So... it has degree of 7, so based on the fundamental theorem of algebra....it can have at most 7 solutions
now.. you have <span>−4, −4i, 2i <--- there are two complex ones there
-4i or 0-4i and 2i or 0+2i
now.. bear in mind that, complex solutions never come all by their lonesome, they come with their sister, the conjugate
thus, that means 0-4i comes with 0+4i and 0+2i comes with 0-2i
that makes only 5 roots though
that simply means that, the -4 one, has a multiplicity of 3
as far as the B) and C) sections, check Descartes Rule of Signs
which surely you've covered already
</span>
Answer:
y = 4x -5
Step-by-step explanation:
First, find the slope by subtracting 11 by 3 and 4 by 2. The slope is 8/2, or 4. This is your current equation: y = 4x + b. Plug in one of your coordinates into the equation; it doesn't matter which one. However, I'm going to use the first point so it should look like this: 3 = 4(2) + b. 4 times 2 equals 8, so it should look like this: 3 = 8 + b. Subtract 8 from both sides to get -5 = b. Go back to your original equation and plug in -5 for b. This is your final equation: y = 4x -5. Hope this helped!
1) 3.25n
Overall cost of n gallons of gas
2)3.25n = 26
we are spending 26 dollars on 8 gallons of gas
3)40-3.25n
Ammount we have remaining after spending on n gallons of gas out of 40 dollars
4) 40-3.25n = 1.00
The maximum number of gallons of gas we can buy from 40 dollar is 13 gallons and 1 dollar is still remaining to us.
Answer:
is equivalent to ![m^2 \cdot n^{-2}](https://tex.z-dn.net/?f=m%5E2%20%5Ccdot%20n%5E%7B-2%7D)
Step-by-step explanation:
Using exponent rules:
![a^{-n}=\frac{1}{a^n}](https://tex.z-dn.net/?f=a%5E%7B-n%7D%3D%5Cfrac%7B1%7D%7Ba%5En%7D)
Given the expression:
![\frac{m^2}{n^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%5E2%7D%7Bn%5E2%7D)
⇒![\frac{m^2}{n^2} = m^2 \cdot \frac{1}{n^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%5E2%7D%7Bn%5E2%7D%20%3D%20m%5E2%20%5Ccdot%20%5Cfrac%7B1%7D%7Bn%5E2%7D)
Apply the exponent rule, we have;
![m^2 \cdot n^{-2}](https://tex.z-dn.net/?f=m%5E2%20%5Ccdot%20n%5E%7B-2%7D)
Therefore, the given expression
is equivalent to ![m^2 \cdot n^{-2}](https://tex.z-dn.net/?f=m%5E2%20%5Ccdot%20n%5E%7B-2%7D)
We can simplify each equation and find the solution.
6x + 2y = 15 can't be simplified further.
- 8x - 3y = 2 can't be simplified further.
4x - 4y = 6 on simplification gives 2x - 2y = 3 or x - y = 3/2
But, it does not coincide with the given equation.
- 3x + 3y = 6 on simplification gives x - y = - 2 coincides with the given equation.
Hence, - 3x + 3y = 6 can pair with x - y = -2 to create a consistent and dependent system.