Malcolm is filling bags with rice. He starts with a 5 1/4 pound container of rice and fills each bag with 5/8 pound of rice. How
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Answer:
The sequence of transformations involved is a reflection across the x axis, followed by a reflection across the y = x line
Step-by-step explanation:
The polygon ABCD is shown in the image attached. The coordinates of the polygon are A(-6, 6), B(-4, 6), C(-4, 4), D(-6, 2), while the polygon A'B'C'D' is at A'(-6, -6), B'(-6, -4), C'(-4, -4), D'(-2, -6)
A transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, dilation and rotation.
If a point O(x, y) is reflected across the x axis, the new coordinate is O'(x, -y).
If a point O(x, y) is reflected across the y = x line, the new coordinate is O'(y, x)
Hence if polygon ABCD is reflected across the x axis, the new coordinates are A*(-6, -6), B*(-4, -6), C*(-4, -4), D*(-6, -2). If a reflection across the y = x line, the new coordinates are A'(-6, -6), B'(-6, -4), C'(-4, -4), D'(-2, -6)
<h3>Answer:</h3>
- f(x) = -2x^3 +3x^2 +11x -6
- see attached
- an infinite number. Since the magnitude of the leading coefficient is not specified, it may be any negative number. (We have chosen the smallest magnitude integer that makes all coefficients be integers.)
1. When "a" is a root of a polynomial, (x -a) is a factor of it. For the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).
In order to make the leading coefficient be negative, we need to multiply this product by a negative number. Any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.
Then ...
... f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)
... = -(2x² +3x -2)(x -3)
... = -(2x³ -3x² -11x +6)
... f(x) = -2x³ +3x² +11x -6
2. A graph created by the Desmos on-line graphing calculator is shown, and the zeros are highlighted.
3. As indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. You want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.