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3 years ago

A population of 550 cheetahs decreases by 10% per year. How many cheetahs will there be in the population after 10 years

Mathematics

1 answer:

atroni [7]3 years ago

3 0

Answer:

192

Step-by-step explanation:

550 - 10% = 495

495 - 10% = 445

445 - 10% = 400

400 - 10% = 360

360 - 10% = 324

324 - 10% = 292

292 - 10% = 263

263 - 10% = 237

237 - 10% = 213

213 - 10% = 192

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Given points A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1), which of the following proves that

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<h3>How to determine the similarity statement</h3>

The coordinates of the two triangles are:

A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1)

Calculate the lengths of both triangles using the following distance formula

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

For triangle ABC, we have:

$AB = \sqrt{(0 -4)^2 + (0 -0)^2} = 4$

$BC = \sqrt{(4 -0)^2 + (0 -2)^2} = 2\sqrt 5$

$CA = \sqrt{(0 -0)^2 + (0 -2)^2} = 2$

For triangle DEF, we have:

$DE = \sqrt{(0 -2)^2 + (0 -0)^2} = 2$

$EF = \sqrt{(2 -0)^2 + (0 -1)^2} = \sqrt 5$

$FD = \sqrt{(0 -0)^2 + (1 -0)^2} = 1$

Divide corresponding sides of the triangles to calculate the scale factor k

$k = \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$

This gives

$k = \frac{4}{2} = \frac{2\sqrt 5}{\sqrt 5} = \frac{2}{1}$

Evaluate the quotients

$k = 2 = 2 = 2$

Since the quotients are equal, then the triangles are similar

Hence, triangles ABC and DEF are similar by SSS theorem

Read more about similar triangles at:

brainly.com/question/14285697

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