Write a Polynomial in standard form with a degree of 6 with only complex solutions.
Answers
A polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.
A polynomial in standard form with a degree of 6 is written as P(x) = a₆x⁶ + a₅x⁵ + a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀, where a₆ ≠ 0 and a₀, a₁, a₂, a₃, a₄, a₅, and a₆ are coefficients.
To ensure that the polynomial has only complex solutions, we need to make sure that all of its roots are complex numbers.
Complex numbers have the form a + bi, where a and b are real numbers and i is the imaginary unit (√(-1)).
By factoring the polynomial into linear factors, we can ensure that each factor (x - zᵢ) contributes a complex root.
Here, z₁, z₂, z₃, z₄, z₅, and z₆ represent complex numbers.
Since the polynomial has a degree of 6, we need six complex factors to form the polynomial.
The product of these factors will give us the desired polynomial with complex solutions.
Therefore, the polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.
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Related Questions
Solve the quadratic equation by completing the square: x^(2)+8x+4=-3 Give the equation after completing the square, but before taking the square root.
Answers
After completing the square, the equation becomes (x + 4)^2 + 7 = 0, but there are no real solutions for x.
To solve the quadratic equation x^2 + 8x + 4 = -3 by completing the square:
x^2 + 8x + 4 + 3 = 0
(x^2 + 8x + ___) + 4 + 3 = 0
(x^2 + 8x + 16) + 4 + 3 = 0
(x + 4)^2 + 7 = 0
Now, we can solve for x by isolating the squared term:
(x + 4)^2 = -7
To eliminate the square, we take the square root of both sides (remembering to consider both the positive and negative square roots):
x + 4 = ±√(-7)
Since the square root of a negative number is not a real number, this equation has no real solutions. The quadratic equation x^2 + 8x + 4 = -3 does not have any real roots.
Thus, the equation obtained is (x + 4)^2 + 7 = 0 which has no real solutions.
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What are straight line graphs called?
Answers
Straight-line graphs are commonly referred to as "linear graphs" or "linear equations."
We have,
A straight line graph, often referred to as a linear graph or linear equation, represents a relationship between two variables that can be expressed by a linear equation in the form y = mx + b.
In this equation, 'x' and 'y' are the variables, 'm' is the slope of the line, and 'b' is the y-intercept (the point where the line crosses the y-axis).
The slope 'm' determines the steepness or incline of the line.
A positive slope indicates the line rises as 'x' increases, while a negative slope indicates the line descends as 'x' increases.
The y-intercept 'b' represents the value of 'y' when 'x' is zero, determining where the line crosses the y-axis.
Thus,
Straight line graphs are commonly referred to as "linear graphs" or "linear equations.
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After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The number of bacteria decays by a factor of \dfrac{1}{15} 15 1 start fraction, 1, divided by, 15, end fraction every 6.76.76, point, 7 minutes, and can be modeled by a function, NNN, which depends on the amount of time, ttt (in minutes). Before the medicine was introduced, there were 90{,}00090,00090, comma, 000 bacteria in the Petri dish. Write a function that models the number of bacteria ttt minutes since the medicine was introduced.
Answers
Complete Question
After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The number of bacteria decays by a factor of 1/15, every 6.76minutes, and can be modeled by a function, N, which depends on the amount of time, t (in minutes). Before the medicine was introduced, there were 90,000 bacteria in the Petri dish. Write a function that models the number of bacteria t minutes since the medicine was introduced.
Answer:
Nt = 90,000 × e^t/15
Step-by-step explanation:
The function that models the number of bacteria t minutes since the medicine was introduced is written as
Nt = No×e^λt
Where:
No = The initial number of the bacteria after time t
Nt = The current number of the bacteria after time t
λ = Decay constant or factor
t = Time in years
From the question,
No = 90,000 bacteria
Nt = The current number of the bacteria after time t
λ = 1/15
t = Time in years
Therefore, our function is written as:
Nt = 90,000×e^1/15 × t
Nt = 90,000 × e^t/15
Answer:
90,000*(1/15)^t/6.7
Step-by-step explanation:
Khan told me it's correct.
assume that when adults with smartphones are randomly selected, 59% use them in meetings or classes. if 12 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes
Answers
The probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.
