Answer:
12
Step-by-step explanation:
-4 + 4 = 0
0 + 8 = 8
4 + 8 = 12
Find a polynomial function of degree 3 with real coefficients and the numbers 6, 3i as some of its zeros.
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].
PLEASE HELP AS FAST AS YOU CAN ASAP DUE IN 30 MINUTES!!!!
the prism is made up of unit cubes. the side length of the unit cube is 1/4 inch
what us the volume of the prism
A. 3/8
B. 8
C. 24
D. 1/64
please explain as well
Answer:
C
<$&#&#;#;#;#;#
Step-by-step explanation:
1/4= 4x6=24
Answer:
C
Step-by-step explanation:
Simplify -51/4-(-71/2). Which of the following is correct
Answer:
91/4 as a fraction, 22.75 as a decimal
Step-by-step explanation:
(-51/4) - (-71/2)
=
(-51/4) + (71/2)
=
(-51/4) + (142/4)
=
(-51+142/4)
=91/4
Your answer is 91/4. The decimal version is 22.75. Hope this helps :)
write 1/64^2 using a negative exponent
▪ Answer:
2^(-12)
▪ Step-by-step explanation:
Hi there!
1/64^2 =
= 1/(2^6)^2
= 1/2^12
= 2^(-12)
Good luck !
use
(a^b)^c = a^(b×c)
1/a^b = a^(-b)
THIS IS URGENTTDetermine whether each table represents a function. Select Function or Not a Function for each table.
Answer:
1st table: Not a function
2nd table: Function
3rd table: Not a function
4th table: Function
Step-by-step explanation:
The functions pass the verticle line test
meaning, there is only one x value for any y value
What do numbers have a difference of 8
Answer:
20-12=8
here it is the difference is 8.
what is the slope of the line
Answer:
M=[tex]-\frac{3}{4}[/tex]
Step-by-step explanation:
M=[tex]\frac{rise}{run}[/tex]
From left to right, the line goes down. Therefore, it is a negative slope.
[tex]-\frac{3}{4}[/tex]
i already know the answer can someone explain or show me how to do it on a numberline
Answer:
I'm not sure what the question is but an example question could be
"Take 5 away from 3."
For this you would go to three on the number line and then move left five gaps. You would land on -2
another example: "Add 4 to -3."
For this, you would go to -3 on the number line, and then move right 4 times. you would land on 1.
Answer:
4.5
Step-by-step explanation:
just move 1 1/2 steps to the left
D is the midpoint of CE and EC = 18. Find the length of DE
Answer:9
Step-by-step explanation:
23.85 + 7.42 + 16.15
Answer:
47.42
Step-by-step explanation:
Try solving this way
23.85
+07.42
+16.16
=======
47.42
Choose a true statement.
g(x) is not a function because f(x) is not a
function.
O g(x) is not a function because f(x) is not one-
to-one.
O g(x) is a function because f(x) is one-to-one.
O g(x) is a function because f(x) is not one-to-
one.
Answer: c
Step-by-step explanation:
The correct statement is that g(x) is a function because f(x) is one-to-one.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
We know a function f(x) has its inverse g(x) if and only if f(x) is a one-to-one function.
From the given statements the only true statement is, g(x) is a function because f(x) is one-to-one.
learn more about inverse functions here :
https://brainly.com/question/14627458
#SPJ6
state which of the following sets of ordered pairs represents a function. Please pick the best option
Set A: (5, 2), (4, 3), (3, 4), (2, 5) Set B: (-1, -6), (0, 2), (1, 2), (3, 6)
Set B: (-1, -6), (0, 2), (1, 2), (3, 6)
Set C: (2, 1), (4, 2), (2, 3), (8, 4)
a. Set C
b. Set B
c. Set A
d. Set A and Set B
I would really appreciate it if you could help me out!
Answer:
set A and set B...it is the best and right option bro...option c is wrong because 2 elements of domain has relation with 1 range
Which phrase matches the algebraic expression below? (1 point)
3(x + 7) + 10
Answer:
Add 10 to three times the value of x minus 7.
Step-by-step explanation:
Answer:
Three times the difference of X and seven plus ten
Step-by-step explanation:
Can somebody pls answer these three questions ASAPPPP!!!!
Answer:
1) x = 3/2 2) x = 6 3) x = 3
Step-by-step explanation:
For Number 1:
4(x+8)−4=34
Step 1: Simplify both sides of the equation.
4(x+8)−4=34
(4)(x)+(4)(8)+−4=34(Distribute)
4x+32+−4=34
(4x)+(32+−4)=34(Combine Like Terms)
4x+28=34
Step 2: Subtract 28 from both sides.
