Express x^2-2x+1/x^2-4x+3
1 answer:
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Answer:
20%
Step-by-step explanation:
We can start by finding out how much the price of the television was reduced by.
250 - 200 = 50
Now, we need to know what percent of 250 is 50? Let x represent the percent of 250 that is 50. Using this, we can set up an equation:
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Notice that a percentage can also be written as that number over 100.
Reduce the fraction (250 and 100 have a common factor of 10)
Reduce the fraction again (25 and 10 have a common factor of 5)
Multiply both sides by two
Divide both sides by 5
Therefore the price of the television was reduced by 20%.
Answer:
√3 is irrational
Step-by-step explanation:
The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.
<h3 /><h3>Location of point C</h3>With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC <em>never passes through a point with integer coordinates</em>. (Any point with integer coordinates would be on a line with rational slope.)
<h3>Equilateral triangle</h3>The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.
The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...
Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...
cos(60°)·x + sin(60°)·y
will be irrational.
As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.
Refer to the edited figure.
Triangles ABC and A'B'C' are similar because of AAA.
Also,
Therefore
ΔA'B'C' is 1/3 the size of ΔABC.
This means that the scale factor from ΔABC to ΔA'B'C' is a 3-factor reduction.
Answer: reduction; one-third.
The dilation is a reduction.
The scale factor of the dilation is one-third.
Triangles ABC and A'B'C' are similar because of AAA.
Also,
Therefore
ΔA'B'C' is 1/3 the size of ΔABC.
This means that the scale factor from ΔABC to ΔA'B'C' is a 3-factor reduction.
Answer: reduction; one-third.
The dilation is a reduction.
The scale factor of the dilation is one-third.