help
state the multiplicity for each root
[tex]3(x^{2} + 5)^ {2} ( {x}^{2} - 25)^{3} (x - 8)^{4} = 0[/tex]
state the multiplicity for each root​

Answers

Answer 1
x
=
i

5

x
=
i

5
,

i

5
,

5
,
5
,
8
Answer 2

Answers:

The two complex or imaginary roots [tex]x = i\sqrt{5}[/tex] and [tex]x = -i\sqrt{5}[/tex] have multiplicity 2.The two real roots x = 5 and x = -5 have multiplicity 3The root x = 8 has multiplicity 4

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

Explanation:

We'll use the zero product property to solve.

[tex]3(x^2+5)^2(x^2-25)^3(x-8)^4 = 0\\\\(x^2+5)^2=0 \text{ or } (x^2-25)^3=0 \text{ or } (x-8)^4 = 0\\\\x^2+5=0 \text{ or } x^2-25=0 \text{ or } x-8 = 0\\\\x^2=-5 \text{ or } x^2=25 \text{ or } x = 8\\\\x=\pm\sqrt{-5} \text{ or } x=\pm\sqrt{25} \text{ or } x = 8\\\\x=\pm i\sqrt{5} \text{ or } x=\pm 5 \text{ or } x = 8\\\\[/tex]

where [tex]i = \sqrt{-1}[/tex]

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

The notation [tex]x=\pm i\sqrt{5}[/tex] breaks up into [tex]x=i\sqrt{5} \text{ or } x=-i\sqrt{5}[/tex]. The multiplicity of these two roots is 2 as it's the exponent of the factor [tex](x^2+5)^2[/tex]. Focus on the outermost exponent.

The notation [tex]x = \pm 5[/tex] becomes [tex]x = 5 \text{ or } x = -5[/tex]. The multiplicity of these two roots is 3 since it's the outermost exponent of the factor [tex](x^2-25)^3[/tex]

And finally, the multiplicity of the root x = 8 is 4 because it is the outermost exponent of the factor [tex](x-8)^4[/tex]


Related Questions

Find x no need for explanation I just need answer thanks

Answers

Answer:

x = 12 m

Step-by-step explanation:

Length = x m

Width = 3⅔ = 11/3

Area = 44 m²

Area of rectangle = length × width

Plug in the values into the equation

[tex] 44 = x \times \frac{11}{3} [/tex]

[tex] 44 = \frac{11x}{3} [/tex]

Multiply both sides by 3

[tex] 44 \times 3 = \frac{11x}{3} \times 3 [/tex]

[tex] 132 = 11x [/tex]

Divide both sides by 11

[tex] 12 = x [/tex]

x = 12

Please help
How many solutions can be found for the system of linear equations represented on the graph?
A)
no solution
B)
one solution
C)
Two solutions
D)
Infinitely many solutions

Answers

C it is c ajdbdiwdidnwisnxidnend

Answer: One solution

Step-by-step explanation:

When the lines intersect in one spot, there's one solution. The lines have different slopes, so there's only one solution.

80 points!

A store had 250 bottles of water. Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments.

Which recursive function best represents the number of bottles of water in the store, given that f(0) = 250?


A. f(n) = f(n − 1) ⋅ 0.6 + 48, n > 0

B. f(n) = 250 − f(n − 1) ⋅ 0.4 + 48, n > 0

C. f(n) = f(n − 1) ⋅ 0.4 + 48, n > 0

D. f(n) = 250 − f(n − 1) ⋅ 0.6 + 48, n > 0

pls give reason

Answers

Answer:

A

Step-by-step explanation:

Given:  

Initial number of bottles = 250

Every week = 40% is sold and 48 bottles arrive.

Week 1 = 250 - (250 x 0.40) + 48 = 250 - 100 + 48 = 198

Week 2 = 198 - (198 x 0.40) + 48 = 198 - 79 + 48 = 167

Answer is: A. f(n ) = f(n - 1) • 0.6 + 48, n > 0.

Please help!

Find the slope

-2x + 4y = 36

Thank you!

Answers

-2x+4y=36
Add +2x to both sides
4y=2x+36
Decide every term by 4
y= 2/4x + 9

The slope is 2/4

Express it in slope-intercept form.

Answers

Find slope: pick any two points
(1,3), (2,7)
(y2-y1)/(x2-x1)
(7-3)/(2-1) = 4
Y=4x+b
Plug in any point to solve for b
I used (2,7), 7=8-1, b=-1
Slope intercept form: y = 4x -1

help plss me ndfkfhfiklfjkfbufjriowxrkoek
UwU

Answers

Answer:

[tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

We can use the rise over run method to do this question.

