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elena-14-01-66 [18.8K]

2 years ago

10

Plz help me with this

1 answer:

Jlenok [28]2 years ago

6 0

Answer: $\bold{b)\quad \dfrac{-\sqrt{13}-5}{4}}$

<u>Step-by-step explanation:</u>

$\dfrac{3}{\sqrt{13}-5}\bigg(\dfrac{\sqrt{13}+5}{\sqrt{13}+5}\bigg)\\\\\\=\dfrac{3(\sqrt{13}+5)}{13-25}\\\\\\=\dfrac{3(\sqrt{13}+5)}{-12}\\\\\\=\dfrac{\sqrt{13}+5}{-4}\\\\\\=\dfrac{-\sqrt{13}-5}{4}$

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frosja888 [35]

Answer:

Step-by-step explanation:

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3 years ago

Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha

Brums [2.3K]

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

$a = 20$ --- tree distance from north gate

$b =14$ --- movement from south gate

$c = 1775$ --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

$AE:DE = AB:CB$

Where:

$AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775$

Substitute these in the above equation

$20:x/2 = 20 + x + 14: 1775$

$20:x/2 = x + 34: 1775$

Express as fraction

$\frac{20}{x/2} = \frac{x + 34}{1775}$

$\frac{40}{x} = \frac{x + 34}{1775}$

Cross multiply

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Open bracket

$x^2 + 34x = 71000$

Rewrite as:

$x^2 + 34x - 71000 = 0$

Expand

$x^2 + 284x -250x - 71000 = 0$

Factorize

$x(x + 284) -250(x + 284)= 0$

Factor out x + 284

$(x - 250)(x + 284)= 0$

Split

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Solve for x

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x can't be negative;

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