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2 years ago

What Transformation creates similar triangles?

Mathematics

1 answer:

xz_007 [3.2K]2 years ago

3 0

Answer:

Dilation

Step-by-step explanation:

A rotation followed by a dilation is a similarity transformation. Therefore, the two triangles are similar.

. . .

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Mohamed and Li Jing were asked to find an explicit formula for the sequence -5, -25, -125, -625,....

Nuetrik [128]

Answer:

Li Jing's formula i.e. $\boxed{g_n=-5\cdot \:5^{n-1}}$ is right.

Step-by-step explanation:

Considering the sequence

$-5,\:-25,\:-125,\:-625,...$

A geometric sequence has a constant ratio r and is defined by

$g_n=g_0\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{g_{n+1}}{g_n}$

$\frac{-25}{-5}=5,\:\quad \frac{-125}{-25}=5,\:\quad \frac{-625}{-125}=5$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=5$

So, the sequence is geometric.

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$g_1=-5$

$r=5$

$g_n=g_1\cdot r^{n-1}$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$g_n=-5\cdot \:5^{n-1}$

Therefore, Li Jing's formula i.e. $\boxed{g_n=-5\cdot \:5^{n-1}}$ is right.

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2 years ago

Which of the following have the same value as the fraction below? 3/8

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1.The population of the world is approximately 6200 million people. It is increasing by approximately 93 million people each yea

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The fraction can simplify down to $\frac{93}{6200}$ convert it to a fraction and the yearly increase is 1.5%

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There are 24 hours in a day, so that figure is further divided by 24.
There are also 60 minutes in an hour therefore furthermore divided by 60.
= 176 therefore true

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