Let's start at the coordinates (1,1)

If we go down 2 from that point and to the right 3 times then we see another point on the line (3, -1).

We would express this as 2 over 3 or [tex]\frac{2}{3}[/tex].

We aren't done yet however.

The line is sloping downwards and this means that the slope is negative.

So, the final answer is [tex]-\frac{2}{3}[/tex]

I hope this helps!!

- Kay

A person who weighs 105 pounds on Earth weighs 175 pound on the moon How much does a pound person weigh on the moon?

Answers

Answer:

1.67 pounds

Step-by-step explanation:

The problem above can be solved by using "direct proportion." This proportion shows that as one quantity increases, the other quantity increases and vice-versa.

Step 1: Represent the weight of the person on the moon by n.

Step 2: Set up a proportion.

            [tex]\frac{105}{175}[/tex] = [tex]\frac{1}{n}[/tex]

Step 3: Cross multiply.

            105 x n = 175 x 1

            105n = 175

Step 4: Find n by dividing both sides by 105.

            n = [tex]\frac{175}{105}[/tex]

            n = 1.666 or 1.67 pounds (lowest term)

A pound of person on Earth will weigh 1.67 pounds on the moon.

deandreh can work three math problems in five minutes . How long will it take him to work fifteen problem ? Plz show ur working out and thank u so much ​

Answers

Answer:

25 minutes

Step-by-step explanation:

Because 3 × 5 is 15 problems so multiple he 5 minutes by 5 and you get 25 minutes.

I’m failing all my classes please help

Answers

Answer:

b

Step-by-step explanation:

Joseph is reading a 32 page book he read 6 pages in 15 minutes if he continues to read at the same rate how long will it take him to read the entire book

Answers

Answer:

80 minutesssssss

Answer:

(edit) your answer is 80 min

Step-by-step explanation:

first we can set this up as a proportion.

so it would be 15 over 6 and your other side would be x over 32

so when u cross multiple your equation would be 6x = 480

then you divide both sides by 6 and when you divide 480 by 6 u will get 80

                         

The Answer and yea idk

Answers

(1-2)
(4-2)
the answer would be
-1/2 :)

a candle is burning at a linear rate. The candle measures five inches two minutes after it was lit. It measures three inches eight minutes after it was lit. What was the original length of the candle?​

Answers

Answer:

5 2/3 inches.

Step-by-step explanation:

8-2=6 minutes and 5-3=2 inches so it lost 2 inches in 6 minutes. This means it loses an inch every three minutes. Since we have to go back by 2 minutes we will have to figure out how much length we have to add to the candle to figure out how long it was originally by multiplying by 2/3 as 2 inches is 2/3 the required to remove an inch, so 1 inch * 2/3 = 2/3 of an inch. Add that to the length at two minutes and we have 5 2/3 inches as its original size.

Heyyyyy plz help I don’t bite

Answers

sorry but isn’t can’t

Answer:

50.24

Step-by-step explanation:

A = Πr^2

A = 3.14(4)^2

A = 50.24

the sum of twice a number and three is 21

Answers

Answer:

9

Step-by-step explanation:

9+9+18

18+3=21

One afternoon, Supreme sub shop sells 15 subs in 45 minutes. If the shop continues to sell subs at the same rate, about how many subs will the shop sell in 3 hours?

Answers

60 subs
Because it’s 15 per 45 and 45 times 4 is 180 which means that in 3 hours or 180 minutes they sold 15 times 4 amount of subs and 15 times four is 60. Hope this helps. Sorry if the explanation isn’t that good

A coach brought 12,000 milliliters of water to a tournament. How many liters of water did the coach bring?

Answers

Answer:

0.012

Step-by-step explanation:

Answer:

12 liters

Step-by-step explanation:

on google

determine whether the triangles are similar by angle-angle similarity. if yes, write a similarity statement.

Answers

Step-by-step explanation:

angle MNP = angle QPL (corresponding angles, //lines) (A)

angle QLP is common angle (A)

By AA, the 2 triangles are similar.

Topic: congruence and similarity

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

solve the equation:
(p + 3)(1 - p)​

Answers

Answer:

p²-2p+3

Step-by-step explanation:

(p + 3)(1 - p)​

p-p²+3-3p

=p²-2p+3

Hope this helps :)

What is 7505 divided by 11?

