Which of these properties is preserved exclusively under dilation?

1 answer:

3 0

The property that is preserved under dilation is the similarity. The answer is letter A. Dilation of a figure starts from the very center of it and then continually increased or decreased depending on the desired size. It is similarity that is under dilation because no matter how big or small the size of the figure is, it has a similar feature from the original one.

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According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation

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<h2>Descartes Rule of Sign</h2><h3>Answer:</h3>

There are $3$ Real Roots for the Equation

<h3>Step-by-step explanation:</h3>

According to Descartes Rule of Sign, The maximum number of real roots a polynomial equation has is the number of times the sign of term changes from a higher power term to a lower power term.

In the given equation, $0=-4x^6-3x^5+2x^2-4x+1$ , we can already see that from $\red -4x^6$ to $\red -3x^5$ we can see that the sign didn't change so there might be no real roots. From $\red -3x^5$ to $\blue +2x^2$ , we can see that the signs change so we now know that there might be $1$ real root for equation. From $\blue +2x^2$ to $\red -4x$ , the signs changed so there might be $2$ real roots. From $\red -4x$ to $\blue +1$ , it changed again so there might be $3$ real roots. There are no other term with lesser power to compare for $\blue +1$ so we are left with $3$ real roots.