The polynomial function of degree 7 with the given zeros and multiplicities is: f(x) = x³(x + 2)³(x - 2)
To find a polynomial function with the specified zeros and multiplicities, we can construct it using the factors that correspond to each zero and multiplicity.
Since -2 has a multiplicity of 3, it means it appears three times as a zero. Similarly, 0 has a multiplicity of 3, and 2 has a multiplicity of 1.
A polynomial function with these zeros and multiplicities can be written as:
f(x) = (x + 2)³ × x³ × (x - 2)
To make it a polynomial of degree 7, we can multiply it by an additional linear factor:
f(x) = (x + 2)³ × x³ × (x - 2) × (x - r)
Where "r" is a constant representing the last factor. This factor ensures the degree of the polynomial is 7.
Now, we need to find the value of "r" to complete the polynomial. Since we already have three factors with multiplicity 3 and one factor with multiplicity 1, the polynomial has already reached its degree of 7.
Therefore, we don't need to include the "x - r" factor, and the final polynomial is:
f(x) = (x + 2)³ × x³ × (x - 2)
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The polynomial function of degree 7 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 2 as a zero of multiplicity 1 is f(x) = x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2.
To find a polynomial function of degree 7 with the given zeros and multiplicities, we can start by constructing the factors of the polynomial.
Since -2 is a zero of multiplicity 3, we have the factor (x + 2)^3. Similarly, since 0 is a zero of multiplicity 3, we have the factor x^3. Lastly, since 2 is a zero of multiplicity 1, we have the factor (x - 2).
Multiplying these factors together, we obtain:
(x + 2)^3 * x^3 * (x - 2)
Expanding this expression, we get:
(x^3 + 6x^2 + 12x + 8) * x^3 * (x - 2)
To simplify further, we multiply the terms:
(x^6 + 6x^5 + 12x^4 + 8x^3) * (x - 2)
Expanding again, we obtain:
x^7 - 2x^6 + 6x^6 - 12x^5 + 12x^4 - 24x^3 + 8x^3 - 16x^2
Combining like terms, we get:
x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2
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A house was valued at $540,000 last year. The house has now appreciated and increased in
value by 4%. What is the house worth now?
Answer:
The house worth now: $540,000*(1+4%)= $561,600
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.
Answer:
See explanation for matching pairs
Step-by-step explanation:
Equations
(1)
[tex]x - y = 25[/tex]
[tex]2x + 3y = 180[/tex]
(2)
[tex]2x - 3y = -5[/tex]
[tex]11x + y = 550[/tex]
(3)
[tex]x - y = 19[/tex]
[tex]-12x + y = 168[/tex]
Solutions
[tex](-17,-36)[/tex]
[tex](47, 33)[/tex]
[tex](51, 26)[/tex]
Required
Match equations with solutions
(1) [tex]x - y = 25[/tex] and [tex]2x + 3y = 180[/tex]
Make x the subject in: [tex]x - y = 25[/tex]
[tex]x = 25 + y[/tex]
Substitute [tex]x = 25 + y[/tex] in [tex]2x + 3y = 180[/tex]
[tex]2(25 + y) + 3y = 180[/tex]
[tex]50 + 2y + 3y = 180[/tex]
[tex]50 + 5y = 180[/tex]
Collect like terms
[tex]5y = 180-50[/tex]
[tex]5y = 130[/tex]
Solve for y
[tex]y =26[/tex]
Recall that: [tex]x = 25 + y[/tex]
[tex]x = 25 + 26[/tex]
[tex]x = 51[/tex]
So:
[tex](x,y) = (51,26)[/tex]
(2) [tex]2x - 3y = -5[/tex] and [tex]11x + y = 550[/tex]
Make y the subject in [tex]11x + y = 550[/tex]
[tex]y = 550 - 11x[/tex]
Substitute [tex]y = 550 - 11x[/tex] in [tex]2x - 3y = -5[/tex]
[tex]2x - 3(550 - 11x) = -5[/tex]
[tex]2x - 1650 + 33x = -5[/tex]
Collect like terms
[tex]2x + 33x = -5+1650[/tex]
[tex]35x = 1645[/tex]
Solve for x
[tex]x = 47[/tex]
Solve for y in [tex]y = 550 - 11x[/tex]
[tex]y = 550 - 11 * 47[/tex]
[tex]y = 550 - 517[/tex]
[tex]y = 33[/tex]
So:
[tex](x,y) = (47,33)[/tex]
(3)
[tex]x - y = 19[/tex] and [tex]-12x + y = 168[/tex]
Make y the subject in [tex]-12x + y = 168[/tex]
[tex]y = 168 + 12x[/tex]
Substitute [tex]y = 168 + 12x[/tex] in [tex]x - y = 19[/tex]
[tex]x - 168 - 12x = 19[/tex]
Collect like terms
[tex]x -12x = 168 + 19[/tex]
[tex]-11x = 187[/tex]
Solve for x
[tex]x = -17[/tex]
Solve for y in [tex]y = 168 + 12x[/tex]
[tex]y =168-12 *17[/tex]
[tex]y =-36[/tex]
So:
[tex](x,y) = (-17,-36)[/tex]
Kiera and her brother, Desmond, are making trail mix to bring on their family's camping trip. Kiera uses 2 cups of raisins and 5 cups of nuts in her trail mix. Desmond uses 3 cups of raisins and 6 cups of nuts in his trail mix. Whose trail mix has a lower ratio of raisins to nuts?
