Given:
Zero: 2, multiplicity: 3
Zero: 0, multiplicity: 2
Degree: 5
Leading coefficient = 1
To find:
The polynomial function.
Solution:
The general form of a polynomial is
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
where, a is a constant, [tex]c_1,c_2,...,c_n[/tex] are zeroes with multiplicity [tex]m_1,m_2,...,m_n[/tex].
Using the given information and the general form of a polynomial, we get
[tex]P(x)=a(x-2)^{3}(x-0)^{2}[/tex]
[tex]P(x)=ax^2(x^3-6x^2+12x-8)[/tex]
[tex]P(x)=a(x^5-6x^4+12x^3-8x^2)[/tex]
Leading coefficient is 1, so the value of a is also 1.
[tex]P(x)=1(x^5-6x^4+12x^3-8x^2)[/tex]
[tex]P(x)=x^5-6x^4+12x^3-8x^2[/tex]
Therefore, the required polynomial is [tex]P(x)=x^5-6x^4+12x^3-8x^2[/tex].
The polynomial for the conditions with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5 is given as
[tex]\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }[/tex]
According to the given condition
The given conditions to write the polynomial equations are as follows
Zero 2 and Multiplicity 3
Zero 0 and Multiplicity 2
Degree of polynomial expression = 5
Leading coefficient of polynomial expression = 1
Let us consider the polynomial equation has only one variable and hence in general form we can write the equation of polynomial as follows
[tex]\rm y (x) = a(x-\alpha)^m (x-\beta)^n........(1)\\Where \\a = Leading \; coefficient\; of\; polynomial\; expression \\\alpha ,\beta = Roots \; of \; the\; polynomial\; expression\\m\; and \; n \; are \; multiplicities \; of \; the \; roots \; \alpha,\beta \; respectively\\Degree = m+n[/tex]
From the general form of polynomial expression as shown in equation (1) we can write
Polynomial expression for the given conditions is formulated in equation (2)
[tex]\rm y(x) = 1\times (x-2)^3(x-0)^2 .......(2)[/tex]
So the polynomial for the conditions given in question is expressed as
[tex]\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }[/tex]
For more information please refer to the link given below
https://brainly.com/question/15301188
why did my dog have diarrhea when it ate a strawberry?
Answer: I don’t know, because strawberries are seen as good for dogs and it provides them with extra vitamin c. Maybe he/she just didn’t like it or it didn’t sit well in the stomach.
Answer: Sometimes a dog may be allergic to a certain food. Vomiting, diarrhea and skin problems may be symptoms of an allergic reaction. Consult your veterinarian if any of those occur. Introduce only one type of fruit at a time to your dog. Hope this helps... Stay safe and have a great weekend...
Plz mark me brainliest... Hope this is what you are looking for...
:D
(10pts) A train left a station at 8:00 am
going at 45 mph. A second train left the station
at 10:00 am going in the same direction at 55
mph. At what time will the second train catch
up with the first train?
Answer:
12:00 i think
Step-by-step explanation:
hope this helps
Zeno jumped 8 meters. Then he jumped half as far again (4 meters). Then he jumped half as far again (2 meters). So after 3 jumps, he was 8 + 4 + 2 = 14 meters from his starting place.
a. Zeno kept jumping half as far again. How far would he be after 4 jumps?
14/2 = 7
7/2 = 3.5
3.5/2 = 1.75
1.75/2 = 0.875
9514 1404 393
Answer:
15 meters
Step-by-step explanation:
Zeno's last jump was 2 meters, so another jump half as far adds 1 meter to the 14 m total.
After 4 jumps, Zeno would have jumped 15 meters from his starting place.
__
Comment on the question
The given distances give a total "after 3 jumps." The question asks for a total "after 4 jumps." It is not clear whether that is 4 jumps total, or 4 more jumps. In the above, we have assumed it is 4 jumps total.
Sarafina had 34 out of 99 hits when she was at bat during the soft ball season. What was her batting average? (use bar notation if needed)
WILL GIVE BRAINLY
SHOW WORK
Answer:
34%
Step-by-step explanation:
34/99÷1/100=
34/99×1/100=
17/99×1/50=
17/4959=34%
What is the slope of the line that connects the points (0,7) and (4,15)
Answer:
[tex]m=2[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (0, 7)
Point (4, 15)
Step 2: Find slope m
Substitute: [tex]m=\frac{15-7}{4-0}[/tex]Subtract: [tex]m=\frac{8}{4}[/tex]Divide: [tex]m=2[/tex]-(x-10)=7
Solve and Explain.
