What is the slope of the line (-3, 3) and (-1, -1)?
1 answer:
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Answer:
<h2>(0.3, -18.45).</h2>Step-by-step explanation:
We need to recur to the extreme value theorem, which states: "If a function is continuous on a closed interval, then that function has a maximum and a minimum inside that interval".
Basically, as the theorem states, if a dunction is continuous, then it has maxium or minium.
In this case, we have a quadratic function, which is a parabola. An important characteristic of parabolas is that they have a maximum or a minium, but they don't have both. When the quadratic term of the fuction is positive, then it has a minium at its vertex. When the quadratic term of the function is negative, then it has a maximum at its vertex.
So, the given function is , where the quadratic term is positive, so the functions has a minimum at
, where
and
, let's find that point
Answer:
This is proved with the help of slope.
Step-by-step explanation:
Given Mr. Johnson is working on constructing a square table for his classroom. He positioned his design on a coordinate grid, as shown. Mr. Johnson will need to put a brace through each diagonal of the table in order to secure the table's stability.
Now, if Johnson use more than one brace then we have to prove that the braces will intersect at a right angle.
From the figure we have to prove the diagonals AC and BD are at right angle. To prove above we have to find the slopes of both diagonals.
As we know, In a coordinate plane, the slopes of perpendicular lines are opposite reciprocals of each other i.e their product is equals to -1.
⇒ AC and BD are perpendicular
⇒ Braces which put through each diagonal intersect at right angle and the table will stable.
