Enter the polnomial function f(x) in standard form given that f has leading coefficient 3 and roots 4, sqrt(2), and -sqrt(2)
Here is a picture of what I mean
Answers
Using the Factor Theorem, the polynomial function that has leading coefficient of 3 and the given roots is given as follows:
f(x) = 3x³ - 12x² - 6x + 24.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule presented as follows.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
a is the leading coefficient of the function f(x), determining if it is positive(a positive) or negative(a negative).
In the context of this problem, the leading coefficient and the roots are given as follows:
f(x) = 3(x - 4)(x - sqrt(2))(x + sqrt(2))
Applying the subtraction of perfect squares, the square root is simplified as follows:
(x - sqrt(2))(x + sqrt(2)) = x² - 2.
Hence the function is defined as follows:
f(x) = 3(x - 4)(x² - 2)
f(x) = 3(x³ - 4x² - 2x + 8)
f(x) = 3x³ - 12x² - 6x + 24.
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
#SPJ1
Related Questions
Seven cards are chosen from a well-shuffled deck of 52 playing cards. In how many selections do at least 3 jacks occur?.
Answers
In 193 selections at least 3 jacks occur.
Combination or permutation?To decide whether to use combination or permutation, we need to look at whether the order matters, as follows:
Order matters: permutation is used.Order does not matter: combination is used.In the context of this problem, the order in which the cards are chosen is not important, hence a combination is used.
The number of combinations of x elements from a set of n elements is given according to the formula presented below.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
There are two cases in which at least 3 jacks occur, as follows, considering that a standard deck has 4 jacks:
3 Jacks selected from a set of 4, and one non Jack card selected from a set of 48.4 Jacks cards from a set of 4.Hence the number of ways to choose the cards is calculated as follows:
[tex]C_{4,3}C_{48,1} + C_{4,4} = 4(48) + 1 = 193[/tex]
A similar problem, also involving combinations, is given at https://brainly.com/question/25821700
#SPJ1
Is this right?
Look at this graph.
What is the equation of the line in slope-intercept form?
Answers
Answer:
I think the answer is (3,10) sorry if I got this wrong!
Step-by-step explanation:
Using coordinates (0,3) for y intercept
Using coordinates to solve (1,6)
y - y1 = m (x - x)
y - 6 = 3 (x - 1)
y - 6 = 3x -3
y = 3x + 3
what is the answer to -9+7x < 47
Answers
The solution of the inequality - 9 + 7x < 47 will be;
⇒ x < 8
What is mean by Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is;
⇒ - 9 + 7x < 47
Now, Solve the expression as;
The inequality is;
⇒ - 9 + 7x < 47
Solve as;
⇒ - 9 + 7x < 47
Add 9 both side;
⇒ - 9 + 7x + 9 < 47 + 9
⇒ 7x < 56
Divide by 7, we get;
⇒ 7x/7 < 56/7
⇒ x < 8
Therefore, The solution of the inequality - 9 + 7x < 47 will be;
⇒ x < 8
Learn more about the inequality visit:
https://brainly.com/question/25275758
#SPJ1
Ryan deposits $775 in an account that pays 4.24% simple interest for four years. Brian deposits $775 in an account that pays 4.24% simple interest for one year.
Answers
The interest earned by Ryan is $131.44 and the interest earned by Brian is $32.86 .
In the question,
it is given that
amount deposited by Ryan = $775
time for which the amount is deposited = 4 years
rate at which the amount is deposited = 4.24%
So the simple interest = (p*r*t)/100
= (775 * 4.24*4 ) /100
= 13144/100
= 131.44
amount deposited by Brian = $775
time for which the amount is deposited = 1 years
rate at which the amount is deposited = 4.24%
So the simple interest = (p*r*t)/100
= (775 * 4.24 * 1 ) /100
= 3286/100
= 32.86
Therefore , the interest earned by Ryan is $131.44 and the interest earned by Brian is $32.86 .
The given question is incomplete , the complete question is
Ryan deposits $775 in an account that pays 4.24% simple interest for four years. Brian deposits $775 in an account that pays 4.24% simple interest for one year. Find the interest earned by both Ryan and Brian ?