Answer:
you need to solve for x
Step-by-step explanation:
the ez way for me is by flipping it so now it is -(7-10)=x and 10 -7=3
Answer:
-7=3
Step-by-step explanation:
Hope this helps :D
show work/ explain it
9514 1404 393
Answer:
$68.00
Step-by-step explanation:
Let s represent the opening price. Then the closing price is ...
s - 3.25% × s = $65.79
s(1 -0.0325) = $65.79 . . . . collect terms
0.9675s = $65.79 . . . . . . . simplify
s = $65.79/0.9675 . . . . . . .divide by the coefficient of s
s = $68.00 . . . . . the opening stock price
Channing earns $13.50 per hour at his job. During one week, he worked a total of 2012hours. He deposited $190.00 in the bank and decided to use the rest of is money to buy shirts for work. If each shirt costs $8.50, what is the most amount of shirts Channing could buy?
Answer:
3173
Step-by-step explanation:
13.50*2012=27,162-190=26,972/8.50=3173
point w is located at -10,20. if point w was across reflected across the y axis what are the coordinates of the reflected point
Answer:
Ill get back to you.
Step-by-step explanation:
Evaluate the expression 5c-2 for c=5.
help
Answer:
= 23
Step-by-step explanation:
(5) (5) - 2 ( multiply )
= 5 * 5 = 25
( subtract ) 25 - 2 = 23
i have a question. How much is 1300 + 200
Answer:
1500
Step-by-step explanation:
1300
200
=1500
hope this helps
What is the common ratio between successive terms in the sequence?
2,-4, 8, -16, 32,-64, ...
A.-2
B.6
C.6
D.2
Answer: A
Step-by-step explanation: -2 because it goes negative i think
Answer: A. -2
Step-by-step explanation: To find the common ratio in a sequence, you divide each number by the number before it. -64 divided by 34 is -2, 32 divided by -16 is -2, and so on.
Evelyn drove 248 miles in 8 hours, If she continued at the same rate, how far would she travel in 6 hours?
Answer:
Continuing at the same rate, Evelyn would travel 186 miles.
Step-by-step explanation:
8/248 6/x. then cross multiply 8*x 248*6 = 8x = 1488 x = 186
Answer:
Evelyn will have driven 186 miles
Step-by-step explanation:
Step 1: 248 miles in 8 hours: Divide 248 by 8 in order to find how much miles she travels per hour. (248/8+31)
You should get 31 miles per 1hr.
Step 2: Multiply 31miles/hr by 6hrs in order to find the distance she travels. (31*6=186)
You should get 186 miles.
krytine has a weekend job advertising an upcoming play. she has two options for being paid. Option A is an hourly wage of $7.50 Option B is 5% commission on all money made at the play. she plans to work 7 hours each day on Saturday and Sunday. krystine estimates the play will make about $2,000 this weekend. Which option gives more earnings this weekend?
The Answer is: The hourly rate option of $112 is higher than the commission rate of $105.
Step-by-step explanation:
She will work 16 hours at $7.00 per hour:
16 * 7 = $112
Or she could take the 5% commission on $2,100:
2100 * .05 = $105.
The hourly rate is higher than the anticipated commission amount.
-x -20 = 4x - 5
please help fast and dont just write anything for point i actually need help fast
i will give 25 points
Answer:
x=-3
Step-by-step explanation:
-x-20=4x-5
-20=5x-5
-15=5x
x=-3
Answer:-
-3
Step-by-step explanation:
-x - 20 = 4x - 5 -> -20 = 5x - 5 -> -15 = 5x -> x = -3
Find the slope of the line.
Answer:
4
Step-by-step explanation:
What is the solution of this equation? Plz help asap!
Answer:
I believe the answer is = 6,-6
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[tex] - \frac{1}{2} {n}^{2} + 18 = 0 \\ [/tex]
Subtract sides 18
[tex] - \frac{1}{2} {n}^{2} + 18 - 18 = - 18 \\ [/tex]
[tex] - \frac{1}{2} {n}^{2} = - 18 \\ [/tex]
Negatives simplifies
[tex] \frac{1}{2} {n}^{2} = 18 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{1}{2} {n}^{2} = 2 \times 18 \\ [/tex]
[tex] {n}^{2} = 36[/tex]
Take √ of the sides
[tex] \sqrt{ {n}^{2} } = \sqrt{36} \\ [/tex]
[tex] |n| = 6[/tex]
[tex]n = ± \: 6[/tex]
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I really need help on this question please it’s solve for x.round to the nearest hundredth if necessary.
Answer:
39.19
Step-by-step explanation:
sin(29°)=(19/x)
x= 19/sin(29°)
/= over
i used sin because it show opposite and hypoteneuse. which formula is SOH=sin opposite/ hypoteneuse
Which of the following is in the solution set of the inequality x + 13 < 9?
