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3 years ago

How many real roots and how many complex roots does this expression have? (x+7)^7

Mathematics

1 answer:

Feliz [49]3 years ago

3 0

Answer:

One real root, with multiplicity 7.

Step-by-step explanation:

The given expresion is

${(x + 7)}^{7}$

This is a seventh degree polynomial.

According to the fundamental theorem of Algebra, the expression has a potential 7 roots both real and complex.

This expression has one real root, with multiplicity , 7.

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Determine the domain of the function (fog)(x) where f(x)=3x-1/x-4 and g(x)=x+1/x

Katarina [22]

Answer: (-∞,-1) ∪ (0,+∞)

Step-by-step explanation: The representation fog(x) is a representation of composite function, meaning one depends on the other.

In this case, fog(x) means:

fog(x) = f(g(x))

fog(x) = $3(x+\frac{1}{x} )-\frac{1}{x+\frac{1}{x} } -4$

$fog(x)=3x+\frac{3}{x} -\frac{1}{\frac{x^{2}+x}{x} } -4$

$fog(x)=3x+\frac{3}{x} -\frac{x}{x^{2}+x} -4$

$fog(x)=\frac{3x^{2}(x^{2}+x)+3(x^{2}+x)-x-4x(x^{2}+x)}{x(x^{2}+x)}$

$fog(x)=\frac{3x^{4}+3x^{3}+3x^{2}+3x-x-4x^{3}+4x^{2}}{x(x^{2}+x)}$

$fog(x)=\frac{3x^{4}-x^{3}-x^{2}+2x}{x(x^{2}+x)}$

This is the function fog(x).

The domain of a function is all the values the independent variable can assume.

For fog(x), denominator can be zero, so:

$x(x^{2}+x) \neq 0$

If x = 0, the function doesn't exist.

$x^{2}+x \neq0$

$x(x+1) \neq0$

$x+1\neq0$

$x\neq-1$

Therefore, the domain of this function is: -∞ < -1 or x > 0

5 0

3 years ago

The distribution of the number of words in text messages between employees at a large company is skewed right

kaheart [24]

The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

The z score is given by:

z = (raw score - mean) / (standard deviation / √sample size)

Given mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages, hence, for x > 10:

z = (10 - 8.6) / (4.3 / √39) = 2.03

P(x > 10) = P(z > 2.03) = 1 - P(z < 2.03) = 1 - 0.9788 = 0.0212

The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%

Find out more on equation at: brainly.com/question/2972832

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8 0

2 years ago

What is the formula for finding the final balance of an account that earns interest compounded annually? State what each variabl

Schach [20]

C=P[(1+r)^n-1]
C = COMPOUND INTEREST
P = PRINCIPAL
r = rate per period
n = number of periods

5 0

3 years ago

Is Figure ABCD congruent to Figure PQRS? Use the drop-down menus to explain your answer. у 6 В. R 4 S a Q N A I Р 8 -6 -4 -2 O -

natali 33 [55]

Answer:

are not and does not

Step-by-step explanation:

7 0

2 years ago

Please show how you solved the problem. 4a - 14 = 7a - 8

lianna [129]

4a - 14 = 7a - 8

4a - 7a = 14 -8

-3a = 6

a = 2

ok done. Thank to me :>

4 0

2 years ago

Read 2 more answers