One root of a third degree polynomial function f(x) is -5 + 2i. Which statement describes the number and nature of all
roots for this function?
f(x) has two real roots and one imaginary root.
f(x) has two imaginary roots and one real root.
f(x) has three imaginary roots.
f(x) has three real roots.

Answers

Answer 1

Answer:

f(x) has two imaginary roots and one real root.

Step-by-step explanation:

Complex roots:

I a complex number [tex]a + bi[/tex] is a root of a polynomial, it's conjugate [tex]a - bi[/tex] is also a root.

One root of a third degree polynomial function f(x) is -5 + 2i.

This means that -5 - 2i is another root of the polynomial, and thus, 2 of the roots are complex.

Third degree, so it has three roots, which means that the third root is real(not possible to have a complex root without it's conjugate), and thus, the correct answer is:

f(x) has two imaginary roots and one real root.

Answer 2

Answer:

B!

Step-by-step explanation:

just did it


Related Questions

Simplify by expressing fractional exponents instead of radicals.

Answers

8(x^2y^4)^1/2 I think this is the answer

The explicit rule for a sequence and one of the specific terms is given. Find the position of the given term.

f(n) = 3.75n − 27.5; 25


Step 1 out of 2:
You know that the value of f(n) is 25. Substitute 25 for f(n) in f(n) = 3.75n − 27.5.
25 = 3.75n − 27.5
= 3.75n

Answers

Answer:

14

Step-by-step explanation:

Given :

f(n) = 3.75n − 27.5

f(n) = 25

Put f(n) = 25 in the equation :

25 = 3.75n - 27.5

25 + 27.5 = 3.75n

52.5 = 3.75n

52.5 / 3 75 = n

14 = n

The position of the term is 14

How do I solve this?

Answers

The answer for the first line segment : (-3,-7) (-4,0)

The answer for 2nd line segment is :(-3,8) (-9,-5)

Step-by-step explanation:

Let do line segment QR and ST. first.

Step 1: Find a line that contains a points that is perpendicular to the line of reflection

"A reflection of a pre image and new image is perpendicular to the line of reflection.

This means for points Q,S,T and R, there is a line that. contains one point that is perpendicular to the line of reflection.

A line that is perpendicular to the line of reflection is the negative reciprocal of the slope so this means all 4 lines must be on a different slopes but the slopes must be 1/2.

To simplify, things, here are the lines that will all 4 points be on

Point R will be on line y=1/2x-11/2Point Q will be on line y=1/2x+2Point S will be on line y=1/2x+19/2Point T will be on line y=1/2x-1/2

Step 2: Find a point where both the line and line of reflection intersect at.

Now we need to find a line where both the line of reflections and the 4 lines will intersect at separately.

The line with Point R will intersect with the line of reflection at point (1,-5)The line with Point Q will intersect with line of reflection at Point (-2,1)The line with Point S will intersect at point (-5,7)The line worth Point T will intersect at Point(-1,-1).

Step 3: Find the endpoints given the midpoint and the originally endpoint.

A reflection per and new image is equidistant from the point of reflection. So we. an say that the point where the line intersect is the midpoint of the pre and new image.

Using this info,

The endpoint for R prime is (-3, -7).The endpoint for Q prime is (-4,0). The endpoint of S prime is (-3,8).The endpoint of T prime is (-9,-5).

Connect R prime and Q prime. And that the new line segments

Connects S prime and T prime and that the new line segments.

the percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.

If one person is selected from each city, what is the probability that all of them are under 18?

Answers

Answer:

0.0158 = 1.58% probability that all of them are under 18.

Step-by-step explanation:

Probability of independent events:

If three events, A, B and C are independent, the probability of all happening is the multiplication of the probabilities of each happening, that is:

[tex]P(A \cap B \cap C) = P(A)P(B)P(C)[/tex]

The percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.

