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serious [3.7K]
2 years ago
6

ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line

y = -x. What are the coordinates of the vertices of the image?
A.
A'(0, 3), B'(2, 3), C'(1, 1)

B.
A'(0, -3), B'(3, -2), C'(1, -1)

C.
A'(-3, 0), B'(-3, 2), C'(-1, 1)

D.
A'(0, -3), B'(-2, -3), C'(-1, -1)
Mathematics
1 answer:
Darina [25.2K]2 years ago
3 0

A: because "reflection across the y axis then across the x axis is the only option that does not work"

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We are given the following information:

the sum of the first number cubed and the second number is 500

their product is a maximum

We are looking for the 2 missing numbers.

To answer this, let's represent the two numbers as x and w.

From the given, we can form the following equation:

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Then we solve for the value of x where f'(x) = 0.

\begin{gathered} -4x^3+500=0 \\ -4x^3=-500 \\ x^3=125 \\ x=5 \end{gathered}

Then we use x = 5 to solve for the second number, w.

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Therefore, the two numbers are 5 and 375.

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