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Tatiana [17]
3 years ago
7

Rectangle DEFG is similar to rectangle LMNP. What is the scale factor of dilation from LMNP to DEFG?

Mathematics
1 answer:
zhuklara [117]3 years ago
6 0
Compare corresponding sides
DE/LM = 15/6

Then simplify the ratio
DE/LM = 5/2
DE/LM = 2.5/1

The scale factor of dilation is 2.5:1
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Domain:\\D:x > 0\\\\\ln x=5.6+\ln(7.5)\ \ \ \ |-\ln(7.5)\\\\\ln x-\ln7.5=5.6\ \ \ |Use\ \log x-\log y=\log\dfrac{x}{y}\\\\\ln\dfrac{x}{7.5}=5.6\ \ \ \ |use\ \log_ab=c\iff a^c=b\\\\\dfrac{x}{7.5}=e^{5.6}\ \ \ \ |\cdot7.5\\\\\boxed{x=7.5e^{5.6}}\in D

\log x=5.6-\log7.5\ \ \ \ |+\log7.5\\\\\log x+\log7.5=5.6\ \ \ \ |use\ \log x+\log y=\log (xy)\\\\\log(7.5x)=5.6\ \ \ \ |use\ \log_ab=c\iff a^c=b\\\\7.5x=10^{5.6}\ \ \ \ |:7.5\\\\\boxed{x=\dfrac{10^{5.6}}{7.5}}\in D

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3 years ago
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