The polynomial function is [tex]g(x) = x^7 - 18x^6 + 68x^5 - 118x^4 + 68x^3 - 21x^2 - 98x + 49[/tex]
What is meant by zeroes of a polynomial?
Zeroes of a polynomial function are the values of the variable for which the function evaluates to zero.
To construct a polynomial function with the given zeros and their corresponding multiplicities, we can use the factored form of a polynomial. Each zero will have a corresponding factor raised to its multiplicity.
Given zeros and their multiplicities:
Zeros: 7 (multiplicity 3), -3 (multiplicity 1), -1 (multiplicity 3)
To construct the polynomial function, we start with the factored form:
[tex]g(x) = (x - a)(x - b)(x - c)...(x - n)[/tex]
where a, b, c, ..., n are the zeros of the polynomial.
Using the given zeros and multiplicities, we can write the polynomial function as:
[tex]g(x) = (x - 7)^3 * (x + 3) * (x + 1)^3[/tex]
Explanation:
- The factor (x - 7) appears three times because the zero 7 has a multiplicity of 3.
- The factor (x + 3) appears once because the zero -3 has a multiplicity of 1.
- The factor (x + 1) appears three times because the zero -1 has a multiplicity of 3.
To expand the polynomial function [tex]g(x) = (x - 7)^3 * (x + 3) * (x + 1)^3[/tex] , we can use the distributive property and perform the necessary multiplication. Let's expand it step by step:
[tex]g(x) = (x - 7)^3 * (x + 3) * (x + 1)^3[/tex]
Expanding the first factor:
[tex]= (x - 7)(x - 7)(x - 7) * (x + 3) * (x + 1)^3[/tex]
Using the distributive property:
[tex]= (x^2 - 14x + 49)(x - 7) * (x + 3) * (x + 1)^3[/tex]
Expanding the second factor:
[tex]= (x^2 - 14x + 49)(x^2 - 4x - 21) * (x + 1)^3[/tex]
Using the distributive property again:
= [tex](x^4 - 18x^3 + 83x^2 - 98x + 49)(x + 1)^3[/tex]
Expanding the third factor:
[tex]= (x^4 - 18x^3 + 83x^2 - 98x + 49)(x^3 + 3x^2 + 3x + 1)[/tex]
Now, we can perform the multiplication of each term in the first polynomial by each term in the second polynomial, resulting in a polynomial of degree 7.
Therefore, the polynomial function with the given zeroes is [tex]g(x) = x^7 - 18x^6 + 68x^5 - 118x^4 + 68x^3 - 21x^2 - 98x + 49[/tex]
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Plsss helppp ASAP
Will mark brainleist
Answer:
B
Step-by-step explanation:
The average rate of change in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a , b ] = [ 15, 35 ]
and f(b) = f(35) = 400 ← from graph
f(a) = f(15) = 200 ← from graph
Then average rate of change is
[tex]\frac{400-200}{35-15}[/tex] = [tex]\frac{200}{20}[/tex] = 10 m/ s → B
Which of the following sets of numbers could not represent the three sides of a right
triangle?
Answer:
{48, 64, 81}
Step-by-step explanation:
What is the greatest number of obtuse angles that a triangle can have?
Answer:
1
Step-by-step explanation:
Right answer gets brainlist !!
Robert takes out a loan for $7200 at a 4.3% rate for 2 years. What is the loan future value?
Answer: 7,833
Step-by-step explanation:
Given v = 4i - j, and w = 3i + 2j, find the angle between v and w. (Type your answer in degrees. Do not round until the final answer. Then round to the nearest tenth as necessary.)
Given [tex]v=4i-j[/tex], and [tex]w=3i+2j\\[/tex], the angle between v and w is 47.7°.
To find the angle between vectors v and w, we can use the dot product formula:
v · w = |v| |w| cos(θ)
where v · w represents the dot product of v and w, |v| and |w| represent the magnitudes of vectors v and w, and θ represents the angle between the vectors.
First, let's calculate the magnitudes of vectors v and w:
|v| = √(4² + (-1)²) = √(16 + 1) = √17
|w| = √(3² + 2²) = √(9 + 4) = √13
Next, let's calculate the dot product of v and w:
v · w = (4)(3) + (-1)(2) = 12 - 2 = 10
Now, we can substitute the values into the dot product formula to find the angle θ:
10 = (√17)(√13) cos(θ)
cos(θ) = 10 / (√17)(√13)
cos(θ) = 10 / (√(17 * 13))
cos(θ) = 10 / (√221)
θ = cos⁻¹ (0.6717)
θ = 47.7°.
Therefore, the angle between vectors v and w is approximately 47.7° .
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An asteroid is heading for the planet Zorgon (diameter of 2600 miles). When it hits, it will create a blast zone that extends 150 miles in all directions from the point of impact. What is the probability that Astronaut Joe, who is on Zorgon currently, will be affected by this impact?
The probability that Astronaut Joe, who is currently on Zorgon, will be affected by the impact is 0.667%.
To determine the probability that Astronaut Joe will be affected by the impact of the asteroid on planet Zorgon, we need to consider the area of the blast zone in relation to the total area of the planet.
An asteroid is heading for the planet Zorgon with a diameter of 2600 miles. When it hits, it will create a blast zone that extends 150 miles in all directions from the point of impact.
What is the probability that Astronaut Joe, who is currently on Zorgon, will be affected by this impact?
The total surface area of Zorgon is given by:2 * 3.14 * (1,300 miles)2 = 10.6 million sq Miles
The blast zone covers an area of:3.14 * (150 miles)2 = 70,685 sq Miles
To calculate the probability that Astronaut Joe will be affected by the impact, we divide the area of the blast zone by the total surface area of the planet.
That is,70,685 / 10.6 million = 0.00667 = 0.667%.
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dba algebra 2 module 2 flvs what's on it
Answer:
Uh i dont really get it
Step-by-step explanation:
best of luck though
On their first dive researchers Explorer part of the ocean that is 60 ft below sea level is that can be responded by the integer on their first dive researchers Explorer part of the ocean that is 60 ft below sea level is that can be responded by the integer 60 on their second dive research to explore a deeper depth
Complete question :
On their first dive, researchers explore a part of the ocean floor that is 60 feet below sea level. This depth can be represented by the integer -60. On their second dive, researchers explore a deeper depth. Write an inequality that represents the possible depth, d, of the researchers' second dive.
Answer:
d < - 60
Step-by-step explanation:
Depth explored during first dive = 60 feets below sea level = - 60 feets
The depth, d explored during second dive is deeper Than that explored during first dive
The inequality representing depth on second,
This means they the depth exceeds 60 feets below sea level. And hence. Deeper than - 60
Therefore, the depth will be values less Than - 60
Hence, d < - 60
What is the answer for 3743x453
Answer:
1695579
Step-by-step explanation:
i get alot of these please help
Answer:
18 is 3 more than 9- false
18 is 3 times as much as 6 - true
9 is 3 times as much as 27- false
9 is 3 more than 6 - true
46 people are going to the beach. Nine people can ride in each van. How many vans are needed?
Answer:
6
Step-by-step explanation:
No. of people going to beach = 46 .
Using Unitary Method ,
9 people can go in one van .
1 person can go in 1/9
46 people can go in 1/9 * 46 = 5.1
Since vans can't be in fraction , 1 extra van for 1 person is need that is for 46th person .
So total number of vans = 5 + 1 = 6
A culture started with 1,000 bacteria. After 7 hours, it grew to 1.200 bacteria. Predict how many bacteria will be present after 14 hours. Round your answer to the nearest whole number.
P= Ae^kt
Answer:
8
Step-by-step explanation:
Because i wanted extra points.
the area of a rhombus is 24 square inches. What is the are of a similar rhombus that is 7 times as big?
Answer:
324
...................
Find slops ;
3y=9x+18
To find the slope of the line, we need to put the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Divide both sides of the equation by 3 to get y by itself on one side of the equation.
3y = 9x + 18
y = 3x + 6
Step 2: Compare the equation to the slope-intercept form y = mx + b, and we can see that the slope is 3.
Therefore, the slope of the line is 3.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
Water treatment plant receives a 5% polymer solution. Calculate how much polymer should be mixed with water to produce 350 gallons of a 0.5% solution.
Answer:
Polymer to be mixed with water to produce 350 gallons of a 0.5% solution is 1.75 gallons.
Step-by-step explanation:
Solution weight-age 100% = 350 gallons
Polymer weight-age = 0.5 % = ?
Water weight-age = 99.5 % = ?
100 =99.5 w + 0.5 p
350 = ? + ?
Using ratios
100 350
0.5 p
Applying the cross product rule
p = 350 *0.5/100= 1.75 gallons
Polymer to be mixed with water to produce 350 gallons of a 0.5% solution is 1.75 gallons
Using ratios
100 350
99.5 w
Applying the cross product rule
w = 350*99.5 /100= 348.25 gallons
Water to be mixed with water to produce 350 gallons of a 0.5% solution is 348.25 gallons
Drag the operations signs to make the number sentence true. Use each operation sign once. +–×÷ 4 (3 2) 6 1 = 14
Answer: its 4x(3+2)-6÷ 1=14
Step-by-step explanation: in the picture
I need help with this question can you guys help me
Answer:
$18.5
Step-by-step explanation:
You just add up all the costs and divide them by two and then you would get your answer
PLEASE ANSWER ASAP
At a carry-out burger restaurant, an order of 4 burgers, 2 orders of French fries and 3 fountain drinks cost $32.25. A second order of 6
burgers, 3 orders of French fries, and 6 fountain drinks costs $51.15. If three burgers and two fountain drink cost $13.05 more than two
orders of French fries, what is the cost of each
Answer:
hmmm I think u need to talk to ur teacher
The width of a table is 2 feet less than the length. The area is 20 square feet. Find the dimensions. Show and explain all work using mathematical concepts in this module. (use quadratic equation)
Let's denote the length of the table as "x" feet. According to the problem, the width is 2 feet less than the length, so the width can be represented as "x - 2" feet. The area of the table is given as 20 square feet.
