Answer:
The proof contains a simple direct proof, wrapped inside the unnecessary logical packaging of a proof by contradiction framework.
Step-by-step explanation:
The proof is rigourous and well written, so we discard the second answer.
This is not a fake proof by contradiction: it does not have any logical fallacies (circular arguments) or additional assumptions, like, for example, the "proof" of "All the horses are the same color". It is factually correct, but it can be rewritten as a direct proof.
A meaningful proof by contradiction depends strongly on the assumption that the statement to prove is false. In this argument, we only this assumption once, thus it is innecessary. Other proofs by contradiction, like the proof of "The square root of 2 is irrational" or Euclid's proof of the infinitude of primes, develop a longer argument based on the new assumption, but this proof doesn't.
To rewrite this without the superfluous framework, erase the parts "Suppose that the statement is false" and "The fact that the statement is true contradicts the assumption that the statement is false. Thus, the assumption that the statement was false must have been false. Thus, the statement is true."
Step-by-step explanation:
![4x+(y+x)=180\\\\\text{Solve for}\ x:\\\\4x+y+x=180\qquad\text{combine like terms}\\\\(4x+x)+y=180\qquad\text{subtract}\ y\ \text{from both sides}\\\\5x=180-y\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{180-y}{5}\\\\\boxed{x=\dfrac{180-y}{5}}\\\\\text{Solve for}\ y:\\\\5x+y=180\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\\boxed{y=180-5x}](https://tex.z-dn.net/?f=4x%2B%28y%2Bx%29%3D180%5C%5C%5C%5C%5Ctext%7BSolve%20for%7D%5C%20x%3A%5C%5C%5C%5C4x%2By%2Bx%3D180%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5C%284x%2Bx%29%2By%3D180%5Cqquad%5Ctext%7Bsubtract%7D%5C%20y%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5C5x%3D180-y%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%205%7D%5C%5C%5C%5C%5Cdfrac%7B5x%7D%7B5%7D%3D%5Cdfrac%7B180-y%7D%7B5%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D%5Cdfrac%7B180-y%7D%7B5%7D%7D%5C%5C%5C%5C%5Ctext%7BSolve%20for%7D%5C%20y%3A%5C%5C%5C%5C5x%2By%3D180%5Cqquad%5Ctext%7Bsubtract%7D%5C%205x%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5C%5Cboxed%7By%3D180-5x%7D)
Answer: 75ml
Step-by-step explanation:
The volume of a rectangular prism is:
= Length × width × height
where,
Volume = 22500ml³
Length = Unknown
Width = 50ml
Height = 6ml
We then slot the values into the formula.
Volume = Length × width × height
22500 = Length × 50 × 6
22500 = Length × 300
Length = 22500/300
Length = 75ml
The length of the cellular phone is 75ml.
Answer:
18.37 is the answer so it should be 18.4
Step-by-step explanation:
100 degrees I think....
I’m writing this because it said it was too short