This means that [tex]P(A) = 0.235, P(B) = 0.258, P(C) = 0.26[/tex]

If one person is selected from each city, what is the probability that all of them are under 18?

Since the three people are independent:

[tex]P(A \cap B \cap C) = 0.235*0.258*0.26 = 0.0158[/tex]

0.0158 = 1.58% probability that all of them are under 18.

What is the simplest form of 0.0115

Answers

23/200

Hope this helps! :)

Answer:

23/2000

Step-by-step explanation:

0.0115 can be written as 115/10000

=23/2000

Please mark me as brainliest.

The function y=5(1/2)^x Models the number of grams of radioactive material, y, left in a container after x days. Sketch the graph of this function below

Answers

Answer:

see graph

Step-by-step explanation:

Can someone help me with this problem?

Answers

no i don't even think albert could

Write a compound inequality to represent all of the numbers between -4 and 6.

Answers

Answer:

-4 < x < 6

Step-by-step explanation:

By way of tree diagram determine all likely outcome when a fair die is tossed

Answers

Step-by-step explanation:

hope it helps

brainliest please

insert a digit in place of each ... to make a number that is divisible by 6
4 . . . 6

Answers

Answer:

2

Step-by-step explanation:

Get brainly if right!! Plsss help

A dozen roses in a gift box cost 21 dollars. Twenty roses in a
gift box cost 32.6 dollars. How much does a gift box cost? How
much does one rose cost?

Answers

Answer: [tex]\$1.45[/tex]; [tex]\$3.6[/tex]

Step-by-step explanation:

Given

A dozen roses in a gift box costs $21

Similarly, 20 roses in a gift box costs $32.6

Suppose the price of single rose and gift box is [tex]x[/tex] and [tex]y[/tex]

[tex]\therefore 12x+y=21\quad \ldots(i)\\\Rightarrow 20x+y=32.6\quad \ldots(ii)[/tex]

Solving (i) and (ii) ,  we get

[tex]x=\$1.45;y=\$3.6[/tex]

Thus, the price of the one rose is [tex]\$1.45[/tex] and the price of gift box is [tex]\$3.6[/tex]

Answer:

1.45 and 3.5

Step-by-step explanation:

Determine the value of the missing letters in the sum of numbers
below:
ab1
+ ba
abb
49x

Answers

Answer:

a=2, b=3,x=6

Step-by-step explanation:

We are given that

We have to find the value of the missing letters in the sum of numbers.

From given sum

1+a+b=x   ....(1)

b+b+b=9  .....(2)

a+a=4       ......(3)

From equation (2) we get

[tex]3b=9[/tex]

[tex]\implies b=3[/tex]

From equation (3) we get

[tex]2a=4[/tex]

[tex]a=4/2[/tex]

[tex]a=2[/tex]

Now, substitute the values in equation (1) we get

[tex]1+2+3=x[/tex]

[tex]x=6[/tex]

Therefore,

231+32+233=496

Which expression is equivalent to…

Answers

Answer:

D

Step-by-step explanation:

In how many ways could nine people be divided into two groups of two people and one group of five people?
Nine people could be divided into two groups of two people and one group of five people ways.
(Type a whole number.)

Answers

Answer:

your can only divide then up in that specific sequence one time

Consider the probability that no less than 37 out of 295 cell phone calls will be disconnected. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.

a. Area to the right of 36.5
b. Area to the right of 37.5
c. Area to the left of 36.5
d. Area to the left of 37.5
e. Area between 36.5 and 37.5

Answers

Answer:  Choice A) Area to the right of 36.5

==========================================================

Explanation:

The phrasing "no less than" means the same as "at least".

Saying "at least 37" means 37 is the lowest we can go.

If x is the number of disconnected calls, then [tex]x \ge 37[/tex] and we want to find the probability of this happening (the max being 295).

We could use the binomial distribution to find the answer, but that would require adding 295-37+1 = 259 different values which could get tedious. So we could use the normal approximation to make things relatively straight forward.