The formula for the area of a rectangle is length times width. Therefore, we can set up the equation:
Length × Width = Area
x(x - 2) = 20
Expanding the equation, we get:
x^2 - 2x = 20
Rearranging the equation in quadratic form:
x^2 - 2x - 20 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -2, and c = -20. Plugging these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)^2 - 4(1)(-20))) / (2(1))
Simplifying further:
x = (2 ± √(4 + 80)) / 2
x = (2 ± √84) / 2
x = (2 ± 2√21) / 2
Simplifying the expression inside the square root:
x = (1 ± √21)
So the possible values for x are 1 + √21 and 1 - √21.
Since the length cannot be negative, we take the positive value:
x = 1 + √21
Now we can find the width by substituting this value of x into the expression for width:
Width = x - 2
Width = (1 + √21) - 2
Width = -1 + √21
Therefore, the dimensions of the table are approximately 1 + √21 feet for the length and -1 + √21 feet for the width.
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The number of dandelions at the beginning of the summer was 2,000. The population of dandelions is expected to grow at a rate of 2.5% each day. How many dandelions should we expect after 30 days?
Answer:
3500 dandelions
Step-by-step explanation:
To start you must multiply the number of dandelions by the growth rate to find the number of dandelions grown each day:
2,000 * 0.025 = 50
Then you multiply the number of dandelions by 30 for each day:
50 * 30= 1500
Lastly, you add the dandelions grown in 30 days to the original for your answer.
Portfolio Benchmark 22.00% 17.88% 16.00% 21.25% -7.50% -9.63% -2.30% -3.88% 8.63% 3.25% 9.15% 9.63% 11.21% 15.25% 6.25% 5.75% -37.00% -42.00% 15.00% 13.75% An analyst is trying to understand the variation of portfolio returns shown in the left column by analyzing the variation of benchmark returns in the right column. Here, the analyst uses the benchmark returns as the explanatory variable, i.e., the x-variable, to explain the variation of portfolio returns, the y-variable. The analyst performs a regression analysis between the x and y variables. The y-intercept and slope coefficient of the x-variable are 0.013 and .892, respectively. If the benchmark return is 14%, the regression model will estimate the portfolio return closest to O 0% O 89.2% 1.3% O 13.79%
The regression model estimates the portfolio return closest to 13.79% when the benchmark return is 14%.
The analyst performed a regression analysis using the benchmark returns as the explanatory variable and the portfolio returns as the dependent variable. The y-intercept of the regression line is 0.013, indicating that when the benchmark return is zero, the estimated portfolio return is 0.013%. The slope coefficient of the benchmark returns is 0.892, meaning that for every 1% increase in the benchmark return, the estimated portfolio return increases by 0.892%.
To estimate the portfolio return when the benchmark return is 14%, we plug the value of 14 into the regression model. The estimated portfolio return is calculated as follows: 0.013 + 0.892 * 14 = 13.79%.
Therefore, based on the regression analysis, the model estimates that the portfolio return would be closest to 13.79% when the benchmark return is 14%.
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Need help due in 30 mins Find the area of each. Round to the nearest tenth. Do not include units in your answer (ie. ft, in, km, etc)(triangle-FR)
Your answer
Answer:
1)
Triangle formula:
A = 1/2bh
A = 1/2(3)(5.9)
A = 8.85
2)
Parallelogram Area:
A = bh
A = (8.9)(6)
A = 53.4
The sum of two numbers is 18 and their difference is 6.
What are the two numbers?
Larger number
Smaller number
Answer:
Large number=12
Smaller number=6
Step-by-step explanation:
Let the two numbers be x and y
x+y=18
x-y=6
Solve for the values of x and y.
Answer:
x = 20
y = 7.2
Step-by-step explanation:
12/x = 9/15
9x = 180
x = 20
12/x= y/12
12/20 = y/12
144 = 20y
y = 7.2
y = 20
Margaret's garden is 36 feet long and has a perimeter of feet. She is wanting to plant flowers along the diagonal of the garden. How long in the diagonal of her
Answer: Where is the rest of the question?
