The two additional roots of a polynomial function P(x) = 0 with rational coefficients are -i and 7-8i.
We have to find the determine the two additional roots of a polynomial function P(x) = 0.
The answers to any given polynomial for which we must ascertain the value of the unknowable variable are known as the roots of polynomials. We can evaluate a polynomial's value to zero if we know its roots.
The given roots of P(x) = 0 is i and 7+8i.
So there conjugate are also the roots of P(x).
So the two additional roots of P(x) = 0 should be -i and 7-8i.
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The complete question is:
Find two additional roots of a polynomial function P(x) = 0 with rational coefficients given below where additional roots of P(x) = 0, i and 7+8i.
How do you factor this problem by grouping?
4x∧3-3x∧2-28x+21
Answer:
(x^2 - 7)(4x - 3)
Step-by-step explanation:
first, we split the expression by grouping the first two terms in parentheses and the last two terms in parentheses. this gives us:
[tex](4x^{3}-3x^{2})(-28x+21)[/tex]
next, we factor out the GCF of each group. this gives us:
[tex]x^{2}(4x-3)-7(4x-3)[/tex]
finally, all you have to do is take each factored-out term and put them together into a group/expression. the leftover expression from both groups is the same value, so you get:
[tex](x^{2}-7)(4x-3)[/tex]
hope this helped, good luck!
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 5 m/s.
h=2+5t-5t^2
The ball's height of (in meters) after seconds is given by the following. Find all values of for which the ball's height is 3 meters.
Answer: The height of the ball (in meters) after t seconds is given by the equation h = 2 + 5t - 5t^2. We can use this equation to find the values of t for which the ball's height is 3 meters.
We need to find the values of t that make h = 3, so we can substitute 3 for h in the equation:
3 = 2 + 5t - 5t^2
Then we can solve for t by moving all the terms to one side of the equation and factoring it:
-5t^2 + 5t - 1 = 0
And we can use the quadratic formula to find the solutions of this equation:
t = (5 +/- sqrt(5^2 - 4*(-1)(-1)))/ 2(-1)
t = (5 +/- sqrt(25 + 4))/ -2
t = (5 +/- sqrt(29))/ -2
The solutions of this equation are t = (5 +/- sqrt(29))/ -2
Since the time, t, is a real value the square root of 29 should be positive.
The values of t for which the ball's height is 3 meters are not real values, so there's no time when the ball's height is 3 meters.
Step-by-step explanation:
TEXT ANSWER
A dog weighs 45 pounds 12 ounces. How much does the dog weigh in kilograms?
If needed, round your answer to the nearest hundredth.
Conversion ratios:
• 1 lb = 16 oz
1 kg = 2.2 lb
Use the equation editor to show your work.
.
Answer:
20,45 kg,
Step-by-step explanation:
45 Lb * (1 kg / 2,2 Lb) + (12 Austrália * (1 kg / 35 ,2 Austrália)) = 20,45 kg
Um resposta é 20,45 kg.
which of the following is equivalent to the probability of less than 50% democrats in a sample size of
Probability of less than 50 % democrats for the example based on sample proportion is equal to 0.1562.
Sample size 'n' = 100
Registered voters 'p' = 55%
= 0.55
σ = √ p( 1- p )/ n
= √0.55( 0.45)/ 100
= 0.04975
Mean 'μ' = 55%
= 0.55
Probability of getting less than 50% democrats in a sample size of 100 voters
X = 0.5
Z = ( X - μ ) / σ
= ( 0.5 - 0.55) / 0.4975
= -1. 005
= -1.01
p-value pf -1.01 is equal to 0.156248
Therefore, the probability of getting 50% democrats for the given sample size id equal to 0.1562. The given example represents sample proportion.
The above question is incomplete , the complete question is :
In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?
Is this an example of a sample proportion OR a sample mean?
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fraction numerator dover denominator d x end fraction open square brackets in parentheses 4 x minus 7 close parentheses to the power of 4 open parentheses 7 x plus 8 close parentheses to the power of 5 close square brackets.
Differentiating the expression [tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex] with respect to x will be [tex]16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]
We are given with
[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]
Here we will be using the chain rule. According to the chain rule, we will first have to solve the parentheses as a variable. Then we will have to solve the expression within the parenthesis
First, we will differentiate [tex](4x-7)^4[/tex] keeping [tex](7x+8)^5[/tex] constant. Here we will first assume [tex](4x-7)[/tex] as one variable and differentiate using the formula d/dx[x^n] then we will differentiate 4x - 7 to get just 4. They would be multiplied by one another
Hence we get
[tex]4 X4(4x-7)^3(7x+8)^5[/tex]
[tex]16(4x-7)^3(7x+8)^5[/tex]
Now, we will keep [tex](4x-7)^4[/tex] constant and differentiate [tex](7x+8)^5[/tex] and adding it up we get
[tex]16(4x-7)^3(7x+8)^5 + 5X7(4x-7)^4(7x+8)^4[/tex]
[tex]= 16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]
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Complete Question
[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]
Jacob has a smart phone data plan that costs $25 per month that includes 5 GB of data, but will charge an extra $20 per GB over the included amount. How much would Jacob have to pay in a month where he used 4 GB over the limit? How much would Jacob have to pay in a month where he used went over by � x GB?