Assuming this binomial meets the requirements of the normal approximation, then we'd look under the normal curve for the area to the right of 36.5; which is why the answer is choice A.

Why 36.5 and not 37? This has to do with the continuity correction factor when translating from a discrete distribution (binomial) to a continuous one (normal).

If we used 37, then we'd be missing out on the edge case. So we go a bit beyond 37 to capture 36.5 instead. It's like a fail safe to ensure we do account for that endpoint of 37. It's like adding a buffer or padding.

------------

Side notes:

Choice B would be the answer if we wanted to excluded 37 from the group, ie if we wanted to calculate [tex]P(x > 37)[/tex] instead of [tex]P(x \ge 37)[/tex]. So we're moving in the opposite direction of choice A to avoid that edge case. We go with "right" instead of "left" since this is what the inequality sign says.

Question 19 of 30
An angle is formed by two rays or segments that share a(n).
A. Vertex
B. Side
Ο Ο Ο Ο
O C. Endpoint
OD. Ray

Answers

I think the answer is C. Hope this helps!

Answer:

A a vertex

Step-by-step explanation:

When rays meet they form a point is formed known as the vertex.

Which rectangle has an area of 18 square units? On a coordinate plane, a rectangle is 2 units high and 7 units wide. On a coordinate plane, a rectangle is 2 units high and 6 units wide. On a coordinate plane, a rectangle is 3 units high and 5 units wide. On a coordinate plane, a rectangle is 3 units high and 6 units wide.

Answers

Answer:

On a coordinate plane, a rectangle is 3 units high and 6 units wide.

Answer:

option "B"

You Welcome

Step-by-step explanation:

What transformation to the linear parent function, f(x) = x, gives the function
g(x) = x + 7?
A. Shift 7 units left.
B. Shift 7 units right.
C. Vertically stretch by a factor of 7
D. Shift 7 units down

Answers

Answer:

I think A

Step-by-step explanation:

There are eggs in a dozen. If a farmer's chickens produce an average of dozen eggs in a month, how many eggs are reported per month?

Answers

Complete Question:

There are 12 eggs in a dozen. If a farmer's chickens produce an average of 423 dozen eggs in a month,  how many eggs are reported per month?

Answer:

The eggs reported per month are:

= 5,076 eggs.

Step-by-step explanation:

a) Data and Calculations:

A dozen eggs = 12 pieces of eggs

Average of dozen eggs produced in a month = 423

Therefore, the eggs that are reported per month should average 5,076 (12 * 423)

b) The arrangement or measurement of eggs in dozens makes it easier to calculate the number of eggs produced in the farm each period.  The result is obtained by multiplying the average of dozen eggs produced by 12.

How would you write 8^5 as a multiplication expression?

Answers

8•8•8•8•8 is the correct answer

Answer:

8 * 8 * 8 * 8 * 8

Step-by-step explanation:

8^5 is basically 8 times itself five times.

Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.

1. f(x) is exponential; an exponential function increases more slowly than a linear function.
2. f(x) is exponential; f(x) increased more overall than g(x).
3. g(x) is exponential; g(x) has a higher starting value and higher ending value.
4. g(x) is exponential; an exponential function increases faster than a linear function.

Answers

Hi there!

[tex]\large\boxed{\text{Choice 4}}[/tex]

We can look at each function, f(x) and g(x), to determine which is exponential.

Use slope formula: m = y2-y1/x2-x1

f(x) starts off with a slope at about $1800/year, but becomes about $1100/year.

g(x) starts off with a slope of about $1500/year, but becomes about $1874/year.

Thus, g(x) is exponential, because g(x)'s slope is increasing across the interval.


