Answer:
![y = \frac{3}{2}x - 3](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B2%7Dx%20-%203)
![y = \frac{1}{8} x - \frac{7}{8}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B8%7D%20x%20-%20%20%5Cfrac%7B7%7D%7B8%7D%20)
Step-by-step explanation:
The given system is
3x-2y=6
0.4(20y+15)=x
The slope intercept form is y=mx+c.
For the first equation, 3x-2y=6, we add -3x to both side -2y=-3x+6
![y = \frac{3}{2}x - 3](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B2%7Dx%20-%203)
For 0.4(20y+15)=x, we expand to get:
![8y + 7 = x](https://tex.z-dn.net/?f=8y%20%20%2B%207%20%3D%20x)
![8y= x - 7](https://tex.z-dn.net/?f=8y%3D%20x%20-%207)
Divide through by 8
![y = \frac{1}{8}x - \frac{7}{8}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B8%7Dx%20-%20%20%5Cfrac%7B7%7D%7B8%7D%20)
Therefore the system in slope-intercept form is:
![y = \frac{3}{2}x - 3](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B2%7Dx%20-%203)
![y = \frac{1}{8}x - \frac{7}{8}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B8%7Dx%20-%20%20%5Cfrac%7B7%7D%7B8%7D%20)
Answer:
The population in 2011 will be of 34.88 million people.
Step-by-step explanation:
The population after t years is modeled by an exponential function is the following format:
![P(t) = P(0)e^{rt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7Brt%7D)
In which P(0) is the initial population and r is the growth rate.
At the beginning of 1990, 21.7 million people lived in the metropolitan area of a particular city.
This means that ![P(0) = 21.7](https://tex.z-dn.net/?f=P%280%29%20%3D%2021.7)
The 1998 population was 26 million.
1998 is 8 years after 1990. So ![P(8) = 26](https://tex.z-dn.net/?f=P%288%29%20%3D%2026)
We use this to find the value of r.
![P(t) = P(0)e^{rt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7Brt%7D)
![26 = 21.7e^{8r}](https://tex.z-dn.net/?f=26%20%3D%2021.7e%5E%7B8r%7D)
![e^{8r} = \frac{26}{21.7}](https://tex.z-dn.net/?f=e%5E%7B8r%7D%20%3D%20%5Cfrac%7B26%7D%7B21.7%7D)
![\ln{e^{8r}} = \ln{\frac{26}{21.7}}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B8r%7D%7D%20%3D%20%5Cln%7B%5Cfrac%7B26%7D%7B21.7%7D%7D)
![8r = \ln{\frac{26}{21.7}}](https://tex.z-dn.net/?f=8r%20%3D%20%5Cln%7B%5Cfrac%7B26%7D%7B21.7%7D%7D)
![r = \frac{\ln{\frac{26}{21.7}}}{8}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B%5Cln%7B%5Cfrac%7B26%7D%7B21.7%7D%7D%7D%7B8%7D)
![r = 0.0226](https://tex.z-dn.net/?f=r%20%3D%200.0226)
So
![P(t) = P(0)e^{rt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7Brt%7D)
![P(t) = 21.7e^{0.0226t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%2021.7e%5E%7B0.0226t%7D)
If this trend continues, how large will the population be in the year 2011?
2011 is 21 years after 1990. So this is P(21).
![P(t) = 21.7e^{0.0226t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%2021.7e%5E%7B0.0226t%7D)
![P(21) = 21.7e^{0.0226*21}](https://tex.z-dn.net/?f=P%2821%29%20%3D%2021.7e%5E%7B0.0226%2A21%7D)
![P(21) = 34.88](https://tex.z-dn.net/?f=P%2821%29%20%3D%2034.88)
The population in 2011 will be of 34.88 million people.
Answer:
Because it is terminating.
Step-by-step explanation:
0.71875 is rational because it is terminating (has a clear end). If it were a bunch of random numbers that never ended, then it would be irrational.
Answer:
m = variables
+4 = Coefficients
-7 = Coefficients
and 2 and 6 are Constants
Hope this helps!
Step-by-step explanation:
Answer:
Step-by-step explanation:
These problems where you are not told what basic shape you are working with and have to assume some properties, just should not be asked. You are to assume that this is a parallelepiped.
The answer that you want is B
The length of the rectangle is 8 in given along the bottom. The top is also 8 in. The width of that rectangle is 4. The rectangle is the top of the drawing.