The amount Jacob has to pay in a month where he used x GB over the limit is y=25+20x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Jacob has a smart phone data plan that costs $25 per month that includes 5 GB of data, but will charge an extra $20 per GB over the included amount.
Amount Jacob has to pay in a month where he used 4 GB over the limit is
25+4×20
= $105
Amount Jacob has to pay in a month where he used x GB over the limit is
y=25+20x
Where, y is total amount of money
Hence, the amount Jacob has to pay in a month where he used x GB over the limit is y=25+20x.
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Answer:
Step-by-step explanation:
I don’t know just 5 point
Need to know answer to question !
the fourth one. I know it is correct, you may look it up on the desmos graphing calculator if you have suspicion it is not.
As of summer 2020, Voyager 1 is about 13.8 billion miles from Earth. Express this distance in AU,
using scientific notation, with two significant figures.
Answer:
1.478 x 10^2 AU
Step-by-step explanation:
To convert this distance to astronomical units (AU), we can use the fact that 1 AU is approximately equal to 93 million miles.
So, 13.8 billion miles is approximately:
13.8 billion miles / 93 million miles/AU = 147.8 AU
In scientific notation, this distance would be written as: 1.478 x 10^2 AU
Tyler's brother earns $14 per hour. The store offers him a 5% increase in wages per hour. After the raise, how much will tyler's brother make per hour?
After the raise, Tyler's brother will make $14 x 1.05 = $14.70 per hour.
Answer:
14 x 1.05 = 14.70
Step-by-step explanation:
Write this in exponential form
5^2 x 5^6
Select the 2 fractions that are equivalent to 1
Answer: Anything that has the same two numbers
Step-by-step explanation:
You don't have a picture, so I'm basing this off of what I know. A number over another number that is the same is equivalent to one.
What is the chance of exactly 1 of population members A , B, and C being in a sample of 100 , drawn randomly from a population of 100,000?
The chance of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000 is 0.0003%.
What is the chance of exactly 1 of population members A , B, and C being in a sample of 100 , drawn randomly from a population of 100,000?The probability of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000, is equal to the product of the probability of selecting each of the members and the probability of not selecting the other two members. Mathematically, this is expressed as: P(A, not B, not C) = (1/100,000) x (99,999/100,000) x (99,998/100,000) The probability of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000, is equal to 0.00299970 or approximately 0.003.This is an example of the binomial probability formula which is used to calculate the chance of a certain number of successes in a given number of trials. In this example, the population members A, B, and C represent the successes and the 100 randomly selected sample of 100,000 is the number of trials.To learn more about the binomial probability formula refer to:
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Two bicycle ramps each cover a horizontal distance of 8 feet. Once ramp has a 20° angle of elevation, and the other ramp has a 35° angle of elevation
How much taller is the second ramp than the first?
a project consists of 150 jobs. the expected completion time for each job is given in days. the project has three critical paths with two jobs in common, j and k. in order to finish the project one day early, the completion time should be reduced one day for
Reducing the completion average time for Jobs J and K by one day will shorten the overall project completion time by one day, allowing the project to finish one day early.
In order to finish the project one day early, the completion time for Jobs J and K should be reduced by one day. This is because these two jobs are part of the three critical paths of the project. By reducing the completion time for these two jobs by one day, the entire project will be completed one day early. This is because the critical paths are the paths that will determine the overall project completion time. By reducing the completion time for these two jobs, the overall project completion time will be shortened. This will allow the project to be finished one day earlier than expected.
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Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour. How long does it take the second airplane to overtake the first?
it would take 29.5 hours the second airplane to overtake the first.
What is Speed?speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.
Given, Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour.
So, in 3 hours first airplane will reach at;
Distance = speed *time
Distance = 590 * 3
Distance travels by first airplane in 3 hours will be = 1770 km
Since, Relative speed of given two planes = 650 - 590
Relative speed of given two planes = 60 km/hour
To reach 1770 km it would take = 1770/60 hours
Thus,
To reach 1770 km it would take = 29.5 hours
therefore, it would take 29.5 hours the second airplane to overtake the first.
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A triangle with a perimeter of 48 meters was created from a triangle with a perimeter of 3 meters using a scale factor. What is the scale factor?