Find the volume of the figure. Express answers in terms of t, then round to the nearest whole number


Please help :)

Answers

Answer:

729π ft³

Step-by-step explanation:

Applying,

Volume of a cone

V = πr²h/3.............. Equation 1

Where r = radius of the base, h = height, π = pie

From the question,

Given: r = 9 ft, h = 27 ft

Substitite these values into equation 1

V = π(9²)(27)/3

V = 729π ft³

Hence the volume of the figure in terms of π is 729π ft³

convert 23/4 into mixed number

Answers

5 3/4 is the mixed number

Simplify this math problem plz show your work

Answers

9514 1404 393

Answer:

  (8a -a²)/(a +2)

Step-by-step explanation:

Cancel common factors from numerator and denominator.

  [tex]\dfrac{-56+15a-a^2}{a^2+2a}\div\dfrac{a-7}{a^2}=-\dfrac{(a-7)(a-8)(a^2)}{a(a+2)(a-7)}\\\\=-\dfrac{a(a-8)}{a+2}=\boxed{\dfrac{8a-a^2}{a+2}}[/tex]

A film distribution manager calculates that 5% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 572 released films would be greater than 6%

Answers

Answer:

0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A film distribution manager calculates that 5% of the films released are flops.

This means that [tex]p = 0.05[/tex]

Sample of 572

This means that [tex]n = 572[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.05[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.05*0.95}{572}} = 0.0091[/tex]

What is the probability that the proportion of flops in a sample of 572 released films would be greater than 6%?

1 subtracted by the p-value of Z when X = 0.06. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.05}{0.0091}[/tex]

[tex]Z = 1.1[/tex]

[tex]Z = 1.1[/tex] has a p-value of 0.8643

1 - 0.8643 = 0.1357

0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%

Tiham is the only striker of his team. He can catch one of the four passes delivered to him and when he get a pass he takes the shot. One of his four shots go towards the net but the goal keeper of the opposite team stop one of every two shots. What is the minimum number of passes have to be delivered to Tiham to score minimum one goal?

Answers

Answer:

1/4 *1/4*1/2 =0.03125

which as a fraction is 1/32

so the minimuim number of passes that will get him a goal is 1 since he could get it on the first try

Hope This Helps!!!

What is the value of b?

Answers

Answer:

?

Step-by-step explanation:

Kaitlin is riding her bike. The number of revolutions (turns) her wheels make varies directly with the distance she travels. See the graph below.



How far does Kaitlin travel per revolution?

What is the slope of the graph?

Answers

Answer:

m = Δy/Δx = 4/32 = 1/8

8 ft/rev.

Step-by-step explanation:

Answer:

[tex]\frac{1}{8}[/tex] for both

Step-by-step explanation:

1. Distance per revolution

We see that the distance travelled at 2 revolutions is 16

This means that she travels [tex]\frac{1}{8}[/tex] of a mile per revolution

2. Slope

The slope formula is rise/run, or ([tex]y[/tex]₂[tex]-y[/tex]₁)/([tex]x[/tex]₂[tex]-x[/tex]₁)

We can take two points, (16,2) and (32,4)

[tex]\frac{4-2}{32-16}=\frac{2}{16}=\frac{1}{8}[/tex]

The slope is [tex]\frac{1}{8}[/tex]

Hope this helps! Please mark brainliest :)

Find the greatest common factor of 15 x²y³ and -18 x³yz .

Answers

Answer:

3 x² y¹

Step-by-step explanation:

15 x²y³ = 3. 5. x². y³

-18x³yz = -2. 3². x³. y¹. z¹

so, the GCF = 3. x². y¹

Answer:

Solution given:

15x²y³=3*5*x*x*y*y*y

-18x³yz=-3*2*3*x*x*x*y*z

over here common is

3*x*x*y

so

greatest common factor is 3x²y¹

The vertical test line

Answers

Step-by-step explanation:

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines. and, as a result, any vertical line in the plane can intersect the graph of a function at most once.

hope it helpsstay safe healthy and happy....

Answer:

It is a graphical method

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