check the picture below.
make sure your calculator is in Degree mode.
Answer: ( 0, 2 )
Step-by-step explanation:
You have to put coordinates of each graph on these equations y = -x + 2 and y = (1/2)x + 2. If putting coordinates satisfies both equations, then that coordinate will be the solution.
For example, let's put (0, 2) to equations.
y = -x + 2
2 = -0 + 2
2 = 2, true
y = (1/2)x + 2
2 = (1/2) × 0 + 2
2 = 2, true
So, ( 0, 2 ) is the solution.
Answer:
The home would be worth $249000 during the year of 2012.
Step-by-step explanation:
The price of the home in t years after 2004 can be modeled by the following equation:
![P(t) = P(0)(1+r)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281%2Br%29%5E%7Bt%7D)
In which P(0) is the price of the house in 2004 and r is the growth rate.
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.
This means that ![r = 0.047](https://tex.z-dn.net/?f=r%20%3D%200.047)
$172000 in 2004
This means that ![P(0) = 172000](https://tex.z-dn.net/?f=P%280%29%20%3D%20172000)
What year would the home be worth $ 249000 ?
t years after 2004.
t is found when P(t) = 249000. So
![P(t) = P(0)(1+r)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281%2Br%29%5E%7Bt%7D)
![249000 = 172000(1.047)^{t}](https://tex.z-dn.net/?f=249000%20%3D%20172000%281.047%29%5E%7Bt%7D)
![(1.047)^{t} = \frac{249000}{172000}](https://tex.z-dn.net/?f=%281.047%29%5E%7Bt%7D%20%3D%20%5Cfrac%7B249000%7D%7B172000%7D)
![\log{(1.047)^{t}} = \log{\frac{249000}{172000}}](https://tex.z-dn.net/?f=%5Clog%7B%281.047%29%5E%7Bt%7D%7D%20%3D%20%5Clog%7B%5Cfrac%7B249000%7D%7B172000%7D%7D)
![t\log(1.047) = \log{\frac{249000}{172000}}](https://tex.z-dn.net/?f=t%5Clog%281.047%29%20%3D%20%5Clog%7B%5Cfrac%7B249000%7D%7B172000%7D%7D)
![t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B%5Cfrac%7B249000%7D%7B172000%7D%7D%7D%7B%5Clog%281.047%29%7D)
![t = 8.05](https://tex.z-dn.net/?f=t%20%3D%208.05)
2004 + 8.05 = 2012
The home would be worth $249000 during the year of 2012.
.91 times 4000=3640 people prefer Pedro’s
4000-3640= 360 people prefer other brands