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2 years ago

When factoring the equation 9x2+9x+2 what two numbers will the "9x" term be broken into?

Mathematics

2 answers:

Andrew [12]2 years ago

6 0

Answer:

it will be broken into 9*what ever x is

Hope This Helps!!!

Ivan2 years ago

3 0

Answer:

9×x

Step-by-step explanation:

18+9x+2

20+9×x

that means 9 and x

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Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

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3 years ago

Explain how you would use the number line to solve the following equation. You can write out the fraction names or use the forwa

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Answer: 2

Step-by-step explanation:

1. Convert the mixed numbers to improper fractions,

2. then find the LCD and combine.

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2 years ago

How do you find the area of this composite figure?

Illusion [34]

If you notice the picture below

the composite figure is just a trapezoid sitting on top of a rectangle
and then, the rectangle has a triangular hole in it

so.. get the area of the trapezoid $\bf \textit{area of a trapezoid}=A=\cfrac{h}{2}(a+b)\qquad 
\begin{cases}
h=height\\
a,b=\textit{parallel sides or bases}
\end{cases}$

then get the area of the rectangle, which is just a 12x14
and then get the area of the triangle, which surely you know is 1/2 bh

then, subtract the triangle's area from the rectangle's area

and whatever is left, namely the difference, add that to the area of the trapezoid, and that's the composite's area

namely the area of the trapezoid plus the rectangle's, minus the triangle's

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