Answer:
Proof
Step-by-step explanation:
PROOF can be said to be logical mathematical argument in which every statement of fact is supported by a reason
due to the fact mathematical proof is an inferential argument for a mathematical statement because it help to shows that the assumptions stated logically guarantee and enables the conclusion.
Therefore Proofs can be said to be an examples of exhaustive deductive reasoning because they tend to often establish logical certainty which can be differentiated from empirical arguments which inturn help to establish reasonable and effectively expectation as well as employ logic expressed in mathematical symbols which is why proofs are often written in terms of rigorous informal logic
Slope = 
So taking 2 points (0,0) and (60,120)
we have slope = (120-0)/(60-0) = 120/60 = 2
general equation of linear graph is y=mx+b with m be the slope
so y=2x+b
Now to find b, just plug any point of the graph in, such as (0,0)
so we get something like 0=2(0) + b => b=0
So your equation is y=2x
Answer:

Step-by-step explanation:

Applying the Laplace transform:
![\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%2B5%5Cmathcal%7BL%7D%5By%27%5D%2B4%5Cmathcal%7BL%7D%5By%27%5D%3D0)
With the formulas:
![\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%3Ds%5E2%5Cmathcal%7BL%7D%5By%5D-y%280%29s-y%27%280%29)
![\mathcal{L}[y']=s\mathcal{L}[y]-y(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%5D%3Ds%5Cmathcal%7BL%7D%5By%5D-y%280%29)
![\mathcal{L}[x]=L](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5Bx%5D%3DL)

Solving for 




Apply the inverse Laplace transform with this formula:
![\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs-a%7D%5D%3De%5E%7Bat%7D)
![y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}](https://tex.z-dn.net/?f=y%3D3%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs%2B4%7D%5D%3D3e%5E%7B-4t%7D)
We know that
<span>foci on x-axis-------> is a ellipse with horizontal major axis
the equation is
(x</span>²/a²)+(y²/b²)=1
major axis is th<span>e </span>x<span>-axis with length </span><span>2<span>a
2a=14--------> a=7
</span></span>minor axis is the y<span>-axis with length </span><span>2<span>b
2b=4-----> b=2
the equation is
</span></span>(x²/a²)+(y²/b²)=1------> (x²/7²)+(y²/2²)=1-----> (x²/49)+(y²/4)=1
the answer is(x²/49)+(y²/4)=1
see the attached figure