Check the picture below.
so, we know the parabola has a vertex at (0 , 50), we also know it passes through (60 , 0), so then
![~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=~~~~~~%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%5C%5C%5C%5C%20%5Cstackrel%7B%22a%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22a%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\stackrel{vertex}{(0~~,~~50)}\implies y=a(x-0)^2+50\implies y = ax^2+50 \\\\\\ \begin{cases} x =60\\ y = 0 \end{cases}\implies 0=a6^2+50\implies -50=3600a\implies -\cfrac{50}{3600}=a \\\\\\ -\cfrac{1}{72}=a~\hfill therefore~\hfill \boxed{y=-\cfrac{1}{72}x^2+50}](https://tex.z-dn.net/?f=%5Cstackrel%7Bvertex%7D%7B%280~~%2C~~50%29%7D%5Cimplies%20y%3Da%28x-0%29%5E2%2B50%5Cimplies%20y%20%3D%20ax%5E2%2B50%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20x%20%3D60%5C%5C%20y%20%3D%200%20%5Cend%7Bcases%7D%5Cimplies%200%3Da6%5E2%2B50%5Cimplies%20-50%3D3600a%5Cimplies%20-%5Ccfrac%7B50%7D%7B3600%7D%3Da%20%5C%5C%5C%5C%5C%5C%20-%5Ccfrac%7B1%7D%7B72%7D%3Da~%5Chfill%20therefore~%5Chfill%20%5Cboxed%7By%3D-%5Ccfrac%7B1%7D%7B72%7Dx%5E2%2B50%7D)
so then, what's "y" when x = 25?
![y=-\cfrac{1}{72}25^2+50\implies y = -\cfrac{625}{72}+50\implies y = \cfrac{2975}{72}\implies y\approx 41.32](https://tex.z-dn.net/?f=y%3D-%5Ccfrac%7B1%7D%7B72%7D25%5E2%2B50%5Cimplies%20y%20%3D%20-%5Ccfrac%7B625%7D%7B72%7D%2B50%5Cimplies%20y%20%3D%20%5Ccfrac%7B2975%7D%7B72%7D%5Cimplies%20y%5Capprox%2041.32)
Answer:
x = 1
Step-by-step explanation:
![\frac{2}{3} x - \frac{5}{6} = - \frac{5}{12} x + \frac{1}{4} \\ \frac{2}{3}x + \frac{5}{12} x = \frac{1}{4} + \frac{5}{6} \\ \frac{8}{12} x + \frac{5}{12}x = \frac{3}{12} + \frac{10}{12} \\ \frac{13}{12} x = \frac{13}{12} \\ x = 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B5%7D%7B6%7D%20%20%3D%20%20-%20%20%5Cfrac%7B5%7D%7B12%7D%20x%20%2B%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5C%5C%20%20%5Cfrac%7B2%7D%7B3%7Dx%20%2B%20%20%5Cfrac%7B5%7D%7B12%7D%20%20x%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%2B%20%20%5Cfrac%7B5%7D%7B6%7D%20%20%5C%5C%20%20%5Cfrac%7B8%7D%7B12%7D%20x%20%2B%20%20%5Cfrac%7B5%7D%7B12%7Dx%20%3D%20%20%5Cfrac%7B3%7D%7B12%7D%20%20%2B%20%20%5Cfrac%7B10%7D%7B12%7D%20%20%5C%5C%20%20%5Cfrac%7B13%7D%7B12%7D%20x%20%3D%20%20%5Cfrac%7B13%7D%7B12%7D%20%20%5C%5C%20x%20%3D%201)
Answer:
The Answer is 4
Step-by-step explanation:
1/2 / 8/3
______
1 * 8
2 * 3
______
8/2 *3
______
8/6
______
4/3
______
= 4
Answer:
Answer is 91.5%
Step-by-step explanation:
In 1963= 10,000 sq miles; In 2001= 850 sq miles
- Now applying formula of percentage of decrease we get:
% = Decrease in Amount/ Actual Amount
- Applying values in formula:
= 10000-850/10000
= 9150/10000
% = 0.915
In percentage we get 91.5%
Answer:
x = 3, v = -8
Step-by-step explanation:
Substitute x.
![\frac{-67-11v}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B-67-11v%7D%7B7%7D)
[5 •
= -73 - 11v]
Isolate v.
5
= -73 - 11v
v = -8
Substitute v.
x = ![\frac{-67-11(-8)}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B-67-11%28-8%29%7D%7B7%7D)
x = 3