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Anastaziya [24]
3 years ago
13

Which graph shows the solution set of x^2+4x-12/x>0?

Mathematics
2 answers:
ExtremeBDS [4]3 years ago
6 0

Answer:

D

Step-by-step explanation:

Consider the inequality

\dfrac{x^2+4x-12}{x}>0

First, factor the numerator:

x^2+4x-12=x^2+6x-2x-12=x(x+6)-2(x+6)=(x+6)(x-2)

Now, the inequality is

\dfrac{(x+6)(x-2)}{x}>0

The equivalent inequality is

x(x+6)(x-2)>0

On the number line plot doted points -6, 0 and 2 and put signs +, -, +, - from the right to the left. Intervals with + signs are the solution of the inequality:

x\in(-6,0)\cup(2,\infty)

that is represented by D number line.

postnew [5]3 years ago
6 0

Answer:

D

Step-by-step explanation:

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<h3>Answer:  x = 20</h3>

========================================================

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2 years ago
Read 2 more answers
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If

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The ODE in terms of these series is

\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0

\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0

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We can solve the recurrence exactly by substitution:

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\implies a_n=\dfrac{(-2)^n}{n!}a_0

So the ODE has solution

y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}

which you may recognize as the power series of the exponential function. Then

\boxed{y(x)=a_0e^{-2x}}

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