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Mathematics

1 answer:

Nady [450]3 years ago

8 0

Answer:

It is B and D

Step-by-step explanation:

They are both x and y functions

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Need help on this Please answer ASAP

Vedmedyk [2.9K]

$Domain:\ x\neq0\\\\\dfrac{1}{x}+\dfrac{1}{3x^2}=\dfrac{1}{3x}\\\\\dfrac{1\cdot3x}{x\cdot3x}+\dfrac{1}{3x^2}=\dfrac{1}{3x}\\\\\dfrac{3x}{3x^2}+\dfrac{1}{3x^2}=\dfrac{1}{3x}\\\\\dfrac{3x+1}{3x^2}=\dfrac{1}{3x}\qquad\text{cross multiply}\\\\(3x)(3x+1)=(3x^2)(1)\qquad\text{use distributive property}\\\\(3x)(3x)+(3x)(1)=3x^2\\\\9x^2+3x=3x^2\qquad\text{subtract}\ 3x^2\ \text{from both sides}\\\\6x^2+3x=0\\\\3x(2x+1)=0\iff3x=0\ \vee\ 2x+1=0\\\\3x=0\qquad\text{divide both sides by 3}\\x=0\notin Domain$

$2x+1=0\qquad\text{subtract 1 from both sides}\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\boxed{x=-\dfrac{1}{2}}\to\boxed{A)}$

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3 years ago

A town orchestra is holding auditions for 3 new flute players and 4 new trumpet players. If8 flutists try out, and 11 trumpeters

tensa zangetsu [6.8K]

A town orchestra needs 3 new flute players and 4 new trumpet players. 8 flutists and 11 trumpeters try out, then the orchestra should select 3 flutists from 8 and 4 trumpeters form 11.

They can choose 3 flutists from 8 in

$C_8^3=\dfrac{8!}{3!(8-3)!}=\dfrac{8!}{3!\cdot 5!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8}{1\cdot 2\cdot 3\cdot 1\cdot 2\cdot 3\cdot 4\cdot 5} =56$ ways.

They can choose 4 flutists from 11 in

$C_{11}^4=\dfrac{11!}{4!(11-4)!}=\dfrac{11!}{4!\cdot 7!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11}{1\cdot 2\cdot 3\cdot 4\cdot 1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7} =330$ ways.