Learn more about Interest here
https://brainly.com/question/19091875
#SPJ1
Suki has placed $800 in an account that pays 4 percent interest compounded quarterly. at the end of two years (eight quarters), the balance in the account will be $ 0.08 . that means suki will have earned $ in interest during that time. (round your answers to the nearest cent.) what will be the balance in the account at the end of two years (eight quarters)? how much interest will suki have earned during that time? (round your answers to the nearest cent.)
Answers
The balance in the account at the end of two years is $864.
The interest earned by Suki during that time is $64.
The initial principal amount "P" is $800.
The interest rate "R" is 4%.
The interest is compounded quarterly.
This means the value of "n" is 4.
The time period for which the interest is earned is 2 years.
The formula for compound interest is :
A = P*[1 + (R/n)]^(n*t)
A = 800*[1 + (0.04/4)]^(4*2)
A = 800*[1 + 0.01]^(4*2)
A = 800*[1.01]^(8)
A = 800*1.08
A = 864
The total interest earned is the final amount minus the principal amount.
The total interest earned is $864 - $800.
The total interest earned is $64.
Learn more about interest here:
https://brainly.com/question/13324776
#SPJ4
f(x)=5x+10 solve when f(x)=20
Answers
When f(x) = 20
Then
5x + 10 = 20
Therefore
5x=20-10=10
x = 10 / 5 = 2
x= 2
Find the inverse of f(x) = 12x - 3
Answers
ANSWER
[tex]f^{-1}(x)\text{ = }\frac{y}{12}+\frac{1}{4}[/tex]EXPLANATION
We want to find the inverse of the function given:
f(x) = 12x - 3
First, replace f(x) with y:
y = 12x - 3
Now, make x the subject of the function:
y + 3 = 12x
[tex]\begin{gathered} \Rightarrow\text{ x = }\frac{y}{12}\text{ + }\frac{3}{12} \\ x\text{ = }\frac{y}{12}\text{ + }\frac{1}{4} \end{gathered}[/tex]Now, replace x with f-1(x) and y with x:
[tex]f^{-1}(x)\text{ = }\frac{y}{12}+\frac{1}{4}[/tex]That is the inverse function.
This shape is made up of one half-circle attached to a square with side lengths 11 inches. You can use 3.14 as an approximation for π. help i don't know it
Answers
The approximate perimeter of the entire shape is 50.27 inches.
How to find the perimeter of a figure?The perimeter of a figure is the sum of the whole sides of the figure.
Therefore, the perimeter of the entire shape can be calculated as follows:
The shape is made of three sides of a square and half a circle.
Therefore,
circumference of the semi circle = πr
r = 11 / 2 = 5.5 inches
circumference of the semi circle = 5.5π
Hence,
perimeter of the shape = 11 + 11 + 11 + 5.5π
perimeter of the shape = 33 + 5.5(3.14)
perimeter of the shape = 33 + 17.27
Therefore,
perimeter of the shape = 50.27 inches
learn more on perimeter here: https://brainly.com/question/5550237
#SPJ1
A tissue factory produces 3,876 tissues a day. How many tissues does it produce after 7 days?
Answers
Answer:
27,132 tissues
Step-by-step explanation:
if it produces 3,876 tissues a day, and a week has 7 days, then the answer would be 3,876 x 7=27,132 tissues
Answer:
27132 tissues
Step-by-step explanation:
everyday 3876 tussues are made
so the equation would be 3876×7 to get how many tissues are made in 7 days
A contractor purchases 7 dozen pairs of padded work gloves for $99.96 . She incorrectly calculates the unit price as $14.28
per pair for the expense report. What is the correct unit price? What is the error?
Answers
The cost or unit price for purchasing each pair of work gloves is $1.19.
The cost of 7 dozen pairs of padded work gloves purchased by the contractor is $99.96.
The incorrect unit price calculated by the contractor is $14.28 per pair.
Now, we know 1 dozen is equal to 12 units.
Therefore,
The number of pairs of gloves purchased = 7 × 12 = 84
As the total cost is $99.96, the cost of each pair will be:
= $99.96 ÷ 84
= $1.19
The error by the contractor was that she didn't consider the word dozen in his calculation. She simply divided the total cost by 7 to calculate the price per pair.
The unit price of purchasing each pair of work gloves is $1.19.
