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N76 [4]
3 years ago
5

The volume of a suitcase is 4.2 cubic feet. what is the volume of a suitcase that is smaller by a factor of 0.9? round to the ne

arest tenth.
Mathematics
1 answer:
ANEK [815]3 years ago
3 0
The volume would be 0.9 x 4.2

This means it is 90% smaller

Don't forget to round the nearest tenth place. That's the first decimal, so you answer should only have 2 digits.
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Step-by-step explanation:

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Find the distance between the point (-2, -3) and the line with the equation y=4-2/3x
otez555 [7]

Answer:

D = \frac{25\sqrt{13}}{13}

Step-by-step explanation:

Given

y = 4 - \frac{2}{3}x

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Required

Determine the distance

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Ax + By + C = 0

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The distance is calculated using:

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This gives:

D = \frac{|\frac{2}{3} * (-2) + 1 * (-3) - 4|}{\sqrt{(\frac{2}{3})^2 + 1^2}}

D = \frac{|-\frac{4}{3} -3 - 4|}{\sqrt{\frac{4}{9} + 1}}

Take LCM

D = \frac{|\frac{-4-9-12}{3}|}{\sqrt{\frac{4+9}{9}}}

D = \frac{|\frac{-25}{3}|}{\sqrt{\frac{13}{9}}}

D = |\frac{-25}{3}|/\sqrt{\frac{13}{9}}

D = \frac{25}{3}/\sqrt{\frac{13}{9}}

Split the square root

D = \frac{25}{3}/\frac{\sqrt{13}}{\sqrt{9}}

Change / to *

D = \frac{25}{3}*\frac{\sqrt{9}}{\sqrt{13}}

D = \frac{25}{3}*\frac{3}{\sqrt{13}}

D = \frac{25}{\sqrt{13}}

Rationalize

D = \frac{25}{\sqrt{13}} * \frac{\sqrt{13}}{\sqrt{13}}

D = \frac{25\sqrt{13}}{13}

Hence, the distance is:

D = \frac{25\sqrt{13}}{13}

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