The scatter plot below shows the relationship between the diameter (x), in mm, and mass f(x), in grams, of a berry: ordered pair
2 answers:
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The polynomial expression for the area of the room is f(x) = x^2 + 16x + 48.
Here, we are given that the side of the length of the rug = x
Now, the square rug is placed on the rectangular room such that on 2 sides the uncovered floor is 6 meters.
This means that the length of the 2 opposite sides of the rectangle will be (x + 6 + 6) = (x + 12)
Similarly, there is 2 feet of uncovered floor on the other 2 sides, which means that the length of other two opposite sides is- (x + 2 + 2) = (x + 4)
Kindly refer to the diagram below for a better clarity of how we found out the sides.
Now, the area of a rectangle = Length × Breadth
Thus, area of the room = (x + 12) (x + 4)
= x^2 + 4x + 12x + 48
= x^2 + 16x + 48
Thus, the polynomial expression for the area of the room is f(x) = x^2 + 16x + 48
Learn more about quadratic equations here-
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g(x) = or g(x) is 3/4 times of f(x) , F(x) and g(x) have common solution or intersecting point in the graph parabola at x=0 i.e. in origin and x =
.
<u>Step-by-step explanation:</u>
We have a function f(x) = and another function , g(x) =
. In the graph of y =
, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.
Graphing y = (x - h)2 + k , where h = 0 & k = 0
Function g(x) can be formed with compression in function f(x) by a factor of 3/4 , i.e. g(x) = or g(x) is 3/4 times of f(x).Domain and range of f(x) and g(x) are same ! Although structure of both functions is same the only difference is g(x) is compressed vertically by a factor 3/4. Both are graph of a parabola with vertex at (0,0). Also, F(x) and g(x) have common solution or intersecting point at x=0 i.e. in origin.