>Hope this helps <3</em>
let's firstly find the equation of the parabola, bearing in mind that x-intercepts or solutions/zeros/roots means y = 0.
![\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2-9 \\\\\\ \textit{we also know that } \begin{cases} x=0\\ y=-6 \end{cases}\implies -6=a(0-1)^2-9\implies 3=a(-1)^2](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Bvertical%20parabola%20vertex%20form%7D%20%5C%5C%5C%5C%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%20%5Cend%7Bcases%7D%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%3D1%5C%5C%20k%3D-9%20%5Cend%7Bcases%7D%5Cimplies%20y%3Da%28x-1%29%5E2-9%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Bwe%20also%20know%20that%20%7D%20%5Cbegin%7Bcases%7D%20x%3D0%5C%5C%20y%3D-6%20%5Cend%7Bcases%7D%5Cimplies%20-6%3Da%280-1%29%5E2-9%5Cimplies%203%3Da%28-1%29%5E2)
![\bf 3=a\qquad \qquad \textit{therefore}\qquad \qquad \boxed{y=3(x-1)^2-9} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{y}{0}=3(x-1)^2-9\implies 9=3(x-1)^2\implies \cfrac{9}{3}=(x-1)^2\implies 3=(x-1)^2 \\\\\\ \pm\sqrt{3}=x-1\implies \pm\sqrt{3}+1=x\implies x= \begin{cases} \sqrt{3}+1\\ -\sqrt{3}+1 \end{cases}\implies x\approx \begin{cases} 2.73\\ -0.73 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%203%3Da%5Cqquad%20%5Cqquad%20%5Ctextit%7Btherefore%7D%5Cqquad%20%5Cqquad%20%5Cboxed%7By%3D3%28x-1%29%5E2-9%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7By%7D%7B0%7D%3D3%28x-1%29%5E2-9%5Cimplies%209%3D3%28x-1%29%5E2%5Cimplies%20%5Ccfrac%7B9%7D%7B3%7D%3D%28x-1%29%5E2%5Cimplies%203%3D%28x-1%29%5E2%20%5C%5C%5C%5C%5C%5C%20%5Cpm%5Csqrt%7B3%7D%3Dx-1%5Cimplies%20%5Cpm%5Csqrt%7B3%7D%2B1%3Dx%5Cimplies%20x%3D%20%5Cbegin%7Bcases%7D%20%5Csqrt%7B3%7D%2B1%5C%5C%20-%5Csqrt%7B3%7D%2B1%20%5Cend%7Bcases%7D%5Cimplies%20x%5Capprox%20%5Cbegin%7Bcases%7D%202.73%5C%5C%20-0.73%20%5Cend%7Bcases%7D)