A. 72:1
B. 16:1
C. 128:1
D. 144:1
The following data show the miles per gallon of small SUVs. Sketch a box plot. Calculate the smallest, Q1, median, Q3, largest value, range, and the interquartile range for a box plot. 19 22 22 26 23 24 21 16 16
Smallest = 16, median=22, largest value of data=26 , interquartile range=Q3-Q1=23-19=4.
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
We have the data 19 22 22 26 23 24 21 16 16, and we have to calculate smallest, Q1, median ...
First rearrange the data 16,16,19,21,22,22,23,24,26
So, Smallest = 16
Median of the data = middle number of data=22
Q1=middle of smallest and median=19
Q3=23
largest value of data=26
range= 19-26
interquartile range=Q3-Q1=23-19=4
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A store sells two sizes of fresh wreaths. An 18-inch wreath costs $15, and a 22-inch wreath costs $30. In one day, the number of 22-inch wreaths sold was FOUR more than TWICE the number of 18-inch wreaths, for a total of $645. How many of each were sold?
The number of 18-inch wreaths is 7, and
the number of 22-inch wreaths is 18.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given the cost of an 18-inch wreath = $15
cost of a 22-inch wreath = $30
let the number of 18-inch wreaths be x and the number of 22-inch wreaths is y,
the total cost of both wreaths = $645
cost of x 18-inch wreaths = $15x
cost of y 22-inch wreaths = $30y
equation is,
$15x + $30y = $654
and the number of 22-inch wreaths sold was four more than twice the number of 18-inch wreaths,
y = 4 + 2x
substitute the value of y in the equation
15x + 30y = 645
15x + 30(4 + 2x) = 645
15x + 60x = 645 - 120
75x = 525
x = 525/75
x = 7
and y = 4 + 2x
y = 4 + 2*7
y = 18
Hence store sells 18 22-inch wreaths and 7 18-inch wreaths.
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Which expression is equivalent to -63y² +27y?
O-9y(7y-3)
O9y(7y-3)
O-9y(7y + 3)
9y(7y + 3)
Answer:
[tex]9y\left(-7y+3\right)[/tex]Step-by-step explanation:
[tex]-63y^2+27y[/tex]
[tex]-63yy+27y[/tex]
[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]
[tex]9y\left(-7y+3\right)[/tex]
5. a random sample of 500 subjects measured their systolic blood pressure, and if they were a smoker or not. the goal is to evaluate if average systolic blood pressure differs by smoking status. summary sample statistics on the dataset follow:
There is a difference in average systolic blood pressure between smokers and non-smokers.
To evaluate if average systolic blood pressure differs by smoking status, we need to calculate the mean systolic blood pressure for both smokers and non-smokers. We can calculate the mean systolic blood pressure for smokers by taking the sum of systolic blood pressure values for all smokers in the sample, divided by the number of smokers in the sample. This formula can be written as:
Mean Systolic Blood Pressure for Smokers = (Sum of Systolic Blood Pressure Values for all Smokers) / (Number of Smokers)
Similarly, we can calculate the mean systolic blood pressure for non-smokers by taking the sum of systolic blood pressure values for all non-smokers in the sample, divided by the number of non-smokers in the sample. This formula can be written as:
Mean Systolic Blood Pressure for Non-Smokers = (Sum of Systolic Blood Pressure Values for all Non-Smokers) / (Number of Non-Smokers)
Once we have calculated the mean systolic blood pressure for both smokers and non-smokers, we can compare the two means to evaluate if there is a difference in average systolic blood pressure between smokers and non-smokers.
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Help me please!!!!!!!
Answer:
Yes, one gallon is enough
Step-by-step explanation:
16ft x 12ft = 192ft
If one gallon covers 250 square feet then she will have enough for another 58ft remaining
The figure below is a cone with the vertex at A and diameter BC. The cone is cut off along 15 cm B =B 6 cm 49 cm-a)find the base radius of the smaller cone.
b) find the volume of the frustum.
divide the lateral height in half, Height squared lateral height squared is subtracted from height squared, the answer from step three, and find its square root. The radius of the cone is the outcome.
What is the volume formula of frustum?The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume.The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.Radius = Diameter/ 2 applies when the diameter is known. Radius = Circumference/2 can be calculated after the circumference is known. The radius is calculated using the formula Radius = ((Area of the circle/π).To learn more about radius refer to:
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Therefore , the solution of the given problem of volume comes out to be 9,003.75π cubic cm.
What is the volume formula of frustum?The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume. The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.
Here,
Given :
=> 15 cm is the AB
=> radius = 49/2 = 24.5 cm
The radius of base is 24.5 cm
and
the volume of frustrum:
=> π(24.5)(24.5)(15)
=> 9,003.75π cubic cm
Therefore , the solution of the given problem of volume comes out to be
9,003.75π cubic cm.
