Answer:
A polynomial function of degree 3 with real coefficients and the numbers 6 and i 3 as some of its zeroes is [tex]p_{3}(x) = x^{3}-6\cdot x^{2}+9\cdot x -54[/tex].
Step-by-step explanation:
A third-order polynomial in standard form is a sum of monomials with natural exponentials such that greatest degree of monomials is 3. This kind of polynomials is described by this definition:
[tex]p_{3}(x) =\Sigma\limits_{i=0}^{3} c_{i} \cdot x^{i}[/tex] (Eq. 1)
Where:
[tex]i[/tex] - Index of a sum component, dimensionless.
[tex]c_{i}[/tex] - i-th coefficient, dimensionless.
Where the highest value of [tex]i[/tex] is the degree of the polynomial.
In addition, the Fundamental Theorem establishes that all polynomials with real coefficients and degree higher than zero have a number of complex roots, an extension of the real set, equivalent to the degree of the polynomial itself.
In our case, we guarantee the existence of three complex roots, of which we know two of them: [tex]r_{1} = 6[/tex] and [tex]r_{2} = i\,3[/tex]. The polynomial can be represented as a product of three binomials:
[tex]p_{3}(x) = (x-r_{1})\cdot (x-r_{2})\cdot (x-r_{3})[/tex] (Eq. 2)
Where [tex]r_{1}[/tex], [tex]r_{2}[/tex] and [tex]r_{3}[/tex] are the roots of the third order polynomial.
If we know that [tex]r_{1} = 6[/tex] and [tex]r_{2} = i\,3[/tex] and assume that [tex]r_{3} = -i\,3[/tex], the resulting polynomial is:
[tex]p_{3} (x) = (x-6)\cdot (x+i\,3)\cdot (x-i\,3)[/tex]
And by Algebra of real numbers we obtain the polynomial in its standard form:
[tex]p_{3}(x) = (x-6)\cdot (x^{2}+9)[/tex]
[tex]p_{3}(x) = x\cdot (x^{2}+9)-6\cdot (x^{2}+9)[/tex]
[tex]p_{3}(x) = x^{3}+9\cdot x -6\cdot x^{2}-54[/tex]
[tex]p_{3}(x) = x^{3}-6\cdot x^{2}+9\cdot x -54[/tex]
A polynomial function of degree 3 with real coefficients and the numbers 6 and i 3 as some of its zeroes is [tex]p_{3}(x) = x^{3}-6\cdot x^{2}+9\cdot x -54[/tex].
What is a better credit score?
Select the correct answer below:
A lower number
An even number
An odd number
O A higher number
Answer:
A higher number.
Step-by-step explanation:
You don't want your credit to be low, and a higher number beats all of them.
You want high credit.
Not low.
Answer:
definately you want a higher number
Please help me out!
On a unit test in statistics class, the teacher determines that the mean test grade was 77.5 with a standard deviation of 5.2. What is the test grade, rounded to the nearest whole number, with a z-score of 2.4?
A.65
B.83
C.90
D.95
Answer:
C: 90
Step-by-step explanation:
Can you help me find abcd please
Answer:
A.2 B.4 C.3 D.4 E.6
Step-by-step explanation:
1/2 ÷ 3/4 = 1/2 x 4/3 (flip 3/4 and keep 1/2)
If you multiply 1/2 x 4/3 you will get 4/6.
The length of a new rectangular playing field is 2 yards longer then double the width. If the perimeter of the rectangular playing field is 322 yards, what are its dimensions?
Answer:
Step-by-step explanation:
First, we want to take the information we have and turn it into an equation, where x is our unknown dimension. For this problem, it would be better if x was equal to the width.
Let's write out the equation:
X is the width, 2x + 2 is the length, and we are multiplying both by two since there are two sides of the field. It will all equal to 322, because that is the perimeter.
2*x + 2(2x +2) = 322
Now, let's solve:
2*x + 2(2x + 2) = 322
2x + 4x + 4 = 322
6x + 4 = 322
6x = 318
x = 318 ÷ 6
x = 53
The width is 53 yards. To find the length, we multiply 53 by two and add two.
53 * 2 + 2 = 106 + 2 = 108 yards, as the length
134d) Graph the hyperbola, identify the center, vertices, foci, and equations of the asymptotes
49y^2−25x^2−196y−200x−1429=0
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Answer:
Step-by-step explanation:
49y^2 - 25x^2 - 196y - 200x = 1429
49y^2-196y+196 - 25x^2-200x-400 = 1429+196-400
49(y-2)^2 - 25(x+4)^2 = 1225
(y-2)^2/25 - (x-4)^2/49 = 1
So now you know that you have an hyperbola with
center at (-4,2)
foci at (-4,2±[tex]\sqrt{74}[/tex])
vertices at (-4,2±5)
asymptotes 7y±20 = ∓5x+14
How many significant figures are in the number: 800
Answer:
1
Step-by-step explanation:
The zeros after 8 are not significant.
What is 1 hundredth ÷ 10?
1 hundredth ÷ 10 =
Answer:
.001 or 1 thousandth
Step-by-step explanation:
.01/10=.001
Graph each function and determine the y-intercept, then use the graph to determine the approximate value of the given expression.
Y=3^x;3^1.2
A. 1;3.7
B. 1;2.9
C. 0;3.9
D. 0;3.5
Answer: Its A) 1 ; 3.7
Step-by-step explanation:i just took the practice on edge 2020
If you lower your monthly payment, do you think the total interest you pay will increase or decrease? Why?
Answer:
increase
Step-by-step explanation:
Once Your Monthly Payment Has Been Lowered, More People Will Be Interested Do To Its Lower Payment.
7)
A bag of five bananas costs £1. A bag of four grapefruits costs £2.40. How much
more does one grapefruit cost than one banana?
Step-by-step explanation:
£2.40 - £1
= £1.40
Therefore,
£1.40 more one grapefruit cost than one banana.
Answer:
4.4 pounds
Step-by-step explanation:
1. Divided 5 by 1. Which equals 5.
2. Divided 2.40 by 4. Which equals 0.6.
3.Last subtract 5 from 0.6. Which is 4.4.
what number is 100 more than 152
Answer:
252
Step-by-step explanation:
252-
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Find the perimeter of the rectangle.
5 in.
9 in.
Answer:
28 inches
Step-by-step explanation:
Tim had $150 to spend on 3 pairs of pants. After buying them, he had $30 left over. What equation expresses how much each pair of pants cost?
Answer:
Step-by-step explanation:
3x+30=150
its 120 then divide by 3 which is 40
Write an equation for a line perpendicular to y= -4x - 3 and passing through the point (-4,2)
Answer:
y = (x/4) + 3
Rewrite the following equation in slope-intercept form.
17x + 18y = -6
Answer:
y= -17/18x-1/3
Step-by-step explanation:
The slope-intercept form of the equation is y = (-17/18)x -1/3.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A linear equation 17x + 18y = -6.
To find the slope-intercept form:
Simplifying,
17x + 18y = -6
18y = -6 -17x
y = -17/18x -1/3
Therefore, y = (-17/18)x -1/3 is the slope-intercept form.
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Order the following from least to greatest.
0.67,6.7%, 6/7
Answer:
from least to greatest.= 6.7%, 0.67, 6/7
Answer: 6.7%, 0.67, 6/7
Step-by-step explanation:
6.7% is less than 0.67.
0.67 is less than 6/7.
So, the order is 6.7%, 0.67, and 6/7.
The price of lunch increased from $4.00 to $5.00 . What is the percent increase?
Answer: 1% ?
Step-by-step explanation:
Answer:
That is a 25% increase
Step-by-step explanation:
Hope this helps!!
Find DF
D
20
E 10 F
DF =
Answer:
30
Step-by-step explanation:
it is right
in 2009,Alaska suffered an earthquake of magnitude m=7.1. find the intensity of that earthquake
Answer:
Here you go :)
7.0 to 7.9 Major earthquake. Serious damage. 20
Or
Major 7 - 7.9
________
Answered by James
Step-by-step explanation:
The circumference of a circle can be found using the formula C = 2tr.
Answer:
r = c/2pi
Step-by-step explanation:
what is 100,789,388,369,012 times 479,000,000
Answer:
4.8278117e+22
Step-by-step explanation:
determine the slope of the line given this two points (-2,4) and (1,6) with solution
Answer:
Slope = y2 - y1/x2 - x1
Slope = 6-4 / 1--2
Slope = 2/3
Step-by-step explanation:
hope that will help you
The slope of the line will be 2/3.
The formula for the slope will be:
= (y2 - y1) / (x2 - x1)
where,
y2 = 6
y1 = 4
x2 = 1
x1 = -2
We will slot the values into the equation which will be:
= (y2 - y1) / (x2 - x1)
= (6-4) / (1- -2)
= 2/(1+2)
= 2/3
Therefore, the slope is 2/3.
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HELPPS PLEASE FOR BRIANILIST
can i have 300mn + 500mn =_________________________________________________________________________________________________i need help
Answer:
yes it would be 800mn
Step-by-step explanation:
Every quarter, the Food and Drug Administration (FDA) produces a report called the Total Diet Study. The FDA's report covers a variety of food items, each of which is analyzed for potentially harmful chemical compounds. A Total Diet Study reported that no pesticides at all were found in % of the domestically produced food samples. Consider a sample of food items analyzed for the presence of pesticides. Complete parts a and b. a. Compute and for the random variable x, the number of food items found that showed no trace of pesticide. nothing (Type an integer or a decimal.)
Answer:
a) Mean = 600
Standard deviation = 12.24
B)No it is not likely because our probability of no pesticide is 75% which means that more than half of food items are without any pesticide
Step-by-step explanation:
Total number of food items = 800
We are given that no pesticides were found at all in 75% of domestically produced food samples.
So, Probability of success = p = 0.75
Probability of failure = q = 1-p = 1-0.75=0.25
Now we are supposed to find [tex]\mu[/tex] and [tex]\sigma[/tex] for random variable x
a) Mean = E(x)= [tex]n \times p = 800 \times 0.75=600[/tex]
Standard deviation =[tex]\sqrt{npq}=\sqrt{800 \times 0.75 \times 0.25}=12.24[/tex]
b)Is it likely that you would observe fewer than half of the food items without any traces of pesticides ? Why or why not ?
No it is not likely because our probability of no pesticide is 75% which means that more than half of food items are without any pesticide
how do you find the solution to this inequality? please explain to me step by step how to do this
x - 8 > -3
Answer:
x > 5
Interval form: (5, infinity)
Step-by-step explanation:
Just add 8 to both sides of the inequality:
x > 5
Therefore, x must be greater than 5.
What is the volume of a sphere with a radius of 7 centimetres?
Use 3.14 for pi. Round your answer to the nearest hundredth. Use the formula provided.
V=
1077.02 cm3
1436.03 cm3
1975.43 cm3
11,494.04 cm3
Answer:
[tex]V=1436.03 \ cm^3[/tex]
The second choice provides the correct answer.
Step-by-step explanation:
The Volume of a Sphere
The volume of a sphere of radius r is given by:
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3[/tex]
The radius of the sphere is r=7 cm, thus:
[tex]\displaystyle V=\frac{4}{3}\cdot 3.14\cdot 7^3[/tex]
[tex]V=1436.03 \ cm^3[/tex]
Note: We have used an approximated value for pi=3.14.
The volume of the sphere rounded to the nearest hundredth is
[tex]\boxed{V=1436.03 \ cm^3}[/tex]
The second choice provides the correct answer.
The amount of milk that the bakery used this month was a 75% decrease relative to last month. What is the new amount of milk using percent?
Answer:
25%
Step-by-step explanation:
the answers
The new amount of milk using percent is 25.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then the percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
We are given that the amount of milk that the bakery used this month was a 75% decrease relative to last month.
Therefore, for last month, we have a rectangle with four equal areas 75% decrease,
we have to remove 3 areas to make the remaining = 25%
So, the difference will give a 75% decrease
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Help please, only right answers get brainliest!
Answer:
90
Step-by-step explanation:
The number of possibilities is the the product of the number of choices of each category.
size: 3 choices
cheese: 2 choices
side dish: 3 choices
drink: 5 choices
number of difference possibilities: 3 * 2 * 3 * 5 = 90
Answer: 90
please help it’s due in a couple of min
Answer:
C
I have done this.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The first 3 answer is wrong so Its d