Answer:
Kiera has a lower ratio of raisins to nuts. (2:5)
Step-by-step explanation:
To find this, you would have to make the number of nuts the same in each to accurately compare them.
It starts with Kiera's 2 cups of raisins and 5 cups of nuts. So it will be 2:5 (raisins first then nuts.)
Desmond will be 3:6 (have to make it the same order, raisins and then nuts.)
So I multiplied both the 2 and the 5 in 2:5 by 6 first.
Then multiply both the 3 and 6 in 3:6 by 5 to make the number of nuts the same in both.
So Kiera will have 12:30 and Desmond will have 15:30.
Then you can conclude that Kiera has the lower ratio.
The circumference of a circle is approximately 39.25 mm. What is the length of the diameter?
Answer:
12.5 millimeters (mm).Step-by-step explanation:
Explain/define:
CIRCUMFERENCE: THE DISTANCE AROUND A CIRCLE.
DIAMETER: THE LENGTH OF A STRAIGHT LINE THROUGH THE CENTER OF A CIRCLE.
Mathematics: Formula
[tex]d=c/3.14[/tex]
[tex]d-diameter[/tex]
[tex]c-circumference[/tex]
Mathematics: Solve
To find the length of the diameter from the circumference, divide the circumference by pi. The quotient is the diameter.
3.14 is often used for pi.
[tex]39.25/3.14=12.5.[/tex]
Conclude:
Therefore, the length of the diameter of the circle is 12.5 millimeters (mm).
isaiah draws three different diagrams to represent the samples space of picking a marble from the bag and spinning the spinner . NEED HELP NOWWW YOU WILL GET BRAINLIEST FASTTT
Answer:
Step by step explanation:
Using the tables as experimental data, determine whether it is more likely for a new food establishment to succeed and earn up to $25,000, or whether it is more likely for a new financial establishment to succeed and earn profits in either the $25,000-50,000 range or the $50,000-75,000 range, and how much more likely the one situation is than the other. Express all probabilities as percentages to two decimal places, and express differences by number of percentage points (for example, 23% is 5 percentage points greater than 18%). a. The situation involving the financial establishment has a probability 11.14 percentage points higher than the situation involving the food establishment. b. The situation involving the financial establishment has a probability 12.03 percentage points higher than the situation involving the food establishment. c. The situation involving the food establishment has a probability 2.08 percentage points higher than the situation involving the financial establishment. d. The situation involving the food establishment has a probability 2.36 percentage points higher than the situation involving the financial establishment.
The situation involving the food establishment has a probability of "2.08 % " points higher than the situation involving the financial establishment
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
The question is incomplete, as the required table which is not given.
we have the following parameters:
The probability that the establishment earns up to $25k = 10.59%
The probability that the establishment earns between $25k - $50k or $50k - $75k = 8.56%
Using the above values, the difference in the probabilities are;
d = 10.59% - 8.56
d = 2.03%
Hence, the true statement about the probability is option (d)
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p l e a s e h e l p
(Only spaced it cus I needed 20 characters, danke)
Answer:
y = 63
Step-by-step explanation:
A straight line is equal to 180 degrees.
180 = 2y - 18 + y + 9
180 = 3y -9
189 = 3y
189/3
y = 63
Answer:
63
Step-by-step explanation:
2y-18+y+9=180 degrees
3y-9=180 degrees
3y=189 degrees
y=63 degrees
Test question........................
You Have Passed Thy Test!!! BADAAAA (\•o•/)
15 feet tree cast a shadow that is 15 feet long. What is the distance from the top of the tree to the tip of its shadow?
Answer: Hi. The height of the tree is 27 ft
Step-by-step explanation:
Answer link- https://socratic.org/answers/601885
find the value of x
16
14
10
9
Answer:
x = 9
Step-by-step explanation:
create a ratio between the triangles:
x/6 = 12/8; cross multiply
72 = 8x; divide 8 on both sides
x = 9
Find the area of each parallelogram.
Answer:
1 is 45yd²
2 is 21in²
3 is 63in²
4 is 20ft²
5 is 48yd²
Find the length of TU.
Answer:
0.5 (8x+15)?
Step-by-step explanation:
i really hope this helps-
not the greatest at math ._.
Step-by-step explanation:
I hope ill help you.
TU(4x+7.5)
There is a bag with only milk and dark chocolates. The probability of randomly choosing a dark chocolate is 3 8 . There are 21 dark chocolates in the bag and each is equally likely to be chosen. Work out how many milk chocolates there must be.
Answer:
Number of milk chocolate in beg = 56
Step-by-step explanation:
Given:
Probability of randomly choosing a dark chocolate = 3/8
Number of dark chocolate = 21
Find:
Number of milk chocolate in beg
Computation:
Number of milk chocolate in beg = Number of dark chocolate / Probability of randomly choosing a dark chocolate
Number of milk chocolate in beg = 21 / [3/8]
Number of milk chocolate in beg = 21[8/3]
Number of milk chocolate in beg = 7[8]
Number of milk chocolate in beg = 56
30) Find the sine, cosine, and tangent of
Answer:
sin < C = c/a
cos < C = b/a
tan < C = c/b
PLEASE HELP!!
ILL GIVE MORE POINTS TO THE FASTEST ANSWER
PLEASE ANSWER THIS QUESTION IM BEGGING YOU !
Answer:
5/36
Step-by-step explanation:
There are 12 tiles
P( blue) = blue /total = 5/12
We put the first tile back so there are still 12 tiles in the bag
P(yellow) = yellow/total = 4/12 = 1/3
P( blue, yellow) = 5/12 * 1/3 = 5/36
When -3x + 6 − 3x − 24 + 2y is simplified, the result is
Answer:
- 6x - 18 + 2y
Step-by-step explanation:
- 3x + 6 - 3x - 24 + 2y
- 6x + 6 - 24 + 2y
- 6x - 18 + 2y
Answer:
-6x -18 + 2y
Step-by-step explanation:
1. Collect like terms:
-3x + -3x = -6x
-24 + 6 = -18
2. Rewrite expression:
-6x -18 +2y
Hope this helps, good luck! :D
A square picture is 8 inches on each side. It is scaled by 74%. What are the dimensions of the new picture
9514 1404 393
Answer:
5.92 inches on a side
Step-by-step explanation:
The new dimension is the original dimension multiplied by the scale factor.
(8 in)(74%) = 5.92 in
Victor wanted to know the height of a tree at his friend’s house. On Saturday morning, he measured the shadow of the tree along the ground to be 24 feet long. At the same time, he measured his own shadow to be 3 feet long. Victor is 6 feet tall. Find the height of the tree
Ratio remains same
Let that be x[tex]\\ \rm\rightarrowtail \dfrac{6}{3}=\dfrac{x}{24}[/tex]
[tex]\\ \rm\rightarrowtail 2=x/24[/tex]
[tex]\\ \rm\rightarrowtail x=48[/tex]
The question and multiple choice answers are in the image. Hope you can help!
Answer:
answer b, SAS rule
Step-by-step explanation:
The ASA rule states that: If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.
Jacob cuts 4 meters of a ribbon into 3 pieces, the length of the first piece is 1.28 meters.The length of the second one is 1.65 meters. Work out the length of the 3rd piece.
