Answer: Theorems About Roots of Polynomial Equations
Step-by-step explanation:
Theorems About Roots of Polynomial Equations
In the given case we can conclude that the polynomial is \(-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.\)
To create a polynomial with 4 terms, a degree of 6, a leading coefficient of -1, and a constant term of -5.5, we can use the general form of a polynomial:
A "polynomial" is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers, combined using addition and multiplication. Polynomials are fundamental objects in algebra and are used to represent a wide range of mathematical relationships, including functions, curves, and various mathematical concepts.
P(x) = \(ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g\)
Plugging in the given values, we have:
P(x) = \(-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5\)
Remember that the degree of a polynomial is determined by the highest exponent of x.
In this case, the degree is 6.
The leading coefficient is the coefficient of the term with the highest degree, which is -1. The constant term is -5.5.
So, the polynomial is \(-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.\)
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[HELP! WILL GIVE BRAINLIEST] Determine the value of θ.
Answer:20.9248 degrees
Step-by-step explanation:
sin(θ)=opposite/hypotenuse
θ=sin⁻¹(opposite/hypotenuse)
θ=sin⁻¹(5/14)
θ=20.9248 degrees or θ=0.3652 radians
convert this rational number to its decimal form and round to the nearest thousandth
Step-by-step explanation:
divide 1 by seven in long division it will be 0.142857 then it repeat it self ...so to the nearest thousand is 0.143
Answer:
Step-by-step explanation:
What is the equation of the given line?
y = 5
x = 3
x = 1
y = 3
Answer:
y=x+2
Step-by-step explanation:
use the formula y=mx+c
first u find m which is the gradient 3-1/5-3 = 2/2=1
sub in any point to find the c
5=1(3)+c
c=2
y=1x+2
5 less than 2/3 of a number is 19. Find the number
Answer:
the anser in 60
Step-by-step explanation:
Let the original number be x.
According to the question we can write as (2/3)x+20x
On rearranging x−(2/3)x=20
Now taking the L.C.M od 1 and 3 is 3
(3x−2x)/3=20
x/3=20
Again by transposing x=60
So the original number is 60
The price of everything in the store is reduced by 1/4 each hour until closing time. Liz wants to purchase a shirt that was originally marked at 24$. You can use a function to describe the shirts price x hours after the sale starts.
TRUE/FALSE. Refer to the following ANOVA table from a multiple regression. The F statistic for assessing overall fit is 2.83.
TRUE. The ANOVA table from a multiple regression includes the F statistic for assessing overall fit. In this case, the F statistic is 2.83. The F statistic is a ratio of two variances, the between-group variance and the within-group variance.
It is used to test the null hypothesis that all the regression coefficients are equal to zero, which implies that the model does not provide a better fit than the intercept-only model. If the F statistic is larger than the critical value at a chosen significance level, the null hypothesis is rejected, and it can be concluded that the model provides a better fit than the intercept-only model.The F statistic can also be used to compare the fit of two or more models. For example, if we fit two different regression models to the same data, we can compare their F statistics to see which model provides a better fit. However, it is important to note that the F statistic is not always the most appropriate measure of overall fit, and other measures such as adjusted R-squared or AIC may be more informative in some cases.Overall, the F statistic is a useful tool for assessing the overall fit of a multiple regression model and can be used to make comparisons between different models. In this case, the F statistic of 2.83 suggests that the model provides a better fit than the intercept-only model.
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what is ??? 5(m-n) It’s distributive property and simply it
Determine which is the better investment: 3.38% compounded semiannually or 3.51% compounded quarterly. Round your answers to 2 decimal places.
The 3.38% semiannual investment gives an effective rate of ____ %.
The 3.51% quarterly investment gives an effective rate of ____ %.
Therefore, the _______ investment is a better investment.
The 3.51% compounded quarterly investment is the better investment in terms of higher returns.
We need to compare the effective rates of return for both options in order to determine which investment is superior.