To find the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where:
- P(X = k) is the probability of exactly k successes,
- n is the number of trials,
- k is the number of successes,
- p is the probability of success in a single trial, and
- C(n, k) is the combination of n choose k.
In this case, n = 12, k can be 0, 1, or 2, and p = 0.59 (the probability of using smartphones in meetings or classes).
Now we can calculate the probabilities for each value of k and sum them up:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)
P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)
P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)
Calculating these probabilities and summing them up will give us the desired probability that fewer than 3 out of 12 users use their smartphones in meetings or classes.
Let's calculate the probabilities.
P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)
Using the combination formula, C(12, 0) = 1, and simplifying the equation:
P(X = 0) = 1 * 1 * (1 - 0.59)^12 = 0.0003159
P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)
Using the combination formula, C(12, 1) = 12, and simplifying the equation:
P(X = 1) = 12 * 0.59^1 * (1 - 0.59)^11 = 0.0065294
P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)
Using the combination formula, C(12, 2) = 66, and simplifying the equation:
P(X = 2) = 66 * 0.59^2 * (1 - 0.59)^10 = 0.0470972
Now, let's sum up these probabilities to find P(X < 3):
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
P(X < 3) = 0.0003159 + 0.0065294 + 0.0470972 = 0.0539425
Therefore, the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.
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A line parallel to the line produced by 6x-2y=25 has what gradient?
Answers
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
\(6x-2y=25\implies -2y=-6x+25\implies y=\cfrac{-6x+25}{-2} \\\\\\ y=\cfrac{-6x}{-2}+\cfrac{25}{-2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{3}x-\cfrac{25}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\)
convert 4 feet 6 inches to inches
Answers
Answer:
54 inches
Step-by-step explanation:
how many solutions does the equation have? 3y - 5 = y + 2y - 9
Answers
Answer:
V Down Below V
Step-by-step explanation:
3y - 5 = y + 2y - 9
3y - 5 = 3y -9
-5 = -9
Statement is false, Lines are parallel
0 Solutions or No Solution
What is the image of (4,-2) after a dilation by a scale factor of 1/2 centered at the origin?
Answers
Answer:
That point would now be half as close to the origin, so (2,-1).
A scuba diver descends from the surface at a rate of 28 feet per minute. what is the position of the scuba diver relative to the surface after diving for 4 minutes?
Answers
The position of the scuba diver relative to the surface after diving for 4 minutes is 112 feet.
A scuba diver descends from the surface at a rate of 28 feet per minute. we have to find the position of the scuba diver relative to the surface after diving for 4 minutes?
Since we are given the information that the scuba diver descends from the surface at a rate of 28 feet per minute, therefore, in order to get the position of the scuba diver relative to the surface after diving for 4 minutes, we've to multiply 28 by 4 and this will be:
= 28 × 4
= 112 feet.
The position of the scuba diver relative to the surface after diving for 4 minutes is 112 feet.
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a farmer collected some eggs from his farm and found b eggs broken. he packed the remaining eggs in c egg cartons. each egg carton can hold a dozen eggs and no eggs were leftover. write an algebraic expression for the number of eggs he collected initially in terms of b and c.
Answers
The algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.
What is an algebraic expression?
In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.).
The total number of eggs he collected = 12c + b.
Because 12 eggs are a dozen multiplied by unknown, you get a multiple of twelve then you add your broken eggs for the total.
Hence, the algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.
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what is 55 + (12-4) ÷ 5
Answers
Answer
56.6
Explanation
To solve this, we will use one of the principles for the order of operations.
55 + (12 - 4) ÷ 5
BODMAS or PEMDAS indicates that the expression in the bracket is simplified first before the multiplication or division, then, the addition or subtraction follows.
So,
55 + (12 - 4) ÷ 5
= 55 + 8 ÷ 5
= 55 + 1.6
= 56.6
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10. An employee was conducting a service at the local supermarket. In his survey, he found that
63% of the shoppers intended to purchase produce on their trip. 80% of those shoppers
intended to purchase both fruits and vegetables. What percentage of total shoppers surveyed
intend to purchase only fruits or vegetables (not both)?
Answers
To solve this question, we analyze the percentages, and doing this, we get that the percentage of total shoppers surveyed intend to purchase only fruits or vegetables (not both) is 12.6%.
Percentages:
63% of the shoppers will make a purchase.