4x=6
Step 3: Divide both sides by 4.
4x/4 = 6/4
x = 3/2
For Number 2:
2/3(9+x)=−5(4−x)
Step 1: Simplify both sides of the equation.
6 + 2/3x = −20+5x
Step 2: Subtract 5x from both sides.
−13 /3 x+6=−20
Step 3: Subtract 6 from both sides.
-13/3x = -26
Step 4: Multiply both sides by 3/(-13)
x = 6
For Number 3:
−3(x+4)+15=6−4x
Step 1: Simplify both sides of the equation.
−3(x+4)+15=6−4x
(−3)(x)+(−3)(4)+15=6+−4x(Distribute)
−3x+−12+15=6+−4x
(−3x)+(−12+15)=−4x+6(Combine Like Terms)
−3x+3=−4x+6
−3x+3=−4x+6
Step 2: Add 4x to both sides.
−3x+3+4x=−4x+6+4x
x+3=6
Step 3: Subtract 3 from both sides.
x+3−3=6−3
x = 3
How long is the blue ribbon if the red ribbon is 12 inches
Answer:
can I have more info plz
Karen scored a 76 on an exam meaning is 74 and one standard deviation of eight. Find her Z score.
Answer:
0.25
Step-by-step explanation:
(76-74)/8
=2/8
=1/4
=0.25
Cuál es el 30% de 100.000?
Porfaaaaaa ayudenmeeeeeee
Answer:
30
Step-by-step explanation:
make a table and graph the solutions of each equation y=3x+1
Answer:
i can't graph it but i'll give you the points to graph
Step-by-step explanation:
(-2, -5) (-1,-2) (0,1) (1,4) (2,7)
start at the point in bold
Task: Use the following situation to answer Parts A and B Instructions At noon, a tank contains 100 gallons of water. The table shows the input and output of water from pipes A, B, and C. The pipes begin operating simultaneously at noon. A B C Pipe Flow IN (gallons per minute) a (2) = 172 6(2) = 80 Flow OUT (gallons per minute) c (2)=30r Complete each of the 2 activities for this Task. Activity 1 of 2 Let T (2) represent the amount of water in the tank x minutes after all of the pipes A, B, and C are opened. Which of the following functions represents T (x)? O A T (2) = 100 + a(z) +b(2) - c(x) OCT (x) = 100 + a (x) +b(2) + c(2) OBT () = a (x) + b() +(2) ODT (2) = a (x) +b(x) - c(:) Activity 2 of 2 Using the equation, after how many minutes will the tank be empty?
Answer:
See referenced question
Step-by-step explanation:
Refer to this answer:
https://brainly.com/question/18638278Attached is the question in original form
What is the apparent range of the function of x shown?
A) The set of all real numbers greater than or equal to 1
B) The set of all real numbers less than or equal to 1
C) The set of all real numbers greater than or equal to 4
D) The set of all real numbers
(PLEASE LOOK AT THE PICTURE BEFORE ANSWERING)
Brian May, guitarist for Queen, does not know how to price his signature Antique Cherry Special that cost him £340 to make. He knows he wants 80% markup on cost. What price should Brian May ask for the guitar?
9514 1404 393
Answer:
£612
Step-by-step explanation:
If Brian wants to add 80% of the cost to the cost, the selling price will be ...
£340(100% +80%) = £340·1.80 = £612
Brian May should ask £612 for the guitar.
I WILL GIVE BRAINLIEST
All of the following statements describe the relation shown except _____.
The diagram represents a function.
The inputs are {-1, 0, 3, 4}.
The outputs are {-2, -1, 1}.
This relation could also be represented as {(-1, 1), (0, -2), (3, 1), (4, -1)}.
Answer:
132
Step-by-step explanation:
Answer:
{-1, 0, 3, 4}.
Step-by-step explanation:
sorry if this is incorrect
In the inequality -2|2x-3|>-12, what is the range for x?
9514 1404 393
Answer:
-3/2 < x < 9/2
Step-by-step explanation:
You can divide the inequality by -2, then rewrite as a compound inequality:
|2x -3| < 6
-6 < 2x -3 < 6
Add 3 and divide by 2:
-3 < 2x < 9
-3/2 < x < 9/2
Mid point between (0,0) (11,9)
9514 1404 393
Answer:
(5.5, 4.5)
Step-by-step explanation:
The midpoint coordinates are the average of the end point coordinates.