A) For the 3.38% accumulated semiannually, we can work out the successful rate utilizing the equation:
The effective rate is as follows: Effective Rate = (1 + (Annual Interest Rate / Number of Compounding Periods)) Number of Compounding Periods - 1 Annual Interest Rate = 3.38 percent Number of Compounding Periods = 2 (since it is compounded semiannually) Effective Rate = (1 + (0.0338 / 2)) 2 - 1
The 3.38% compounded semiannual investment has an effective rate of approximately 3.59%, which is calculated as follows: Effective Rate = (1 + 0.0169)2 - 1 Effective Rate 0.0359385 or 3.59% (rounded to two decimal places).
B) We can use the same formula to determine the effective rate for the quarterly compound interest rate of 3.51 percent:
Since it is compounded quarterly, there are four compounding periods, and the annual interest rate is 3.51 percent. The effective rate is equal to (1 + (0.0351 / 4))4 - 1.
The compounded quarterly investment at 3.51% has an effective rate of approximately 3.53%, which is calculated as follows: Effective Rate = (1 + 0.008775)4 - 1 Effective Rate 0.0353157 or 3.53% (rounded to two decimal places).
When we look at the effective rates, we can see that the compounded quarterly investment with a rate of 3.51 percent has a slightly higher effective rate (3.53%) than the compounded semiannual investment with a rate of 3.38 percent (3.59%). Consequently, the higher-return investment at 3.51 percent compounded quarterly is superior.
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Find a number which is increased by 12 is two times its opposite.
N = _____
Final equation: ______
The number which when increased by 12 is two times its opposite. is
N = -4
final equation N + 12 = -2N
What is additive inverse?Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.
To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.
The problem says
N + 12 = -2N
N + 2N = -12
3N = -12
N = -4
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The function p(x) = 25x represents the number of pages p(x) a printer can print in x minutes. How many pages can the
printer print in 5 hours?
Answer:
7,500 Pages
Step-by-step explanation:
So this printer can prink 25 pages in 1 (x) minute.
There are 60 minutes in an hour and we are waiting 5 hours, so 5x60 = 300 minutes.
Then you take the 300 and plug it in for x because that is how many minutes we are waiting for. Now your equation should look like this:
p(x) = 25(300)
Next you multiply 25 x 300 and you get 7,500 pieces of paper
After reviewing her driving record for the past 3 years, Cindy's insurance company offers her a good driver discount of 4.5%. Her original policy was based on the premiums listed below. What is her new annual premium including the discount? Cindy's Auto Insurance Policy Type of Insurance Coverage Coverage Limits Bodily Injury $50/100,000 Property Damage $25,000 Collision $500 deductible Comprehensive $100 deductible Annual Premiums $31.75 $120.50 $275.75 $100.00 a $504.24 b. $523.50 C. $528.00 d. $551.76
Answer:
its A
Step-by-step explanation:
I just took the test on EDGE
The new annual premium including the discount is $504.24.
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To calculate the new annual premium with the discount, we need to find the total premium and then subtract the discount.
The total premium is the sum of the individual premiums:
Total premium.
= $31.75 + $120.50 + $275.75 + $100.00
= $528.00
The discount is 4.5% of the total premium:
So,
Discount = 0.045 × $528.00 = $23.76
The new annual premium including the discount is:
New premium = Total Premium - Discount
= $528.00 - $23.76
= $504.24
Therefore,
The new annual premium including the discount is $504.24.
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23, 24, 25, 20, 25, 29, 24, 25, 30
Mean?
Median?
Mode?
Range?
Please help?
Answer:
median = 25. that's the answer
Answer:
Mean - 25
median - 25
range - 10
mode - 25
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.lim x→[infinity] (ex + x)6/x
The limit of \((ex + x)^(^6^/^x^)\) as x approaches infinity is 1. As x becomes infinitely large, the exponential term dominates, resulting in the limit approaching 1.
To evaluate this limit, we can rewrite the expression as \((ex)^(^6^/^x^) * (1 + x/ex)^(^6^/^x^)\). As x approaches infinity, the first term \((ex)^(^6^/^x^)\)approaches 1 because the exponent tends to 0.
Now, let's focus on the second term \((1 + x/ex)^(^6^/^x^)\). As x approaches infinity, the x/ex term approaches 1, and we have \((1 + 1)^(^6^/^x^)\).