Answer:
1.07meters
Step-by-step explanation:
Given data
Lenght of ribbon= 4 meters
Number of pieces= 3 pieces
Length of first piece= 1.28meters
Length of second piece= 1.65meters
Let the length of the third piece be x meters
Hence
1.28+1.65+x= 4
2.93+x=4
x= 4-2.93
x=1.07meters
Hence, the length of the third piece is 1.07meters
The polynomial x3 + 8 is equal to
Answer:
The polynomial x3 + 8 is equal to (x + 2)(x2 – 2x + 4)
Step-by-step explain
please help thank you
Answer:
50 ft²
Step-by-step explanation:
ΔABC ≅ ADC; therefore the area of ΔADC is 25 sq feet also
2(25) = 50 sq feet
Liam spent $4.76 on a salad bowl, and $3.81 on a cup of coffee. He paid using TWO ten dollar bills. What was Liam's change?
Answer:
11.43
Step-by-step explanation:
You can start this by adding the total cost of the salad and the coffee.
4.76 + 3.81 = 8.57
Then you have the paid amount of 20 bucks because there was two tens.
20 - 8.57 = 11.43.
pls help me wit this asap
Answer:
not sure but I think the answers c
A geometric sequence starts with 12,.
...,27,..., 60.75,...
where 12 is the first term, 27 is the third term and 60.75 the fifth term.
Work out the common ratio of the sequence.
What’s the answer?
Answer:
b
Step-by-step explanation:
it's right cause I took the quix
HELP WILL GIVE BRAINLIEST SHOW WORK LOOK AT IMAGE
HELP PLSSSSSSSZzzzzzzzzzzzz
Answer:
w equal to 9z
or z equals to w/9
find distance between (0,6) and (8,0)
with process.......
Answer:
answer to the question is 10 units..
Answer:
10 units
Step-by-step explanation:
(0 , 6) = (x1 , y1)
(8 , 0) = (x2 , y2)
distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
=[tex]\sqrt{(8 - 0)^2 + (0 - 6)^2}[/tex]
=[tex]\sqrt{8^2 + (-6)^2}[/tex]
=[tex]\sqrt{64 + 36}[/tex]
=[tex]\sqrt{100}[/tex]
=10 units
2x²+5x-3=0
using completing the square method
Answer:
[tex]2 {x}^{2} + 5x - 3 = 0 \\ 2( {x}^{2} + \frac{5}{2} x - \frac{3}{2} ) = 0 \\ 2( {x}^{2} + \frac{5}{2} x + {( \frac{5}{4} )}^{2} ) - \frac{3}{2} - {( \frac{5}{4} )}^{2} ) = 0 \\ ( {(x + \frac{5}{4} )}^{2} = \frac{49}{16} \\ x + \frac{5}{4} = ± \frac{7}{4} \\ x = 0.5 \: \: and \: \: 3[/tex]
Answer:
x= [tex]\frac{1}{2}[/tex] or x= -3
Step-by-step explanation:
[tex]\boxed{x^{2} +kx=(x+\frac{k}{2})^{2} -(\frac{k}{2})^{2} }[/tex]
First ensure that the coefficient of x² is 1.
x² +[tex]\frac{5}{2}[/tex]x -[tex]\frac{3}{2}[/tex]= 0
[x +([tex]\frac{5}{2}[/tex] ÷2)]² -([tex]\frac{5}{2}[/tex] ÷2)² -[tex]\frac{3}{2}[/tex]= 0
(x +[tex]\frac{5}{4}[/tex])² -([tex]\frac{5}{4}[/tex])² -[tex]\frac{3}{2}[/tex]= 0
(x +[tex]\frac{5}{4}[/tex])²- [tex]\frac{25}{16}[/tex] -[tex]\frac{3}{2}[/tex]= 0
(x +[tex]\frac{5}{4}[/tex])² -[tex]\frac{49}{16}[/tex]= 0
(x +[tex]\frac{5}{4}[/tex])²= [tex]\frac{49}{16}[/tex]
x +[tex]\frac{5}{4}[/tex]= [tex]\sqrt{\frac{49}{16} }[/tex] (square root both sides)
x +[tex]\frac{5}{4}[/tex]= ±[tex]\frac{7}{4}[/tex]
x= -[tex]\frac{5}{4}[/tex] +[tex]\frac{7}{4}[/tex] or x= -[tex]\frac{5}{4}[/tex] -[tex]\frac{7}{4}[/tex]
x= [tex]\frac{1}{2}[/tex] or x= -3
