What is the image of (-6,-4) after a dilation by a scale factor of 3 centered at the
origin?

The image of the point is (-18, -12)

Step-by-step explanation:

If the point (x, y) dilated by a scale factor k centered at the origin, then its image is (kx, ky)

Let us use this rule to solve the question

∵ The given point is (-6, -4)

∴ x = -6 and y = -4

∵ The scale factor of the dilation is 3

∴ k = 3

∵ The center of dilation is the origin

→ By using the rule above

∴ The image of the point = (-6 × 3, -4 × 3)

∴ The image of the point = (-18, -12)

∴ The image of the point is (-18, -12)

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

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