Answer:
![y=7x+1](https://tex.z-dn.net/?f=y%3D7x%2B1)
Step-by-step explanation:
we know that
The equation of the line into slope intercept form is equal to
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the slope
b is the y-intercept
In this problem we have
![m=7](https://tex.z-dn.net/?f=m%3D7)
![point(1,8)](https://tex.z-dn.net/?f=point%281%2C8%29)
substitute and solve for b
![8=7(1)+b](https://tex.z-dn.net/?f=8%3D7%281%29%2Bb)
![8=7+b](https://tex.z-dn.net/?f=8%3D7%2Bb)
![b=8-7=1](https://tex.z-dn.net/?f=b%3D8-7%3D1)
The equation of the line is equal to
![y=7x+1](https://tex.z-dn.net/?f=y%3D7x%2B1)
Answer:
Answer:
3
×
3
×
4
×
2
=
72
Explanation:
Let's look at the 3 sandwiches and 3 soups first and then expand the calculation. There are 9 ways I can have one of the sandwiches and 1 of the soups:
⎛
⎜
⎜
⎜
⎜
⎝
0
Soup 1
Soup 2
Soup 3
Sandwich 1
1
2
3
Sandwich 2
4
5
6
Sandwich 3
7
8
9
⎞
⎟
⎟
⎟
⎟
⎠
And so we can see that we multiply the number of sandwiches and the number of soups to get the total number of ways to get one of each.
The same works for more categories of choices, and so we multiply the 3 sandwiches, the 3 soups, 4 salads, and 2 drinks to get:
3
×
3
×
4
×
2
=
72
Answer:
Deduction in the step-by-step explanation
Step-by-step explanation:
If a P0=50.000 deposit is compound every instant, the ammount in the account can be modeled as:
![P(t) = P_{0}*e^{it}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P_%7B0%7D%2Ae%5E%7Bit%7D)
If you pull out d dollars a year, the equation becomes:
![P(t) = P_{0}*e^{it}-d*t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P_%7B0%7D%2Ae%5E%7Bit%7D-d%2At)
If we derive this equation in terms of t, we have
![P(t) = P_{0}*e^{it}-d*t\\dP/dt=d(P_{0}*e^{it})/dt-d(d*t)/dt\\dP/dt=i*P_{0}*e^{it}-d\\](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P_%7B0%7D%2Ae%5E%7Bit%7D-d%2At%5C%5CdP%2Fdt%3Dd%28P_%7B0%7D%2Ae%5E%7Bit%7D%29%2Fdt-d%28d%2At%29%2Fdt%5C%5CdP%2Fdt%3Di%2AP_%7B0%7D%2Ae%5E%7Bit%7D-d%5C%5C)
The first term can be transformed like this:
![i*P_{0}*e^{it} = i*P(t)](https://tex.z-dn.net/?f=i%2AP_%7B0%7D%2Ae%5E%7Bit%7D%20%3D%20i%2AP%28t%29)
So replacing in the differential equation, we have
![dP/dt=i*P_{0}*e^{it}-d\\dP/dt=i*P(t)-d](https://tex.z-dn.net/?f=dP%2Fdt%3Di%2AP_%7B0%7D%2Ae%5E%7Bit%7D-d%5C%5CdP%2Fdt%3Di%2AP%28t%29-d)
Rearranging
![dP/dt-i*P(t)=-d](https://tex.z-dn.net/?f=dP%2Fdt-i%2AP%28t%29%3D-d)
The answer is D. 9(y+3) and 27 + 9y
You would distribute the 9 to both the 3 and the y.