Of those, 80% purchase both fruits and vegetables.
Thus, 100 - 80 = 20% purchase only one.
Percentage of shoppers who purchase only one:
20% of 63%, so:
\(p = 0.2*0.63 = 0.126\)
0.126*100% = 12.6%.
Thus, the percentage of total shoppers surveyed intend to purchase only fruits or vegetables (not both) is 12.6%.
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helmholtz coil is a simple device consisting of two circular coils with the same radius r and the same current i, centered on the same axis, and whose planes are a distance r apart. (a) treat the common axis of the coils as the y-axis, and set y
Answers
A Helmholtz coil is designed to create a relatively uniform magnetic field between the two coils. To find the magnetic field at the midpoint between the coils, we can use the Biot-Savart law, which calculates the magnetic field produced by a current-carrying wire.
Step 1: Define the position of the coils
Let's define the positions of the coils as y1 = -r/2 and y2 = r/2. This places the midpoint between the coils at the origin (0, 0).
Step 2: Use the Biot-Savart law
The Biot-Savart law states that the magnetic field dB produced by a small segment of wire is given by:
dB = (μ₀ * i * dl × r') / (4π * |r'|³)
where μ₀ is the permeability of free space, i is the current in the wire, dl is the length of the wire segment, and r' is the vector from the wire segment to the point where we want to calculate the magnetic field.
Step 3: Calculate the magnetic field for each coil
Integrate the magnetic field dB along the entire circumference of each coil to find the total magnetic field B produced by each coil.
Step 4: Add the magnetic fields from both coils
Since the two coils have the same current and are symmetric about the y-axis, their magnetic fields at the midpoint will add up. Add the magnetic fields from both coils to find the total magnetic field B_total at the midpoint:
B_total = B1 + B2
By following these steps, you can calculate the magnetic field at the midpoint between the two Helmholtz coils along the y-axis.
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-5x’2+9x-3=0
Descriminant:
Number of real solution:
Answers
Answer:
2 x ^2 − 2 x + 4 = 0
x ^2 − 2 x + 4 = 0
2 x ^2 − x = 0
Step-by-step explanation:
Find f if f ''(x) = 12x2 + 6x − 4, f(0) = 5, and f(1) = 4
Answers
Step-by-step explanation:
f''(x) = 12x² + 6x - 4
f'(x) = 4x³ + 3x² - 4x + c
f(x) = x⁴ + x³ - 2x² + cx + d
f(0) = 5 = 0⁴ + 0³ - 2×0² + c×0 + d
d = 5
f(1) = 4 = 1⁴ + 1³ - 2×1² + c×1 + 5
4 = 1 + 1 - 2 + c + 5
4 = c + 5
c = -1
f(x) = x⁴ + x³ - 2x² - x + 5
A rectangle has an area of
5x^2+ 7x-6 what are expressions
For the length and width
Answers
The expression for the area of the rectangle is $(5x - 3)(x + 2)$.
What is the expressions for the length and width of the rectangle?To find expressions for the length and width of the rectangle, we need to factor the given expression for its area. We can do this by finding two factors that multiply to give $5x^2 + 7x - 6$. We can do this by using the factoring method of "AC grouping":
$5x^2 + 7x - 6$
First, we need to find two numbers whose product is $5 \cdot (-6) = -30$ and whose sum is $7$. These numbers are $10$ and $-3$.
$5x^2 + 10x - 3x - 6$
Next, we group the terms and factor out the common factors:
$(5x^2 + 10x) - (3x + 6)$
$5x(x + 2) - 3(x + 2)$
$(5x - 3)(x + 2)$
So the expression for the area of the rectangle is $(5x - 3)(x + 2)$.
Since the length and width of a rectangle are usually represented by two different variables, we can let $l$ represent the length and $w$ represent the width. Then we have:
$lw = (5x - 3)(x + 2)$
We can choose either factor to represent the length and the other factor to represent the width. For example, we can choose:
$l = 5x - 3$
$w = x + 2$
Or we can choose:
$l = x + 2$
$w = 5x - 3$
Both choices will give us the same area of $5x^2 + 7x - 6$.
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Which simplified expression matches the perimeter of the shape?
Answers
hope it helps
Choose the graph of y < –x2 + 4x + 5.
