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photoshop1234 [79]
3 years ago
10

Help appreciated on question in image! Thanks:)

Mathematics
2 answers:
Verdich [7]3 years ago
5 0

Answer:

x=-1,\:x=-7,\:x=i,\:x=-i

Step-by-step explanation:

Considering the equation

x^4+8x^3+8x^2+8x+7=0

Solving

x^4+8x^3+8x^2+8x+7

\mathrm{Factor\:}x^4+8x^3+8x^2+8x+7:\quad \left(x+1\right)\left(x+7\right)\left(x^2+1\right)

As

\mathrm{Use\:the\:rational\:root\:theorem}

a_0=7,\:\quad a_n=1

\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:7,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1

\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:7}{1}

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

=\left(x+1\right)\frac{x^4+8x^3+8x^2+8x+7}{x+1}...[A]

Solving

\frac{x^4+8x^3+8x^2+8x+7}{x+1}

=x^3+7x^2+x+7

Putting \frac{x^4+8x^3+8x^2+8x+7}{x+1} =  x^3+7x^2+x+7 in equation [A]

So,

\left(x+1\right)\frac{x^4+8x^3+8x^2+8x+7}{x+1}...[A]

=\left(x+1\right)x^3+7x^2+x+7

As

x^3+7x^2+x+7=\left(x+7\right)\left(x^2+1\right)

So,

Equation [A] becomes

=\left(x+1\right)\left(x+7\right)\left(x^2+1\right)

So,  the polynomial equation becomes

\left(x+1\right)\left(x+7\right)\left(x^2+1\right)=0

\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\mathrm{Solve\:}\:x+1=0:\quad x=-1

\mathrm{Solve\:}\:x+7=0:\quad x=-7

\mathrm{Solve\:}\:x^2+1=0:\quad x=i,\:x=-i

\mathrm{The\:solutions\:are}

x=-1,\:x=-7,\:x=i,\:x=-i

Keywords: polynomial equation

Learn polynomial equation from brainly.com/question/12240569

#learnwithBrainly

Katarina [22]3 years ago
3 0

Answer:

x^4+8x^3+8x^2+8x+7=0

Step-by-step explanation:

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Suppose the contact rate for a phone survey is 78% and that 22% of people will participate in that survey. Assume that agreeing
Gnoma [55]
Remember that, for independent events, the probability that both occurr is the product of the individual probabilities.

a) Probability of being contacted: 78% = 0.78

Probaility of refusing: 1 - 22% = 1 -0.22 = 0.78

Combined probability: 0.78*0.78 = 0.6084

b) The probability of failing to contact or making contact and not geeting them to agree 1 - the probability of contacting and getting them to agree.

The probabilityof contacting and getting them to agree is 0.78*0.22 = 0.1716

The the answer to this question is 1 - 0.1716 = 0.8284


 
8 0
3 years ago
(35 points) answer 5 and 7 only please
tatyana61 [14]
A2+b2=c2 and get your answer

3 0
3 years ago
Which expression is equivalent to (–3y – x) – (5y – 8x)? –8y – 8x –8y 7x 2y – 7x 8y 8x.
IRINA_888 [86]

The expression is equivalent to -8y + 7x.

Given

Expression; (-3y - x) - (5y - 8x)

<h3>How to find the equivalent expression?</h3>

To find the equivalent expression multiply the expression and add and simplify.

Then,

The expression is equivalent to;

 (-3y - x) - (5y - 8x)

-3y - x - 5y + 8x

-8y + 7x

Hence, the expression is equivalent to -8y + 7x.

To know more about expression click the link given below.

brainly.com/question/13040575

6 0
2 years ago
According to data from a medical​ association, the rate of change in the number of hospital outpatient​ visits, in​ millions, in
GaryK [48]

Answer:

a) f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient​ visits, in​ millions, is given by:

f'(t)=0.001155t(t-1980)^{0.5}

a) To find the function f(t) you integrate f(t):

\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt

To solve the integral you use:

\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}

Next, you replace in the integral:

\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C

Then, the function f(t) is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient​ visits.

Hence C' = 264,034,000

The function is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000

b) For t = 2015 you have:

f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7

3 0
3 years ago
Please help 60 points!!
Katen [24]

Answer:

The answer to your question is FJ = 18

Step-by-step explanation:

Data

FG = 30

FH = 12

HE = 8

JH ║GE

These triangles are similar, so we can use proportions to find the length of FJ.

                            \frac{FJ}{FH} = \frac{FG}{FH + HE}

Substitution

                          \frac{FJ}{12} = \frac{30}{12 + 8}

Simplification

                         \frac{FJ}{12} = \frac{30}{20}

Solve for FJ

                        FJ = 12 \frac{30}{20}

Result

                        FJ = 18

4 0
3 years ago
Read 2 more answers
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