Determine if triangle DEF with coordinates D (3, 2), E (4, 6), and F (7, 3) is an equilateral triangle. Use evidence to support
your claim. If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific.
1 answer:
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The function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.
<h3>What is a function?</h3>It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function that has vertex at (2, 6)
The options are:
f(x) = 2|x – 2| – 6
f(x) = 2|x – 2| + 6
f(x) = 2|x + 2| + 6
f(x) = 2|x + 2| – 6
As we know the vertex form of a quadratic function is given by:
f(x) = a(x - h)² + k
Similarly, mod function can be expressed as:
m(x) = a|x - h| + k
Here (h, k) is the vertex of a function.
In the function:
f(x) = 2|x – 2| + 6
The vertex of the function is (2, 6)
Thus, the function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.
Learn more about the function here:
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Answer:
3/2 < x < 2
Step-by-step explanation:
We assume the problem is ...
[tek]\dfrac{1}{x-2}<-2[/tex]
This will not be true for x-2 > 0 because that would make the left side positive. So, we must have x < 2, which makes the denominator negative. Multiplying by (x-2), we get ...
1 > -2(x -2)
1 > -2x +4
2x > 3 . . . . . . add 2x-1
x > 3/2
From above, we also have x < 2, so the solution set is ...
3/2 < x < 2