Learn more about unit price here:
brainly.com/question/14286952
#SPJ1
What are the terms of each expression?
4x + 3z
Answers
Answer:
4x and 3z are the only 2 terms in this esxpression.
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.964.
What percent of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers?
Answers
The correlation coefficient between the number of volunteers x and the number of bags of trash collected y, so the percentage of variation in the number of bags of trash collected is 92.92 %.
What is the Correlation coefficient?You may gauge how closely two variables are related by looking at their correlation coefficients. Pearson's correlation coefficient is the most often used of the several correlation coefficient types. Often employed in linear regression, Pearson's correlation (also known as Pearson's R) is a correlation coefficient. It's likely that you'll learn about Pearson's R first if you're just getting started in statistics. Actually, Pearson's is typically mentioned when someone mentions the correlation coefficient.
According to the question,
The correlation coefficient i.e., r between x and y is 0.964.
r = 0.964
Squaring on both sides :
r² = 0.964²
r² = 0.9292
Now, convert this into percentage form by multiplying it will 100.
⇒0.9292 × 100
= 92.92 %.
Hence, the percentage of the variation will be 92.92 %.
To get more information about the correlation coefficient :
https://brainly.com/question/15577278
#SPJ1
annarose read 93.50 books in 8.5 months. Her favorite book is the outsiders. At that rate how many books does she expect to read annually?
number sentence 1:
number sentence 2:
Answers
At the unit rate of reading 93.5 books in 8.5 months, Annarose expects to read 132 books annually.
What is the unit rate?The unit rate is the ratio or speed that Annarose reads books.
From her established unit reading rate, she reads 11 books in a month.
The unit rate is computed by ensuring that the denominator becomes 1 after the division operation.
The number of books she read in 8.5 months = 93.5 books.
The number of books she can read in 1 month = 11 books (93.5/8.5).
The number of books she can read in 12 months = 132 books (11 x 12).
Thus, given Annarose's reading unit rate, she expects to read 132 books annually, at an average of 11 books every month.
Learn more about the unit rate at brainly.com/question/4895463
#SPJ1
Juan Fuentes is a computer programmer. His annual salary is
$32,190.00. Benefits he receives consist of $1,881.73 in vacation time,
holidays worth $1,287.60, health insurance premiums of
$2,300.00 paid by the employer, Social Security of $1,995.78,
Medicare of $466.76, and unemployment insurance of $541.06.
a. What are the total benefits?
b. What is the rate of benefits?
Answers
In linear equation,$7185.33 is the total benefits.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.the total benefits of Juan Fuentes = $1,881.73 + $2,300.00 + $1,995.78 +
$466.76 + $541.06
= $7185.33
the rate of benefits of Juan Fuentes = $1,287.60
Learn more about linear equation
brainly.com/question/11897796
#SPJ13
Calculate rates (backwards)
If you pay $60 for bulk rice, at $4.00 / kg, how many kilograms can you buy?
Answers
Answer:
15kg
Step-by-step explanation:
$60 divide by $4 kg
60/4=15
f(x)=√x+11. Find the inverse of f(x).
O A. f¹(x) = x³ – 11
O B. f¹(x) = (x - 11)³
O c. f¹(x) = x³ + 11
O D. f¹(x) = (x +11)³
Answers
Answer: Your answer would be C: f¹(x) = x³ + 11
Give the domain and range of each relation below. (help please)
Answers
Answer:
Domain is (-infinity, infinity), range is (-infinity, 0]
Step-by-step explanation:
The x values are infinite on both sides, but the y values are not. Let me know if you want me to explain more :)
how much will Yoona charge to walk 8 dogs
Answers
Yoona will charge $20.75 to walk 8 dogs based on the trend of Yoona charges to walk dogs.
How to find the amount to be charged?First, find the pattern in the amount that Yoona charges to walk each additional dog.
Additional cost to walk 2 dogs:
= 40 - 37.25
= $2.75
Additional cost to walk 3 dogs:
= 37.25 - 34.50
= $2.75
Additional cost to walk 4 dogs:
= 34.50 - 31.75
= $2.75
Every extra dog therefore leads to a fall in price by $2.75. For eight dogs, Yoona would charge:
= 40 - (7 x 2.75)
= 40 - 19.25
= $20.75
Find out more on cost to walk dogs at https://brainly.com/question/24523218
#SPJ1
On the 1:1000 scale plan, the length and width of the house are drawn as 2 cm and 1.5 cm.
a. Find the actual size.
