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3 years ago

What plus 5 equals -2

Mathematics

1 answer:

Ratling [72]3 years ago

7 0

Answer:

-7

Step-by-step explanation:

5+-7

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Find all the zeros of the equation x^4-6x^2-7x-6=0

rusak2 [61]

Answer:

The zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Step-by-step explanation:

We have been given the equation x^4-6x^2-7x-6=0

Use rational root theorem, we have

$a_0=6,\:\quad a_n=1$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:6,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:3,\:6}{1}$

$-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2$

$=\left(x+2\right)\frac{x^4-6x^2-7x-6}{x+2}\\$

$=x^3-2x^2-2x-3$

Again factor using the rational root test, we get

$=\left(x+2\right)\left(x-3\right)\left(x^2+x+1\right)$

Using the zero product rule, we have

$x+2=0:\quad x=-2\\x-3=0:\quad x=3\\x^2+x+1=0\\\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Therefore, the zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

4 0

3 years ago

Read 2 more answers

A bacteria culture initially contains 2000 bacteria and doubles every half hour.

dsp73

Answer:

Can be found below

Step-by-step explanation:

Part A:

So we know that the bacteria doubles every (30) minutes.

2000 times 2 equals 4000 (30 minutes)

4000 times 2 equals 8000 (1 hour)

Answer for Part A:

8000 bacteria

Part B:

Now we do this function 2000(2)^14 (30 minutes long)

Answer to Part B: 

I believe the answer is 32,768,000 (Please correct me if I'm wrong) 

Hope I could help!! Have a great day/night!

Any constructional messages are greatly appreciated!!

5 0

3 years ago

In one lottery game, contestants pick five numbers from 1 through 23 and have to match all five for the big prize (in any order)

mihalych1998 [28]

The probability of matching three out of five numbers is 153/33649

<h3>How to determine the probability?</h3>

The numbers are given as:

1 to 23

There are five matching numbers

The probability of getting a match is:

p = 5-k/n where k = 0, 1, 2

While the complement probability is

q = (n - 2)/n

Using the above formulas, the probability of getting from 5 is:

P = 5/23 * 4/22 * 3/21 * 18/20 * 17/19

Evaluate the product

P = 153/33649

Hence, the probability of matching three out of five numbers is 153/33649