Answers
Answer:
can you show me the graph so I can't answer the question
Answer:
A
Step-by-step explanation:
Edge 2022
How to write three million forty four thousand six hundred twenty one in number form
Answers
3,440,621. Srry if its wrong..
Johnnie runs 4.5 km everyday to stay in shape. It takes him 30 minutes to run his route. What is his average speed per hour?
Answers
Answer:
6.6
Step-by-step explanation:
According to recent data, women make up what percentage of workers in science and technology (STEM) fields in Canada and the United States, respectively?
A. 34% and 40%
B. 23% and 26%
C. 17% and 26%
D. 25% and 27%
E. 34% and 26%
Answers
According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.
According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.
In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.
Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.
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James takes out a loan of 9000 euros which keeps on charging simple interest at a rate of 3% of the original amount per annum until it is cleared. James pays of 770 euros each year to reduce the loan. After how many years will James have fully cleared the loan?
Answers
James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.
To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.
The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.
In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.
In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.
This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.
Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.
Combining like terms, we have 9000 + 270 = 1.04x.
Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.
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PLEASE HELPT
Out of 100 seventh and eight grade CAVA student , there wre 35 student that chose Music as their elective course and the rest chose world language . There were a Titian of 55 eight grade student and 50 of them chose world language
Answers
In Seventh grade, 30 students chose Music and 15 students chose World language while in Eight grade, 5 students chose Music and 50 students chose World language.
Simplified solution on linear algebraTotal students is 100
Total students that chose music is 35
Total students that chose world language is 100-35 = 65
Total students in eight grade is 55
Total students in seventh grade is 100-55 = 45
Students in eight grade that chose world language is 50
Students in eight grade that chose music is 55 - 50 = 5
Students in seventh grade who chose music is 35 - 5 = 30 (total students who chose music - number of eighth grade students who chose music)
Students in seventh grade who chose world language = 45 - 30 = 15 (total student in seventh grade - students in seventh grade who chose music)
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30 POINTS I NEED HELP PLZ
Answers
Answer:
120
Step-by-step explanation:
to find the volume you just do length x width x height.
The mayor surveyed 1000 voters to see if they approve of the job she's doing, what is the population?
Answers
Answer:
1001?
Step-by-step explanation:
I am really sorry if i got this wrong i did not get it. I hope someone else helps :)
What is the product of (7x²y³)(3x⁵y⁸) ?
Answers
Answer:
21 x ^7 y ^11
Step-by-step explanation:
Please help me with edge question .
Answers
\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)
Which of the following is not a property of the normal distribution? The tails asymptotically approach the horizontal axis The area undemeath the curve and to the right of the mean is 1 It has a bell shape The mean, median, and mode are all equal
Answers
The property that is not true for the normal distribution among the given options is: "The mean, median, and mode are all equal."
The normal distribution is characterized by several key properties. It has a bell shape, meaning it is symmetric around its mean. The tails of the distribution asymptotically approach the horizontal axis, which means they gradually decrease in height as they extend toward positive and negative infinity. The area underneath the curve and to the right of the mean is equal to 0.5, not 1. This is because the total area under the curve represents the probability of all possible outcomes and must sum up to 1. Lastly, the mean, median, and mode of the normal distribution are all equal to each other, making them measures of central tendency that coincide.
Therefore, the property that does not hold for the normal distribution is that the area underneath the curve and to the right of the mean is 1, as it is actually 0.5.
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Find an equation of the line that has a slope of -1 and a y intercept of 5. Write your answer in the form
y = mx + b.
y =
Answers
\(y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+\underset{\underset{\textit{\small b }}{\uparrow }}{5}\implies y=-x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)
In a recent school newspaper survey, 3,000 randomly selected teenagers were asked to cite their primary transportation method to school. Fifteen of 20 teenagers said they use their own car to get to school. A 90% confidence interval to estimate the true proportion of teenagers who drive their own car to school is found to be (0.5907, 0.9093). Which of the following is a correct interpretation of the confidence level?
Ninety percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who drive their own car to school.
Ninety percent of all samples of this size would yield a confidence interval of (0.5907, 0.9093).
There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).
Ninety percent of all the samples of size 3,000 lie in the confidence interval (0.5907, 0.9093).
Answers
The correct interpretation of the 90% confidence interval is given as follows:
There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).
What is the interpretation of a x% confidence interval?It means that it is x% likely that the true population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.
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