Answers

Answer:

7505÷11 = 682.27272727

Step-by-step explanation:

or you can just put a line over the 27

Answer:

682.27

Step-by-step explanation:

7505÷11= 682.272727

Find the simple past tense of these verbs in the passage.
is
go
begin
do
make
grow
sell
get
ring​

Answers

Answer:

was

went

began

did

made

grow

sell

get

rang

I don't know if it's right though?

Answer:

was

went

began

did

made

grew

sold

got

rang

in the example,-38+(-24)will be negative before finding the sum? ​

Answers

Answer:

-62

Step-by-step explanation:

Explain how to simplify an expression with negative exponents using the rules for multiplying monomials.
PLZZZZZ I NEED HELP ILL MAKE YOU BRAINLIEST

Answers

Answer:

Purplemath

Recall that negative exponents indicates that we need to move the base to the other side of the fraction line.

(The "1's" in the simplifications above are for clarity's sake, in case it's been a while since you last worked with negative powers. One doesn't usually include them in one's work.)

In the context of simplifying with exponents, negative exponents can create extra steps in the simplification process.

Step-by-step explanation:

are my answers correct ​

Answers

Answer:

yesn't

Step-by-step explanation:

Answer:

yes last Friday i did this and i do it the same i got it correct.

Step-by-step explanation:

Jyoti collects stamps. The table shows the number of stamps she collected over a 12-week period.
Find the rate of change for each time period to the nearest hundredth. Identify the time period
during which the number of stamps increased at the fastest rate.

Answers

where is the table? i need it to answer the question

Someone help meee I hate my teacher she asssign nvm I’m not even gonna say

Answers

Answer:

eating lunch

Step-by-step explanation:

the total time is 60 minutes. 10 minutes is 1/6 of that. 1/6 of 18 (from eating lunch) is 3 minutes. eating lunch is correct. also i hate my teacher sm too

The answer is eating lunch

In the diagram below, AB≅AD, m∠A=48° and m∠BCD=40°. Which statement is true?

Answers

Answer:

3

Step-by-step explanation:

a city has a garden in the shape of an equilateral triangle with 40 feet sides. there is a walkway that runs from a gate located at the midpoint of one side of the equilateral triangle to a fountain at the opposite vertex. approximately how long is the walkway?

Answers

Answer:

The walkway is approximately 34.64 feet long

Step-by-step explanation:

The length of the sides of the equilateral triangle shaped the city garden = 40 feet

The path of the walkway = From the midpoint of a side to the opposite vertex

Therefore, we have;

Let x, represent the length of the walkway

We have that the x, a side of the equilateral triangle, and half the side of the location of the gate, forms a right triangle, with a side of the equilateral triangle representing the hypotenuse side

Therefore, we have;

40² = x² + (40/2)²

40² = x² + 20²

x² = 40² - 20² = 1200

x = √1200 = 20·√3

The length of the walkway = x = 20·√3 ≈ 34.64 feet.

2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4. How many votes did she get?​

Answers

Answer:

473 or 472, depends on how you round

Step-by-step explanation:

378/4 = 94.5

94.5 x 5 = 472.5

The number of votes she gets will be 473.

What is multiplication?

It is also known as the product. If the object n is given to m times then we just simply multiply them.

2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4.

Then the number of votes she gets that will be

→ 378 x 5 / 4

→ 378 x 1.25

→ 472.5 ≅ 473

More about the multiplication link is given below.

https://brainly.com/question/19943359

#SPJ2

What is the fraction 24/4 simplified?

Answers

Answer:

6

Step-by-step explanation:

The fraction 24/4 simplified is 6.

To simplify the fraction 24/4, we find the greatest common divisor (GCD) of the numerator (24) and the denominator (4), and then divide both the numerator and denominator by the GCD to obtain the simplified form.

Step 1: Find the GCD of 24 and 4.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The factors of 4 are 1 and 4.

The GCD of 24 and 4 is 4, as it is the largest number that divides both 24 and 4.

Step 2: Divide both the numerator and denominator by the GCD.

24 ÷ 4 = 6

4 ÷ 4 = 1

So, the simplified form of 24/4 is 6/1. However, any fraction divided by 1 remains the same, so the simplified fraction is 6.

Therefore, 24/4 simplified is 6.

To know more about fraction:

https://brainly.com/question/10354322


#SPJ6

Given ABC, m A= 60 degrees, m c=45 degrees, AB=8 Find the perimeter of ABC

Answers

Answer:113

Step-by-step explanation:

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