Answer:
She used inductive reasoning. (False)
She used the law of detachment. (True)
Her conclusion is valid. (True)
The statements can be represented as "if p, then q and if q, then r." (False)
Her conclusion is true. (True)
Step-by-step explanation:
p = Two lines are perpendicular
q = They intersect at Right angles.
Given: A and B are perpendicular
Conclusion: A and B intersect at right angle.
According to the law of detachment, There are two premises (statements that are accepted as true) and a conclusion. They must follow the pattern as shown below.
Statement 1: If p, then q.
Statement 2: p
Conclusion: q
In our case the pattern is followed. The truth of the premises logically guarantees the truth of the conclusion. So her conclusion is true and valid.
Step-by-step explanation:
the proof is given above
Answer:
Both 
and 
are solutions to the system.
Step-by-step explanation:
In order to determine whether the two given points represent solutions to our system of equations, we must "plug" thos points into both equations and check that the equality remains valid.
Step 1: Plug into 
The solution verifies the equation.
Step 2: Plug into 
The solution verifies both equations. Therefore, is a solution to this system.
Now we must check if the second point is also valid.
Step 3: Plug into
Step 4: Plug into
The solution verifies both equations. Therefore, is another solution to this system.
Answer:
He did not control for lurking variables and their impacts on the results of his experiment. Amount of sunlight and water received are two outside variables(or confounding variables) that may impact the growth of his plants and influence the results. He needs to apply the same amount of sunlight and water to each plant within a different planting soil in order to rule out the influence of those two variables and test the sole effect of the soil brand on the plant growth. Otherwise, it would be hard to determine whether his plant growth was because of the soil brand or the different amounts of sunlight and water received