Taking the limit of this expression as x goes to infinity, we have \((2)^(^6^/^x^)\). Again, as x approaches infinity, the exponent tends to 0, resulting in (2)⁰, which is equal to 1.
Thus, the overall limit is given by the product of the limits of the two terms, which is 1 * 1 = 1.
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Solve the equation for all real solutions in simplest form. 2p? – 3p - 7=0
Answer:
p = -7
Step-by-step explanation:
1) added up the like therms
-p -7 = 0
2) multiply by -1
p+7 = 0
3) add at both members -7
p+7-7 = -7
p= -7
How many grams means 1 pound?
One pound is equal to 453.592 grams, in unit of measurement.
What is unit of measurement?A predetermined, legally recognised, and frequently used magnitude of a quantity that serves as a benchmark when comparing other quantities of the same kind is referred to as a unit of measurement. Any extra quantity of that type can be expressed as a multiple of the measurement unit.
Length is an illustration of a physical quantity. The letter "M" stands for "metre," a measurement that stands in for a specific, predetermined length. "10 metres" refers to a length that is 10 times the exact, predetermined length known as "metre" (or 10 m).
From ancient times to the present, human endeavour has depended on the definition, acceptance, and practical application of units of measurement.
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The discriminant is the part of the quadratic formula under the square root symbol.D=b^2-4ac
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
1. 9x² + 3x - 4 = 0
Step 02:
Discriminant:
D = b² - 4ac
9x² + 3x - 4 = 0
a = 9
b = 3
c = - 4
D = (3)² - 4(9)(-4) = 9 + 144 = 153
The answer is:
D = 153
4x = -12.
What is x?
Answer:
x=-3
Step-by-step explanation:
x=-12/4 divide both sides by 4
Answer:
x = -3
Step-by-step explanation:
Let's solve your equation step-by-step.
4x=−12
Step 1: Divide both sides by 4.
4x/4 = -12/4
x=−3
n a given year, there are 10 million unemployed workers and 120 million employed workers in an economy.
In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.
The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.
Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.
Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.
By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.
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chaslot, g., winands, m., herik, h., uiterwijk, j., and bouzy, b. progressive strategies for monte-carlo tree search. new mathematics and natural computation, 04: 343–357, 11 2008. doi: 10.1142/s1793005708001094.
The given citation is a reference to a research paper titled "Progressive Strategies for Monte-Carlo Tree Search" by Chaslot, G., Winands, M., Herik, H., Uiterwijk, J., and Bouzy, B.
The paper was published in the journal "New Mathematics and Natural Computation" in November 2008.
Here are the details of the citation:
Authors: G. Chaslot, M. Winands, H. Herik, J. Uiterwijk, and B. Bouzy
Title: Progressive Strategies for Monte-Carlo Tree Search
Journal:
Year: 2008
Volume: 04
Pages: 343–357
DOI: 10.1142/s1793005708001094
The DOI (Digital Object Identifier) provided is a unique identifier for the paper and can be used to access the paper online, usually through a database or publisher's website.
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On a coordinate plane, a circle has a center at (0, 0). Point (3, 0) lies on the circle.
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Does the point (2, StartRoot 6 EndRoot) lie on the circle shown? Explain.
Yes, the distance from (3, 0) to (0, 0) is 3 units.
Yes, the distance from (0, 0) to (2, StartRoot 6 EndRoot) is 3 units.
No, the distance from (3, 0) to (2, StartRoot 6 EndRoot) is not 3 units.
No, the distance from (0, 0) to (2, StartRoot 6 EndRoot) is not 3 units.
Answer: Option (4)
Step-by-step explanation:
We know that the radius of the circle is 3.
Using the distance formula, the distance from the given point to the center is
\(\sqrt{(\sqrt{6}-0)^{2}+(2-0)^{2}} = \sqrt{10} \neq 3\)
Answer:d
Step-by-step explanation:
please can someone smart help me,please do not answer if you dont know the answer,also answer all these questions please:).
Answer:
Number 7: 22.10 divided by 2.6 = 8.5 or 8.50 (depending on what your teacher prefers.
Step-by-step explanation:
Not sure about question 2 or 10
How many time does 3 go into 4677?
