How many $10 bills are the same as ten $ 1 bill?
2 answers:
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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:
3.5
Step-by-step explanation:
The attached shows the perpendicular bisector to have a slope of m = -1/2 and a y-intercept of b = 4.
m+b = (-1/2) +4 = 3.5
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The difference of coordinates of the two points is ...
B-A = (-5, 4) -(-3, 8) = (-2, -4)
Then the rise/run ratio is (-4)/(-2) = 2. The slope of the perpendicular bisector will have a slope (m) that is the negative reciprocal of this:
m = -1/2
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The average of the coordinates of the two points is ...
(B+A)/2 = ((-5, 4) +(-3, 8))/2 = (-8, 12)/2 = (-4, 6)
Then the point-slope form of the equation of the perpendicular bisector can be written ...
y = (-1/2)(x +4) +6 = (-1/2)x -2 +6
y = (-1/2)x +4
So, the y-intercept is b = 4, and ...
m + b = (-1/2) +4 = 3 1/2
m + b = 3.5
