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Katyanochek1 [597]
3 years ago
11

Trapezoid WXYZ is shown on the coordinate grid. Trapezoid WXYZ is dilated with the origin as the center of dilation using the ru

le (x, y)→(4x, 4y) to create trapezoid W'X'Y'Z'.
Which statement is true?


Trapezoid W'X'Y'Z' is smaller than trapezoid WXYZ because the scale factor is less than 1.

Trapezoid W'X'Y'Z' is smaller than trapezoid WXYZ because the scale factor is greater than 1.

Trapezoid W'X'Y'Z' is larger than trapezoid WXYZ because the scale factor is less than 1.

Trapezoid W'X'Y'Z' is larger than trapezoid WXYZ because the scale factor is greater than 1.

Mathematics
1 answer:
Paladinen [302]3 years ago
6 0
The answer is “trapezoid W’X’Y’Z’ is smaller than trapezoid WXYZ because the scale factor is greater than 1.”
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Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2
Basile [38]

Answer:

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f(x) = x^3 - 2x^2 -3x + 6

Step-by-step explanation:

According to the Factor Theorem, if (<em>x</em> - <em>k</em>) is a factor of a polynomial P(x), then P(k) must equal zero.

We are given that a polynomial function has the zeros 2, √3, and -√3. So, we can let <em>k</em> = 2, √3, -√3.

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Testing each choice, we can see that only A is true:

\displaystyle f(x) = x^3 - 2x^2 - 3x + 6

Testing all three values yields that:

\displaystyle \begin{aligned} f(2) &= (2)^3 - 2(2)^2 -3(2) + 6 \\ &= (8) - (8) -(6) + (6) \\ &= 0\stackrel{\checkmark}{=}0 \\ \displaystyle  f(\sqrt{3}) &= (\sqrt{3})^3 - 2(\sqrt{3})^2 - 3(\sqrt{3}) + 6 \\ &=(3\sqrt{3}) -(6)-(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \\ f(-\sqrt{3}) &= (-\sqrt{3})^3 - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 \\ &=(-3\sqrt{3}) -(6)+(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0   \end{aligned}

Hence, our answer is A.

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