Step-by-step explanation:
An arithmetic sequence has first term (a) and the common difference (d). The sum of the first 25 terms is 15 times the sum of the first 4 terms. Find (a)
Answer:
a = 12.
Step-by-step explanation:
Sum of n terms = n/2[2a + d(n-1)]
For 25 terms
S25 = 12.5(2a + 24d)
S25 = 25a + 300d
For 4 terms
S4 = 2(2a + 3d)
So:
S25 = 15*2(2a + 3d)
S25 = 60a + 90d
25a + 300d = 60a + 90d
35a = 210d
a = 6d
Take a to be 12 and d to be 2:
25th term = 12.5(2*12 + 24 * 2) = 900
4th term = 2(24 + 6) = 60
900 = 15 * 60 so a = 12.
Find the profit function if cost and revenue are given by C(x) = 150 +5.8x and R(x) = 9x -0.01x?
The profit function is; P(x) = -0.01·x² + 3.2·x + 150
What is a profit?
Profit is the amount gained following a business transaction, which is the difference between the amount received as payment for doing a business transaction, within a specified period, known as the revenue and the amount amount spent or invested in doing the business, including the fixed and variable expenses, which is the cost of the business.
Therefore; Profit = Revenue - CostThe cost and the revenue functions, obtained from a similar question on the internet are;
The cost function is; C(x) = 150 + 5.8·x
The profit function is; R(x) = 9·x - 0.01·x²
The profit function, P(x), is therefore; P(x) = 9·x - 0.01·x² - (150 + 5.8·x) = -0.01·x² + 3.2·x + 150
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b) Abigail (A) and Balan (B) want to share a pizza of size 1. Suppose both agents have the same utility function u(x) = 2 for pizza, Abigail discounts with 8A = 1/2 and Balan discounts with 88 1/2. Abi- gail moves first. Calculate the Rubinstein solution of the bargaining problem. c) Why does Abigail get a larger share of the pizza?.
Solution: Given, Abigail (A) and Balan (B) want to share a pizza of size
1. Both agents have the same utility function u(x) = 2 for pizza, Abigail discounts with 8A = 1/2. Balan discounts with 88 1/2 Abigail moves first.
We have to calculate the Rubinstein solution of the bargaining problem. Bargaining Solution Using Rubinstein's alternating offers model, the bargaining solution is:
Take x as the size of the pizza that Abigail gets.
Hence, Balan gets 1 - x.
The possible utility that they get are:
Abigail: 2x(1/2) + 0(1/2) = x
Balan: 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x The minimum utility that they both need to be satisfied is:
minimum value = 2 x 177/2 = 177
The bargaining range is [0,1], thus there are infinite pairs that satisfy the minimum utility requirement. However, Rubinstein assumes that the final solution should be somewhere between both parties' ideal points, so we can restrict the bargaining range to [1/2, 1]. Abigail gets x and Balan gets 1 - x. Now, we have to see what happens if Balan rejects this offer.
When Balan rejects, the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range,
Abigail's ideal point is 2x(1/2) + 0(1/2) = x and
Balan's ideal point is 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x.
The bargaining range is again restricted to [1/2, 1]. When Balan rejects, the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range, Abigail's ideal point is 2x(1/2) + 0(1/2) = x and Balan's ideal point is 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x.The bargaining range is again restricted to [1/2, x) and (x, 1].
Now, if Abigail rejects, then the bargaining range is (0, x) for Abigail and [x, 1] for Balan. In this range, Abigail's ideal point is 2x(88 1/2) + 0(11 1/2) = 177x and Balan's ideal point is 2(1 - x)(1/2) + 0(1/2) = 1 - x. The bargaining range is again restricted to (1/2, x) and (x, 1/2 + 1/176). In the next step, if Balan rejects, then the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range, Abigail's ideal point is 2x(1/2) + 0(1/2) = x and Balan's ideal point is 2(1 - x)(1/2) + 0(1/2) = 1 - x. The bargaining range is again restricted to [1/2, x) and (x, 1/2 + 1/176).
Repeating the steps,
the solution is: x = 2/3, 177 - 177x = 59.
After calculating the Rubinstein solution of the bargaining problem, we can see that Abigail gets 2/3 of the pizza and Balan gets 1/3 of the pizza. There are two reasons why Abigail gets a larger share of the pizza: Abigail moves first, so she has an advantage because she can propose a deal that is more favorable to her. This is why the bargaining range is initially restricted to [1/2, 1]. Abigail has a lower discount rate than Balan, so she is willing to wait longer for a deal. This means that Abigail can drive a harder bargain because she has a higher reservation utility.
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Guys i need help!!!!
Answer:
1/6
Step-by-step explanation:
1 out of the 6 cards is 4
81.3 x 47.5 = i am lost............
Answer:
3861.75
Step-by-step explanation:
i hope its the good answer