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2 years ago

Simplify. 9(x+3)+15x A. 24x+3 B. 24x+27 C. 9x+27 D. 51x

Mathematics

2 answers:

bonufazy [111]2 years ago

5 0

B. 24x+27. You multiply everything out and add the x's

sergejj [24]2 years ago

5 0

Let's simplify step-by-step.
9(x+3)+15x
Distribute:
=(9)(x)+(9)(3)+15x
=9x+27+15x
Combine Like Terms:
=9x+27+15x
=(9x+15x)+(27)
=24x+27
Answer:
=24x+27
Hope this helps :)

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Multiply both the numerator and denominator by $2+\sqrt3$ , which is called the "conjugate" of $2-\sqrt3$ :

$\dfrac{5+\sqrt3}{2-\sqrt3}\cdot\dfrac{2+\sqrt3}{2+\sqrt3}$

Why do we pick this number? Recall the difference of squares factorization:

$a^2-b^2=(a-b)(a+b)$

Now replace $a=2$ and $b=\sqrt3$ . Then

$(2-\sqrt3)(2+\sqrt3)=2^2-(\sqrt3)^2=4-3=1$

So in your fraction, you end up with

$\dfrac{5+\sqrt3}{2-\sqrt3}=\dfrac{(5+\sqrt3)(2+\sqrt3)}1=(5+\sqrt3)(2+\sqrt3)$

Finally, just expand the product.

$(5+\sqrt3)(2+\sqrt3)=10+7\sqrt3+(\sqrt3)^2=\boxed{13+7\sqrt3}$

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