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Given that f(x) = x3, which equation describes the graph of function g?
The equation which represents the graph function is g ( x ) = f ( x - 3 ) + 3
What is Equation of Graph of Functions?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = x³ be equation (1)
Now , the graph of the function f ( x ) is plotted with the exponent value meeting closely at ( 0 , 0 )
And , the function which describes the function g ( x ) is given by
g ( x ) = f ( x - 3 ) + 3
Hence , the function is g ( x ) = f ( x - 3 ) + 3
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The required value of exponential function for the given values of x are 1.43, 1 , 0.7.
What is exponential function?
Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.
According to question:We have,
f(x) = [tex](0.7)^{x}[/tex]
So, at x = -1
f(x) = (0.7)^-1
f(x) = 1.43
At x = 0
f(x) = (0.7)^0
f(x) = 1
At x = 1
f(x) = (0.7)^1
f(x) = (0.7)
Thus, required value of function are 1.43, 1, 0.7
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AE and CD intersect at point B. Find m
Answer:
m∠ABD = 111
Step-by-step explanation:
69 + x = 180
x = 111
Answer:
< ABD = 111 °
Step-by-step explanation:
< ABD and < DBE form a straight line which is 180 degrees
< ABD + < DBE = 180
< ABD + 69= 180
< ABD = 180 -69
< ABD = 111
please try on this and please give explanation
Answer: In the figure above, clearly the line L is perpendicular to x-axis and passing through the value 'c' on x- axis. So, the equation of a line perpendicular to x axis is x = c
standard form y-100=-50x-3
Answer:
Answer in attached photo.
Step-by-step explanation:
SolutionSolution in attached photo, do take note the standard form of an equation is:
y = mx + c,
where m is the gradient and c is the y-intercept.
Answer: (x– 8)2= 4(1)(y+ 3); vertex: (8, –3); opens upward
For the function f(x) given in the table, find the average rate of change over each specified interval.
x 0 2 2.5 3 3.8 4 5
f(x) 15 16 20 23 19 17 24
(a) [2, 5]
(b) [3.8, 4]
(a) The average rate of change over the interval [2, 5] is given by (f(5) - f(2)) / (5 - 2), which is equal to (24 - 16) / (5 - 2) = 8 / 3 = 2.67.
(b) The average rate of change over the interval [3.8, 4] is given by (f(4) - f(3.8)) / (4 - 3.8), which is equal to (19 - 19.6) / (4 - 3.8) = -0.6 / 0.2 = -3.
The average rate of change over a given interval [a, b] is a measure of how much the value of a function changes on average as the input changes over that interval. It is calculated as the difference between the value of the function at the endpoints of the interval divided by the difference of the corresponding inputs.
Formally, the average rate of change over the interval [a, b] is given by:
f_avg = (f(b) - f(a)) / (b - a)
where f is the function being evaluated and f_avg represents the average rate of change.
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during the winter season, a prominent newspaper reporter is interested in writing a story about the lack of proper heating of apartment buildings in the city in which he lives. during a particularly frigid weekend, this reporter manages to interview almost everyone in his own apartment building. the reporter finds that everyone, including himself, is satisfied with the heating in the apartment building. identify the type of sampling used in this example. a) Cluster sampling b) Convenience sampling c) Voluntary response sampling d) Systematic sampling 1 e) Attempted census
The type of sampling used in this example is Convenience sampling.
Convenience sampling is a type of non-probability sampling in which the sample is selected based on the ease of access or availability of the subjects. The sample is selected based on the researcher's convenience, and it does not use a random selection process.
In this case, the reporter chose to interview people in his own apartment building because it was convenient for him and he had easy access to them.
The other options you listed are:
a) Cluster sampling, which is a form of probability sampling in which the sample is selected by first dividing the population into smaller groups or clusters, and then selecting a random sample of those clusters.
b) Voluntary response sampling, which is a type of non-probability sampling where individuals choose to participate in the study.
c) Systematic sampling, which is a form of probability sampling in which the sample is selected by choosing a random starting point and then selecting every nth subject from the population.
d) Attempted census, which is when the researcher tries to include all members of a population in the sample.
Therefore, The type of sampling used in this example is Convenience sampling.
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a) Estimate the initial and final amounts of water contained in the pool.
The initial amount of water contained in the pool was __ thousands of gallons.
The required initial and final amounts of water contained in the pool are 46 ans 26 gallons of water.
Explain about Graph?A graph is made up of vertices, or points, and edges, or lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and uncorrected graphs, and simple graphs, there are many other forms of graphs.
According to question:As graph says
The initial amount of water contained in the pool is
at t = 0
= 46 gallons of water
And at t = 5, is final amount of water in pool
= 26 gallon of water
Thus, there are 46 ans 26 gallons of water.
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