Equation 1: y = -2x + 1
Equation 2: y = 2x - 3
Since both equations already have y isolated, we are able to simply set the right side of both equations equal to each other. Since we know that the value of y must be the same, we can do this.
-2x + 1 = 2x - 3
1 = 4x - 3
4 = 4x
x = 1
Then, we need to plug our value of x back into either of the original two equations and solve for y. I will be plugging x back into equation 2 above.
y = 2x - 3
y = 2(1) - 3
y = 2 - 3
y = -1
Hope this helps!! :)
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."
Answer:
x intercept is (0.9,0)
y intercept is (0,-1.2)
Step-by-step explanation:
Answer:
18 days
Step-by-step explanation:
Here's a short table of heights:
day 0: height = 1
day 1: height = 1 + (1/2)(1) = 3/2
day 2: height = (3/2) + (1/3)(3/2) = 3/2 + 1/2 = 2
The pattern of heights is ...
(day, height) = (0, 1), (1, 1.5), (2, 2)
The plant is growing 1/2 its original height each day, so we can write the equation ...
h = 1 + d/2
We want to find the number of days (d) that result in a height of 10 (ten times the original height).
10 = 1 + d/2
9 = d/2 . . . . subtract 1
18 = d . . . . . multiply by 2
It took 18 days for the plant to grow to 10 times its original height.