A 22
B. -22
C. 4
D. -4
Answer: B.x = -22
x + 13 < 9
⇔ x < 9 - 13
⇔ x < -4
=> x ∈ {-∞; -4}
=> x = -22
Step-by-step explanation:
Answer:
Step-by-step explanation:
x + 13 < 9
x < - 4
(B). - 22
Just answer correctly to get brainleist and 10 pts! :)
Answer:
a.
Step-by-step explanation:
(2, 10) and (4, 10) have the same y value so it's not a function etc. etc.
Answer:
D. The relation represents y as a function of x, because each value of x is associated with a single value of y
Step-by-step explanation:
As long as no one x-value has two solutions, it can be considered a function. The x-values are {0, 2, 4, 6, 8}. Since there isn't any repetition, this can be considered as a function. The fact that 10 is repeated in the y-values doesn't affect that it is a function.
Find the Value of x if the perimeter of the figure below is equal to it's area.
Answer:
2x + 5 = 3
Step-by-step explanation:
2x + 5 = x = -2 + 5
x = 3
Hat is \text{P(heads})P(heads)start text, P, left parenthesis, h, e, a, d, s, end text, right parenthesis? If necessary, round your answer to 222 decimal places.
Question:
You flip a fair coin ; What is P(heads)? If necessary, round your answer to 2 decimal places
Answer:
[tex]P(Head) =0.50[/tex]
Step-by-step explanation:
Given:
A fair coin
Required
Determine [tex]P(Head)[/tex]
A coin has two faces (Head (1) and Tail (1) )
i.e. 1 head and 1 tail
Both of which have equal probability, which is calculated as follows:
[tex]P(Head) = P(Tail) = \frac{1}{1 + 1}[/tex]
[tex]P(Head) = P(Tail) = \frac{1}{2}[/tex]
[tex]P(Head) = P(Tail) = 0.5[/tex]
Hence:
[tex]P(Head) =0.50[/tex]
Answer: Its 0.50
Step-by-step explanation:
Find the value of x.
Question 16 options:
A)
55°
B)
141°
C)
51°
D)
39°
Answer:
B is the answer
Step-by-step explanation:
Solve for x(one solution,no solution,or infinite solutions) -2(3x+-1)=-6x-1
Answer: 0= -3 No solution
Step-by-step explanation:
Answer:
x = 1/12
you can find answer in algebra solver
Help please I don’t know the answer to this
Answer:
ima just say 10 and 6 my G I'm kinda dumb but u could try it
Answer:
5pt=10cups
24qt=6gal
Step-by-step explanation:
5*2=10
24/4=6
I need this answer ASAP!!!!!!
What is 1 + 2?
Answer:
3
Step-by-step explanation:
Trudy bought a $20 prepaid long distance phone card. for every minute that she talks, $0.25 is deducted from her card. The function f(m)=20-0.25m represents the amount of money f(m) she has left after talking m minutes.FInd the zero and explain what it means in the context of the situation.
Answer:
Step-by-step explanation:
Given the function f(m)=20-0.25m to represent the amount of money f(m) she has left after talking m minutes, the zero of the equation can be gotten by setting f(m) to 0
f(m)=20-0.25m
0 =20-0.25m
-20 = -0.25m
m = -20/-0.25
m = 80
Hence Trudy will have talked for 80minutes if she has no money left
Simba he's looking for a financial institution to give him a loan for a new house. Which of these institutions would be LEAST likely to provide the service.
Hi, you've asked an incomplete question that lacks the options. However, I answered from a general perspective.
Explanation:
Remember, the term financial institution (FI) often refers to any institution that deals with monetary transactions like loans, investments, currency exchange, or deposits.
For example, most specialized financial institutions not under the housing sector may refuse to provide such loans to Simba; such as An Agricultural financial institution, An Industrial financial institution, etc.
Answer:
BROKERAGE FIRM
Step-by-step explanation:
What is the value of the expression 5y² + 4x when x = 2.5 and y = 3?
Answer:
55
Step-by-step explanation:
the value of the expression 5y² + 4x when x = 2.5 and y = 3 will be 55.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression 5y² + 4x
To calculate the value of expression at x = 2.5 and y = 3
Substitute the value of x and y in the expression:
=> 5y² + 4x
=> 5* 9 + 4 * 2.5
=> 45 + 10
=> 55
therefore, 55 is the value of the expression 5y² + 4x when x = 2.5 and y = 3.
Learn more about expression here:
https://brainly.com/question/23246712
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in an examination 60% exam in failed in maths 55% failed in English and 25 failed in both subjects if none of the exam in past in the both subject find the number of exam in who passed in mathematics only
Answer:
60% x 25
55 % x 25
10 in english
25 is total and rest will be math
so 25-10 = 15
15 students failed math