6. Find the ratio of the area of the foundation of the house to the area on the floor plan.
Answers
Answer:
a. Actual size: 20 m x 15m
b. 1,000,000 : 1
Step-by-step explanation:
(a) Since scale is 1:1000, multiply both length and width on the floor pan to get actual length and width of house
a. Actual size
= 2 x 1000 cm x 1.5 x 1000 cm
= 2000 cm x 1500 cm
= 20m x 15m (since 1 m = 100 cm
(b) Area on plan = 2 x 1.5 = 3 cm²
Actual area = 2000 x 1500 = 3,000,000 cm²
Ratio of actual area to floor plan area
= 3,000,000 / 3 = 1,000,000 : 1
The graph of function f is shown.
Which statement correctly compares the two functions?
A. They have the same x- and y-intercepts.
B. They have the same x-intercept and the same end behavior as x approaches ∞.
C. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
D. They have the same y-intercept and the same end behavior as x approaches ∞.
Answers
In the picture, there is a graph and table. It displays the graph of the function f. Option C is correct, As x approaches, they have different x- intercept and y-intercepts but the same end behavior∞.
Given that,
In the picture, there is a graph and table.
It displays the graph of the function f.
Which of the two statements compares the two functions correctly.
A. Their x- and y-intercepts are identical.
B. As x gets closer to, they exhibit the same x-intercept and end behavior∞.
C. As x approaches, they have different x- and y-intercepts but the same end behavior∞.
D. As x gets closer to, they exhibit the same y-intercept and end behavior∞.
So, from the given table and graph we get
Option C is correct.
Therefore, Option C is correct.
To learn more about intercept visit: https://brainly.com/question/14180189
#SPJ1
A side of the triangle below has been extended to form an exterior angle of 156°. Find
the value of x.
Answers
The value of x of angle ∠C is 66°.
What are angles?An angle is a figure formed by two rays or lines that have the same endpoint in plane geometry. The Latin word "angulus," which means "corner," is where the word "angle" originates. The common endpoint of the two rays—known as the vertex—is referred to as an angle's sides. Depending on the measurement, there are various angles in geometry. Basic angles are identified by their names: acute, obtuse, right, straight, reflex, and full rotation.So, the value of x:
As we can see that A is a straight angle. Then ∠BAC will be:
156 + ∠BAC = 180∠BAC = 180 - 156∠BAC = 24°Now, we know that in △ABC, ∠A = 24° and ∠B = 90° (Given), then ∠C will be:
x + ∠A + ∠B = 180x + 24 + 90 = 180x + 114 = 180x = 180 - 114x = 66Therefore, the value of x of angle ∠C is 66°.
Know more about angles here:
https://brainly.com/question/25716982
#SPJ9
graph a linear function is shown.
Which word describes the slope of the line?
O positive
O negative
O zero
O undefined
Answers
Word (C) zero describes the slope of the line of the given graph of the linear function.
What is a graph of a linear function?Function in Linear A straight line on the graph has the expression or formula y = f(x) = px + q. One independent and one dependent variable are present. X and Y are the independent and dependent variables, respectively. P is the y-intercept or constant term, and it also represents the value of the dependent variable.So, we can infer from the provided graph that its equation is:
y = -3Which is also readable as:
y = 0 × x - 5Putting it into comparison with the slope-intercept form:
y = mx + bWe will obtain a slope of 0.
Therefore, word (C) zero describes the slope of the line of the given graph of the linear function.
Know more about the graph of a linear function here:
https://brainly.com/question/27976867
#SPJ9
The correct question is given below;
graph a linear function is shown.
Which word describes the slope of the line?
A. positive
B. negative
C. zero
D. undefined
Estimate the difference by rounding each number
to the nearest hundredth: 0.076 -0.011
A 0.08
B 0.06
C 0.05
D 0.07
Answers
Answer:
answer is D= 0.07
Step-by-step explanation:
The equation:
0.076 - 0.011
By rounding to the nearest hundredth
0.076 = 0.08
0.011 = 0.01
=0.08-0.01
=0.07
Let the graph of g be a translation 2 units left and 1 unit down, followed by a reflection in the y -axis of the graph of f(x)=(2x+1)^2-4 . Write a rule for g .
