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Masja [62]
3 years ago
6

Simplify: x2 + 5x + 6(x + 3) x 42x + 4 4 2 2(x + 2) (x + 2)

Mathematics
2 answers:
umka2103 [35]3 years ago
8 0
252xsquared + 763x +4
Andreyy893 years ago
5 0
252x squared + 763x + 4
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Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator
SpyIntel [72]
\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}
\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)

When x=3, you're left with

147=49a_1\implies a_1=\dfrac{147}{49}=3

When x=\sqrt2 or x=-\sqrt2, you're left with

\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}

Adding the two equations together gives -10=2a_5, or a_5=-5. Subtracting them gives 2\sqrt2=2\sqrt2a_4, a_4=1.

Now, you have

5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)
5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)
2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that a_2x^4=2x^4 and a_3(-3)(-2)=6a_3=-6. These alone tell you that you must have a_2=2 and a_3=-1.

So the partial fraction decomposition is

\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}
7 0
3 years ago
Your next math test is worth 111 points and contains 32 problems. Each problem is worth either 4 points or 3 points. How many 3
Dafna11 [192]
We call x the 4 points-worth problems and y the 3 points-worth problems

You know that x+y = 32

4x+3y = 111

You know that the difference from the x and y is 32 so write:

x = 32-y

Substitute at x the value of 32-y

4(32-y)+3y = 111

128-4y +3y = 111

-4y+3y = 111-128

-y = -17

y = 17
3 0
3 years ago
Read 2 more answers
The random variable X is exponentially distributed, where X represents the waiting time to be seated at a restaurant during the
erastova [34]

Answer:

The probability that the wait time is greater than 14 minutes  is 0.4786.

Step-by-step explanation:

The random variable <em>X</em> is defined as the waiting time to be seated at a restaurant during the evening.

The average waiting time is, <em>β</em> = 19 minutes.

The random variable <em>X</em> follows an Exponential distribution with parameter \lambda=\frac{1}{\beta}=\frac{1}{19}.

The probability distribution function of <em>X</em> is:

f(x)=\lambda e^{-\lambda x};\ x=0,1,2,3...

Compute the value of the event (<em>X</em> > 14) as follows:

P(X>14)=\int\limits^{\infty}_{14} {\lambda e^{-\lambda x}} \, dx=\lambda \int\limits^{\infty}_{14} {e^{-\lambda x}} \, dx\\=\lambda |\frac{e^{-\lambda x}}{-\lambda}|^{\infty}_{14}=e^{-\frac{1}{19} \times14}-0\\=0.4786

Thus, the probability that the wait time is greater than 14 minutes  is 0.4786.

7 0
2 years ago
In a company, 80% of the workers are women. if 880 men work for the company, how many workers are there in all?
ELEN [110]
If 80% are women, then 20% are men

20% of what equals 880
0.20x = 880
x = 880/.20
x = 4400

check..
men : 20% of 4400 = 0.20(400) = 880
women : 80% of 4400 = 0.80(4400) = 3520
totaling : 3520 + 880 = 4400

so there are a total of 4400 workers

6 0
3 years ago
PLEASE HELP! I AM CRYING AND NEED HELP :'(
Svetllana [295]

Answer:

9300

Step-by-step explanation:

To find the total surface are of 150 boxes, all we have to do is multiply the surface area of one box ( 62 which was calculated on this question brainly.com/question/23446865 ) by the total amount of boxes (150)

So your answer = 150 * 62 which equals 9300

4 0
3 years ago
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