((0, 0) +(11, 9))/2 = (11, 9)/2 = (5.5, 4.5) . . . midpoint
For a continuous random variable X, P(23 ≤ X ≤ 66) = 0.25 and P(X > 66) = 0.14. Calculate the following probabilities. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)
Complete question :
For a continuous random variable X, P(23 ≤ X ≤ 66) = 0.25 and P(X > 66) = 0.14. Calculate the following probabilities. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)
a. P(X < 66)
b. P(X < 23)
c. P(X = 66)
Answer:
P(X < 66) = 0.86
P(X < 23) = 0.61
P(X = 66) = 0
Step-by-step explanation:
Given that:
X, P(23 ≤ X ≤ 66) = 0.25 and
P(X > 66) = 0.14 ;
Recall:
P(x ≤ a) + p(x ≥ a) = 1
Then ; P(X < 0.66) = 1 - 0.14 = 0.86
Hence,
P(X < 0.66) = 0.86
P(23 ≤ X ≤ 66) = 0.25
P(X < 66) = 0.86
Hence,
P(X < 23) = 0.86 - 0.25 = 0.61
Probability that a continuous random variable is exactly equal to a particular number equals 0
Hence,
P(X = 66) = 0
How many significant figures are in the number: 9003
Answer:
4
Step-by-step explanation:
Ava read an article claiming that 10% of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225 people from her city to test H0 : p = 0.10, where p is the proportion of people in her city that are senior citizens. Ava found that approximately 14% of those sampled were senior citizens. She conducted an appropriate significance test, and the resulting test statistic was z ≈ 1.89z. Assume that the conditions for inference were met.
Complete Question
Ava read an article claiming that 10% of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225 people from her city to test H0 : p = 0.10, where p is the proportion of people in her city that are senior citizens. Ava found that approximately 14% of those sampled were senior citizens. She conducted an appropriate significance test, and the resulting test statistic was z ≈ 1.89 z. Assume that the conditions for inference were met.calculate the p-value for Ellie's significance test
Answer:
The p-value is [tex]p-value = 0.0588[/tex]
Step-by-step explanation:
From the question we are told that
The percentage of senior citizens is p = 0.10
The sample size is [tex]n = 225[/tex]
The sample proportion is [tex]\^{p} = 0.14[/tex]
The test statistics is [tex] z \approx = 1.89[/tex]
The null hypothesis is [tex]H_o : p = 0.10[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.10[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(Z > 1.89 )[/tex]
From the z-table
[tex]P(Z > 1.89 ) = 0.029379[/tex]
=> [tex]p-value = 2 * 0.029379[/tex]
=> [tex]p-value = 0.0588[/tex]
Answer:
No because 0.06>0.05
Step-by-step explanation:
kahn
Which equation is equivalent to the given equation?
–8(x + 13) = 2(x - 7) + 4x
Answer: Is C
-8x-104=6x-14
Step-by-step explanation: I got the question right
Answer: -8x - 104= 6x - 14
Step-by-step explanation:
-8(x+13) =2(x-7) + 4x
-8x - 104 = 2X - 14 + 4x
-8x - 104 = 6x - 14
Select the correct answer. The steps for solving the given equation are shown below. 8-3x=20 Select the correct equation for the missing step in the table.
Answer:
C
Step-by-step explanation:
Multiplying by the reciprocal is the same as division.
Answer:
its actually (b) addition property of equality
Step-by-step explanation:
i got the answer correct on edmentum
The manufacturer of a soccer ball claims that only 3% of the soccer balls produced are faulty. An employee of this company examines the long-run relative frequency of faulty soccer balls produced as shown in the graph.
A graph titled Faulty Soccer Balls has frequency on the x-axis, and probability on the y-axis. The graph levels out around y = 0.06.
Which conclusion can be drawn from this graph?
The company’s claim seems to be true because the graph shows that when 50 soccer balls were tested, only about 3% of them were faulty.
We should not believe the company’s claim that only 3% of their soccer balls are faulty because this graph shows a continuous increase in probability.
Because the graph shows that the probability of producing a faulty soccer ball is 0.03, we can believe the company’s claim that only 3% of the produced soccer balls are faulty
The graph shows that the probability of producing a faulty soccer ball is about 0.06; therefore, we should not believe the company’s claim that only 3% of the produced soccer balls are faulty.
Answer:
The answer is D
Step-by-step explanation:
Answer:
D. The graph shows that the probability of producing a faulty soccer ball is about 0.06; therefore, we should not believe the company’s claim that only 3% of the produced soccer balls are faulty.
Step-by-step explanation: