3 years ago

I need help with number 3

Mathematics

1 answer:

sattari [20]3 years ago

4 0

You multiply everything inside the brackets by what's outside it:

24-30x + 9
33 - 30x

D is the answer.

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The figure shows △ABC . BD is the angle bisector of ∠ABC .

Misha Larkins [42]

From angle bisector theorem, we know that:

$\dfrac{|AD|}{|DC|}=\dfrac{|BA|}{|BC|}\\\\\\\dfrac{|AD|}{|DC|}=\dfrac{8}{10}=\dfrac{4}{5}$

Moreover:

$|AD|+|DC|=6$

so:

$|DC|=6-|AD|$

and

$\dfrac{|AD|}{|DC|}=\dfrac{4}{5}\\\\\\\dfrac{|AD|}{6-|AD|}=\dfrac{4}{5}\qquad\qquad\text{cross multiplying}\\\\\\ 5\cdot|AD|=4\cdot\big(6-|AD|\big)\\\\5\cdot|AD|=24-4\cdot|AD|\\\\5\cdot|AD|+4\cdot|AD|=24\\\\9\cdot|AD|=24\qquad|:9\\\\\\|AD|=\dfrac{24}{9}=\boxed{\dfrac{8}{3}}$

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artcher [175]

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