In which graph is y a linear function of x will mark brainiest

If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?

Naddik [55]

Answer:

it must also have the root : - 6i

Step-by-step explanation:

If a polynomial is expressed with real coefficients (which must be the case if it is a function f(x) in the Real coordinate system), then if it has a complex root "a+bi", it must also have for root the conjugate of that complex root.

This is because in order to render a polynomial with Real coefficients, the binomial factor (x - (a+bi)) originated using the complex root would be able to eliminate the imaginary unit, only when multiplied by the binomial factor generated by its conjugate: (x - (a-bi)). This is shown below:

$(x-(a+bi))*(x-(a-bi))=\\(x-a-bi)*(x-a+bi)=\\([x-a]-bi)*([x-a]+bi)=\\(x-a)^2-(bi)^2=\\(x-a)^2-b^2(-1)=\\(x-a)^2+b^2$

where the imaginary unit has disappeared, making the expression real.

So in our case, a+bi is -6i (real part a=0, and imaginary part b=-6)

Then, the conjugate of this root would be: +6i, giving us the other complex root that also may be present in the real polynomial we are dealing with.

5 0

3 years ago

52 is what percent of 156

siniylev [52]

The answer is 33.33…(repeating decimal).
Work:
(52)(100)=5,200
5,200/156=33.33…

7 0

3 years ago

Given a normally distributed data set with the mean = 88 and the standard deviation = 6, according to the empirical rule, what p

kumpel [21]

According to the empirical rule, the percent of the data points that are below 100 is; 95.44%

<h3>How to use Empirical Rule in Statistics?</h3>

We are given;

Mean; μ = 88

Standard deviation; σ = 6

Sample mean; x' = 100

Formula for z-score is;

z = (x' - μ)/σ

z = (100 - 88)/6

z = 2

Now, from the empirical rule of normal distribution graph attached, we see that at z = 2, the percentage is 95.44%. However, we want to find the percentage that lie below 100. Thus, this is 95.44%

Read more about Statistics Empirical Rule at; brainly.com/question/10093236

#SPJ1

5 0

2 years ago

Which value of kkk makes 5-k+12=165−k+12=165, minus, k, plus, 12, equals, 16 a true statement?

trapecia [35]

Answer:

k=1

Step-by-step explanation:

Simplify 1/k

3 2 1

(((—+2)-(—•k))-4)-(—-2) = 0

k k k

2.1 Subtracting a whole from a fraction

2 2 • k

2 = — = —————

1 k

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

1 - (2 • k) 1 - 2k

——————————— = ——————

k k

Simplify 2/k

3 2 (1-2k)

(((—+2)-(—•k))-4)-—————— = 0

k k k

Simplify 3/k

3 2 (1-2k)

(((—+2)-(—•k))-4)-—————— = 0

k k k

5.1 Adding a whole to a fraction

3 (1 - 2k)

(((— + 2) - 2) - 4) - ———————— = 0

k k

6.1 Subtracting a whole from a fraction

2 2 • k

2 = — = —————

1 k

7.1 Subtracting a whole from a fraction

3 + 2 • k 2k + 3

————————— = ——————

k k

8.1 Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 2 • k

2 = — = —————

1 k

9.1 Pull out like factors :

2 - 2k = -2 • (k - 1)

10.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

-2•(k-1)

———————— • k = 0 • k

k

Now, on the left hand side, the k cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

-2 • (k-1) = 0

Equations which are never true:

10.2 Solve : -2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

10.3 Solve : k-1 = 0

Add 1 to both sides of the equation :

k = 1

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

HELP ASAP PLZ 100 points

Jlenok [28]

Answer:

5 to 6

0 to 1

Step-by-step explanation:

Just did the quiz

8 0

3 years ago

In which graph is y a linear function of x will mark brainiest ​

In which graph is y a linear function of x will mark brainiest