Answers
The rule for the function g(x) is (2x + 5)² - 5.
We are given a function f(x). The function f(x) is defined as given below :
f(x) = (2x + 1)² - 4
A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.
We first need to do a translation with 2 units left.
The translation is given by f(x + 2).
f(x + 2) = (2x + 5)² - 4
We now need to do a translation with 1 unit downwards.
The translation is given by f(x + 2) - 1.
f(x + 2) - 1 = (2x + 5)² - 4 - 1
f(x + 2) - 1 = (2x + 5)² - 5
The definition of the function is given below :
g(x) = (2x + 5)² - 5
To learn more about functions, visit :
https://brainly.com/question/12431044
#SPJ1
Find the missing number so that the equation has no solutions.
2 x + 4 = – 3 x – 18 + blank x
Answers
The value of x in the equation given is x = -4.4
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.
In this case, the value will be expressed by subtracting the variables that are given in order to get the other term. This will be:
2x + 4 = -3x - 18
Collect like terms
2x + 3x = -18 - 4.
5x = -22
Divide
x = -22 / 5
x = -4.4
This illustrates the concept of equations.
Learn more about equations on
brainly.com/question/2972832
#SPJ1
Scarlett sells designer ponchos. The revenue, RRR, she makes from selling a batch of nnn ponchos is given by the function R(n)=20nR(n)=20nR, left parenthesis, n, right parenthesis, equals, 20, n, and the expenses, EEE, that she incurs from producing a batch of nnn ponchos is given by the function E(n)=10\cdot \sqrt{n}E(n)=10⋅
n
E, left parenthesis, n, right parenthesis, equals, 10, dot, square root of, n, end square root.
Let PPP be the total profit Scarlett makes from producing and selling a batch of nnn ponchos.
Write a formula for P(n)P(n)P, left parenthesis, n, right parenthesis in terms of R(n)R(n)R, left parenthesis, n, right parenthesis and E(n)E(n)E, left parenthesis, n, right parenthesis.
P(n)=P(n)=P, left parenthesis, n, right parenthesis, equals
Write a formula for P(n)P(n)P, left parenthesis, n, right parenthesis in terms of nnn.
Answers
Scarlett should sell more than ¼ of batch of ponchos to make the profit.
Given,
The revenue made by Scarlett from selling batch of ponchos, R = 20n
The expenses she incurs from producing a batch of ponchos, E = 10√n
The total profit, P = R - E
= 20n - 10√n
Now,
Profit is earned when Revenue > Expenses
20n > 10√n
÷10 ÷10
2n > √n
(2n)² > (√n)²
4n² > n
4n² - n > 0
n(4n - 1)> 0
n > 0 and 4n - 1 > 0
n > 1/4
That is, Scarlett should sell more than ¼ of batch of ponchos to make the profit.
Learn more about profit here:
https://brainly.com/question/11851506
#SPJ1
Point-slope form: y minus y 1 = m (x minus x 1).
Use the point-slope form of a line to write the equation of a line that has a slope of 2 and passes through the point (–4, 3). Write the equation in slope-intercept form.
Choose the equation of the line.
y = 2x – 7
y = 2x + 11
y = –4x + 14
y = 3x +14
Help me please!!
Answers
simplify the expression (0.25 to the power of 3)5 using a single whole-number exponent help me
Answers
Using exponent properties, we can rewrite the expression using a single whole-number exponent as:
(0.25³)⁵ = 0.25¹⁵
How to simplify the given expression?Here we have the numerical expression:
(0.25³)⁵
Here we need to use the exponent property:
(xᵃ)ᵇ = xᵃ*ᵇ
Using that in our expression, we will get:
(0.25³)⁵ = 0.25³*⁵ = 0.25¹⁵
So we already have a single whole-number exponent, we can also rewrite:
0.25¹⁵ = (1/4)¹⁵
Learn more about exponents:
https://brainly.com/question/11975096
#SPJ1
The area of a circle is 25 pi ft 2.
Answers
How do I find simple interest? I am currently working on a CYU that requires this information. Thank you!
Answers
think of all the things s you like