3 goes into 4,677, 1559 times!!
Hope this helps!!!
Love: Madoriya~ <3
Answer:
x= 1559
Step-by-step explanation:
3x= 4677
x=4677/3
x=1559
X is deposited into a savings account at time s. The savings account grows according to the accumulation function a(t)=
1−0.05t
1
for 0≤t<20. How long from the time of the deposit will it take for the account to double to 2X if (a) s=0 ? (b) s=5 ? (c) Compare your answer in (a) to your answer in (b) and briefly explain why one is greater than the other.
When s = 0, it will take 20 units of time for the account to double to 2X.
(a) When s = 0, it means the deposit is made at time t = 0. We want to find the time it takes for the account to double to 2X.
To find this time, we need to solve the equation a(t) = 2, where a(t) is the accumulation function.
1 - 0.05t = 2
Simplifying the equation, we have:
-0.05t = 1
Dividing both sides by -0.05, we get:
t = -1 / (-0.05)
t = 20
Therefore, when s = 0, it will take 20 units of time for the account to double to 2X.
(b) When s = 5, it means the deposit is made at time t = 5. We want to find the time it takes for the account to double to 2X.
Using the same equation a(t) = 2 and substituting t = 5, we have:
1 - 0.05(5) = 2
1 - 0.25 = 2
0.75 = 2
This equation is not satisfied, which means the account will not double to 2X when the deposit is made at time t = 5.
(c) The answer in (a) is greater than the answer in (b) because when the deposit is made at time t = 0, the account has more time to accumulate interest and grow compared to when the deposit is made at time t = 5. As time progresses, the effect of compounding becomes more significant, and starting earlier allows for more growth and a shorter time to double the account.
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What is 7 divided by 230
Answer:
0.0304347826
Step-by-step explanation:
Answer: 32.8571428571429 or 0.0304347826086957
Step-by-step explanation:
Hope this helped
Select the correct answer.
A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the
number of tests on the y axis and the time in weeks on the x-axls?
A. 3/4
B. 4/3
C. 3
D. 4
it should be A. 3/4
solve for " f "
\(\sf -f+2+4f=8-3f\)
Answer:
f=1
Step-by-step explanation:
first, we gather all of the f's, and numbers into seperate sides
in result we would get -f+3f+4f=8-2
we can think of this as:
-1+3+4=8-2 then add the f's later
in result we get
6f=6
we divide both sides by 6
and we get f=1 :)
Answer:
f = 1
Step-by-step explanation:
1) Simplify -f+2+4f to 3f+2.
3f+2=8-3f
2) Subtract 2 from both sides.
3f=8-3f-2
3) Simplify 8-3f-2 to -3f+6
3f=-3f+6
4) Add 3f to both sides.
3f+3f=6
5) Simplify 3f+3f to 6f.
6f = 6
6) Divide both sides by 6.
f = 1
What are the first 3 terms of the sequence represented by the expression n(n – 2) – 4 ?
The first 3 terms of the sequence using the expression are -5, -4 and -1
Calculating the first 3 terms of the sequence using the expressionFrom the question, we have the following sequence that can be used in our computation:
n(n – 2) – 4
This means that
T(n) = n(n – 2) – 4
Set n = 1, 2 and 3
So, we have
T(1) = 1 * (1 – 2) – 4 = -5
T(2) = 2 * (2 – 2) – 4 = -4
T(3) = 3 * (3 – 2) – 4 = -1
Hence, the first 3 terms of the sequence using the expression are -5, -4 and -1
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At the beginning of the week, Joshua had $356 in his savings account. At the
end of the week he only had $123 in his savings account. Write and solve an
equation to find the amount of money that Joshua spent during the week.
equation: 356 - x = 123
The x can be changeable
the actual answer:
356 - 356 - x = 123 - 356
-1x/-1 = -233/-1
x =233
1. f(x) = x3 - 3x2 - 8x - 60
Answer:
x = -2
Step-by-step explanation:
hope that helps :)
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
a blue dice and a green dice are rolled. Find the probability that the blue is either 1 or 2 and the green is 1.
Answer:
2
Step-by-step explanation:
green
Answer: 2
Step-by-step explanation: