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].
Evaluate $\frac{33}{33\frac 13}$. Express your answer as a fraction in simplest form. (Thus the numerator and denominator should be integers whose greatest common divisor is $1$.)
Answer:
[tex]\dfrac{99}{100}[/tex]
Step-by-step explanation:
We need to evaluate [tex]\dfrac{33}{33\frac 13}[/tex]. Here, 33 is numerator and [tex]33\dfrac{1}{3}[/tex].
Firstly, we will solve the denominator.
[tex]33\dfrac{1}{3}=\dfrac{33\times 3+1}{3}\\\\=\dfrac{100}{3}[/tex]
The given expression becomes,
[tex]\dfrac{33}{33\frac 13}=\dfrac{33}{\dfrac{100}{3}}\\\\=\dfrac{33\times 3}{100}\\\\=\dfrac{99}{100}[/tex]
Hence, the required answer is 99/100.
Consider the sequence of steps to solve the equation:
7x
5(x - 3) =
Step 1 = 10(x - 3) = 7x
Step 2 = 10x - 30 = 7x
Step 3 = 3x - 30 = 0
Step 4 = 3x = 30
Step 5 = x= 10
Identify the property of equality which yields Step 5.
A)
Division Property
B)
Addition Property
C)
Subtraction Property
D)
Multiplication Property
Can someone help me I really need it
Answer:
No, the figures are similar but not congruent as although width is same, length of fig A is 3 blocks while length of fig. B is 4 blocks. For two fig. to be congruent, their l and b should be eql.
Hope u find this ans useful.
Pls mark me brainliest
HELP!!! Which of the following best describes the slope of the line below?
Answer:
C. Negative
Step-by-step explanation:
A quick reminder: an undefined slope makes the line vertical, a slope of 0 makes the line horizontal, a positive slope makes the line go up as x increases, and a negative slope makes the line go down as x increases.
In this case, the line is going down as x increases, meaning the slope must be negative.
describe the steps to determining and graphing a translation.
Answer:
A TRANSLATION OF A GRAPH is its rigid movement, vertically or horizontally. On the left is the graph of the absolute value function. On the right is its translation to a "new origin" at (3, 4). y = |x|.
Pls help me slove this -2 1/3 - (-5) =
Answer:
4/3
Step-by-step explanation:
-2 1/3= -7/3
-5=-15/3
Answer:
If I'm reading this correctly, -2.33 or -2 1/3 - (-5) should equal to 2 2/3
Step-by-step explanation:
Since a minus sign is close to the minus sign inside the parantheses, you should turn the minus sign into a plus, giving you -2 1/3 + 5 which should equal to 2 2/3. Hope this helps
Write a number that has a 3 that is 10
times the value of the 3 in 7.31
Your answer
Answer:
3
Step-by-step explanation:
7.31
3 in the tenths place
3 = 3/10 or 0.3
0.3*10=3
Your office window is a = 55 feet high. Looking out your window, you find that the top of a statue lines up exactly with the bottom of a building that is b = 700 horizontal feet from your office. You know that the statue is c = 225 feet from the building. How tall is the statue? (See the figure below. Round your answer to two decimal places.)
Answer:
nothing
Step-by-step explanation:
nothing will come because there is no figure
answer for brainliest ! <3
Answer:
1: p=(2,4) q=(1,1) r=(5,2)
2 I am so sorry. the changing in the shape is not any transformation I've heard of before.
3:90 degree rotation (Counterclockwise.)
4: 180 degree rotation (doesn't matter which way.)
5: 90 degree rotation (clockwise)
6: Up 9 units, over 2 units to the right.
Hope this helps!!
Please help me I have no idea what the answer is
Answer:
hi
Step-by-step explanation:
A car rental company charges a daily rate of $ 23 plus $ 0.20 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $ 44.00. How many miles did you drive?
Answer: 105 miles
(44-23)/0.20
IDK WHY IT SAYS IM A COLLEGE PERSON IM NOT BUT UM I NEED HELP WITH THIS PLEASEEEEEE
Answer:
option 3
Step-by-step explanation:
Answer:
it's option 3 i think
Step-by-step explanation:
This is what I meant to ask lol
Answer:
false
Step-by-step explanation:
theyre not proportional because 100*2=200 but 35*2 is not 45 :)
Answer:
True
Step-by-step explanation:
The miles column is increasing steadily by 100The cost column is increasing steadily by 10Neither column is changing the amount that's being increased and neither is decreasing after an increase, therefore, the answer is true.I hope this helps!
3. A change machine contains nickels, dimes, and
quarters. There are 75 coins in the machine, and the
value of the coins is $7.25. There are 5 times as
many nickels as dimes. How many quarters are in
the machine?
Equation #1:
Equation #2:
Equation #3:
# of quarters:
Answer:
50 nickels 10 dimes 15 quarters
Step-by-step explanation:
im pretty sure
(y^3)^2 without exponents
Answer:
y^6
Step-by-step explanation:
Answer:
[tex]y^{6}[/tex]
Step-by-step explanation:
Step 1:
( y³ )² Equation
Step 2:
[tex]y^{3 * 2}[/tex] Multiply
Answer:
[tex]y^{6}[/tex]
Hope This Helps :)
Are these ratios equivalent?
16 shipments every 6 years
8 shipments every 3 years
yes
no
Answer: Yes
Step-by-step explanation:
If you do 16/6 you get 2.667 and if you do 8/3 you also will get 2.667
Which of the following functions has a graph that passes through the origin? Select all that apply.
A. power; y equals x superscript n baseline
B. root; y equals Root Index n Start Root x End Root
C. reciprocal; y equals Start Fraction 1 over x End Fraction
D. exponential; y equals b superscript x baseline
Answer: a and b
power and root
If x = 34, y = 53, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth.
0.74 units
1.17 units
1.64 units
2.14 units
Answer:
2.14 units
Step-by-step explanation:
TO FIND AB:
sin 34=AC/AB
AB=AC/sin34=4/sin34=7.15
TO FIND AD:
sin 53=AC/AD
AD=AC/sin53=4/sin53=5.00
difference in length:
AB-AD=7.15-5.00=2.14 units
Answer:
the answer is 2.14 units
Step-by-step explanation:
took the test and got it right
Brainliest pls
Find the value of x.
(7x + 16)
80°
The value of x is
Robert and Dora need to write 4,300,000,000 using scientific notation. Robert claims that 4,300,000,000 = 4.3 x 108 and Dora claims that 4,300,000,000 = 4.3 x 109. Which of the following best describes whose number is correct and the reason it is correct?
Answer:
Robert is correct
Step-by-step explanation:
we know in scientific notation a positive number goes to the right and if we do 4.3 and we go back the spaces it would be nine spaces so it would be 4.3 X 109
What is the correct decimal point placement for the product of 3.54 × 15.42? 54.5868 545.868 5458.68 54586.8
9514 1404 393
Answer:
54.5868
Step-by-step explanation:
The multiplicands each have 2 digits to the right of the decimal point, so the product will have 2+2 = 4 digits to the right of the decimal point. The correct placement is ...
54.5868
__
Another way to tell is that the product is in the neighborhood of 3·15 = 45, which is nowhere near 545 or 5458 or any higher value.
Answer: 54.5868
Since 3 x 15 is already 45, now we have to multiply the decimals, but we must put a point.
.54 x .42 = 9.5868
45 + 9.5868 = 54.5868.
Hope this helps!
Evaluate:
54 - 75 + 81 - (-27) + 53
Answer:
140
Step-by-step explanation:
Answer:
140.
Step-by-step explanation:
PEMDAS.
Since there isn't any problems that aren't adding, we can just do it step by step.
54 - 75.
-21.
Add 81.
60.
Subtract -27.
87.
Add 53.
140.
Brainiest?
Create a word problem using the math sentence below. Make sure you write in complete sentences. -25 + (-35)
Step-by-step explanation:
john put 25 dollars in a jar and his wife put 35 dollars in the savings jar as well so save for there trip coming up
Answer:
Sally borrowed twenty-five dollars from Alex to buy a movie at the store. Later, she borrowed another thirty-five dollars to buy ride tickets at the state fair. How much money does she owe Alex?
Step by-step explanation:
When you have an even number of negative numbers in an equation, the answer will always be positive. When there's an odd number of negative numbers, the answer will be negative. For a problem like this, you can ignore the negative signs and focus on the numbers. 25+35 is 60, so Sally owes Alex 60 dollars.
Hope this helps!
2(x-5)=4x+7
solve for x
Answer:
x=-6
Step-by-step explanation:
I NEED THIS NOW! PLZ HELP! 1ST GETS BRAINLIEST! PLZ USE THE 3-READ PROTOCOL
manny has 1/2 of a yard of a fabric with which he intends to make bookmarks. each bookmark is made from 1/8 yard of fabric. how many bookmarks can manny make?
Answer:
Manny can make 4 bookmarks
Step-by-step explanation:
1/2 ÷ 1/8 = ?
(flip the second fraction and multiply)
1/2 x 8/1 = 8/2 = 4
f(x)=2|5x+7|−1, evaluate f(−4)
Answer:
Step-by-step explanation:
f(x) = 2 |5(-4)+7| -1
= 2 |(-20)+7| -1
= 2 | -13 | -1
= 26 - 1
= 25
A function assigns the value of each element of one set to the other specific element of another set. The value of the function f(-4) is 25.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The value of f(-4) can be evaluated by substituting the value of x as -4 in the given function, therefore, the value of f(-4) can be written as,
f(x) = 2|5x+7| − 1
f(-4) = 2|5(-4)+7| − 1
= 2|-20 + 7| - 1
= 2|-13| - 1
= 2(13) - 1
= 26 - 1
= 25
Hence, the value of the function f(-4) is 25.
Learn more about Function here:
https://brainly.com/question/5245372
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3+3+3
Please Help....
Answer:
9
Step-by-step explanation:
Find the value of x.
Answer:
x=21
Step-by-step explanation:
180-126=54
54-12=42
42/2=21
x=21
Find value of x, first gets brain
Answer:
53
Step-by-step explanation:
Find the value of x: