Would you say that pythagoras’ theorem holds true for hexagons as well? why or why not

1 answer:

7 0

No, the Pythgorean Theorem only applies to right triangles. To get two right triangles, you divide a rectangle diagonally. Dividing a hexagon into two pieces produces trapezoids or pentagons depending where it is divided.

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What is the difference? startfraction 2 x 5 over x squared minus 3 x endfraction minus startfraction 3 x 5 over x cubed minus 9

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The difference of the expression $\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}$ is $\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}$

<h3>How to determine the difference?</h3>

The expression is given as:

$\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}$

Factor the denominators of the expressions:

$\frac{2x^5}{x(x - 3)} - \frac{3x^5}{x(x^2 - 9)}$

Apply the difference of two squares to x² - 9

$\frac{2x^5}{x(x - 3)} - \frac{3x^5}{x(x - 3)(x + 3)}$

Take LCM

$\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}$

Hence, the difference of the expression $\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}$ is $\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}$