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OverLord2011 [107]
3 years ago
10

What are the roots of the polynomial equation x3 - 10x=-3x2+ 24? Please help

Mathematics
2 answers:
snow_tiger [21]3 years ago
7 0

Answer:

x = -2, 3, -4.

Step-by-step explanation:

x^3 - 10x = -3x2 + 24 = 0

x^3 + 3x^2 - 10x - 24 = 0

The last term is 24 and the coefficient of x^3 is 1 so +/- 1,  +-2, +/- 3 and +/- 4 could be among the roots ( by The Rational Root Theorem).

Let x = 1

f(x) = 1^3 +3(1)^2 - 10 - 24 = -30 so it's no t .

f(-1) = -1 + 3 + 10 - 24 = -12  so it's not -1.

Let  x = 2:

f(2) =  2^3 +3*4 - 20 - 24 = -32  so its not 2

f(-2) = -8 + 12 + 20 - 24 = 0  so x = -2 is a root

and therefore x+ 2 is a factor and we divide:

x + 2 ) x^3 + 3x^2 - 10x - 24   (  x^2 + x - 12   <------ The quotient

          x^3 + 2x^2

                      x^2 - 10x

                       x^2 + 2x

                              -12x - 24

                              -12x - 24

                                ..............

Now x^2 + x - 12 = (x - 3)(x + 4)

So (x + 2)(x - 3)(x + 4) = 0

This gives

x = -2, 3, -4.

Serggg [28]3 years ago
7 0

Answer:

–4, –2, and 3

Step-by-step explanation:

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The domain and f^1(x)
TEA [102]

B

To solve for the inverse, just swap the x and y and solve for the new y.

y=\sqrt{x} -8

x=\sqrt{y}-8

x+8=\sqrt{y}

(x+8)^2=y

Then inspect both functions for the domain.

In the original function, x has to be greater than or equal to 0 or else you would have a negative square root which is impossible.

The inverse function has no limitations as any x could make that true.

The main things that will limit domain is square root of negative or divide by zero.

Therefore, x>=0 is the only domain restriction.

8 0
3 years ago
5
zepelin [54]

The question is incomplete. Below you will find the missing figure.

Two friends, Andrew and Liz, are playing a game using this spinner. If the

spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If it lands on any other region, neither wins. Is this a fair game?

A. Yes. Each friend has a 1/4 probability of winning.

B. Yes. Each friend has a 1/6 probability of winning.

C. No. Andrew has a probability of 1/4 winning and Liz has a probability of 1/6 winning.

D. No. Andrew has a probability of 1/3 winning and Liz has a probability of 1/4 winning.

The correct option is Option A: Yes. Each friend has 1/4 probability of winning.

Probability is the possibility of an event to happen which is the ratio of no. favorable outcomes and no. of total outcomes.

P = no. of favorable outcome/ total no. of outcome

Here given in the question,

If the spinner touches region 2 or 3, Andrew wins

If the spinner touches region 4, Liz wins.

This is fair play because both have the same size of region for winning.

If we cut the circle into 8 pieces,

as region 1 is the sum of 2 sub-parts of the circle,

possibility of spinner touching region 1= 2/8= 1/4

possibility of spinner touching the small region = 1/8

So the possibility of the spinner touching the region 2or 3= 1/8+1/8= 2/8= 1/4

Hence the possibility of Andrew wins= possibility of the spinner touching region 1= 1/4

possibility of Liz wins= possibility of the spinner touching the region 2 or 3= 1/4

Therefore the correct option is Option A: Yes. Each friend has 1/4 probability of winning.

Learn more about the probability

here: brainly.com/question/24756209

#SPJ10

6 0
2 years ago
Use compatible numbers to estimate the quotient.<br> 486/6
Sladkaya [172]
The answer is 81. You just have to do the division in the traditional way.

8 0
3 years ago
Identify the level of measurement of the​ data, and explain what is wrong with the given calculation. In a​ survey, the favorite
Trava [24]

Answer:

The data are at the   <u>Nominal</u>   level of measurement.

The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement.

Step-by-step explanation:

The objective here is to Identify the level of measurement of the​ data, and explain what is wrong with the given calculation.

a)

The data are at the <u> Nominal  </u>  level of measurement due to the fact that it portrays the qualitative levels of naming and representing different hierarchies  from 100 basketball, 200 basketball, 300 football, 400 anything else

b) We are being informed that, the average​ (mean) is calculated for 597 respondents and the result is 256.1.

The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement. At nominal level this type of data set do not measure at all , it is not significant to compute their average​ (mean).

6 0
3 years ago
Okay I don't understand how do I do this. It say :
Lilit [14]

2x+3=17

subtract 3 from each side

2x+3 -3 = 17 -3

2x = 14

divide by 2 on each side

2x/2 = 14/2

x = 7

6 0
3 years ago
Read 2 more answers
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