Given that a polynomial function [tex]f(x)[/tex] has,
leading coefficient= 2roots = 2 , √3 , -√3And we need to find [tex]f(x)[/tex]
as we know that if a polynomial has zeroes as [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the cubic polynomial is given by,
[tex]\longrightarrow f(x)=k (x-\alpha)(x-\beta)(x-\gamma)\\ [/tex]
where ,
k is the leading coefficient.Now substitute the given zeroes, as ;
[tex]\longrightarrow f(x)=2[ (x-2)(x-\sqrt3)(x+\sqrt3)]\\ [/tex]
[tex]\longrightarrow f(x)= 2[(x-2)\{ x^2-(\sqrt3)^2\}][/tex]
[tex]\\\longrightarrow f(x)= 2[ (x-2)(x^2-3)]\\ [/tex]
[tex]\longrightarrow f(x)=2[ x(x^2-3)-2(x^2-3)]\\ [/tex]
[tex]\longrightarrow f(x)= 2[ x^3-3x -2x^2+6]\\ [/tex]
[tex]\longrightarrow \underline{\underline{ f(x)= 2x^3-4x^2-6x+12}}[/tex]
and we are done!
Answer:
[tex]f(x)=2x^3-4x^2-6x+12[/tex]
Step-by-step explanation:
Given characteristics of the polynomial:
leading coefficient = 2roots = 2, √3, and -√3.As the polynomial has 3 roots, it is a cubic polynomial.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a cubic polynomial}\\\\$y=a(x-r_1)(x-r_2)(x-r_3)$\\\\where:\\ \phantom{ww}$\bullet$ $r_n$ are the roots. \\ \phantom{ww}$\bullet$ $a$ is the leading constant.\\\end{minipage}}[/tex]
Substitute the given leading coefficient and roots into the formula:
[tex]f(x)=2(x-2)(x-\sqrt{3})(x+\sqrt{3})[/tex]
Expand to standard form:
[tex]\implies f(x)=2(x-2)(x+\sqrt{3}x-\sqrt{3}x-3)[/tex]
[tex]\implies f(x)=(2x-4)(x^2-3)[/tex]
[tex]\implies f(x)=2x^3-6x-4x^2+12[/tex]
[tex]\implies f(x)=2x^3-4x^2-6x+12[/tex]
The graph of g shows the percent of battery power remaining on a laptop after it is turned on. The function f(x)=0.75-0.125x represents the percent (in decimal form) of battery power remaining on a tablet x hours after it is turned on. Which device stays on longer?
By finding the x-intercepts of the two linear functions, we can see that the laptop can stay on for 5 hours and the tablet for 6 hours, so the tablet can stay on for longer.
Which device stays on longer?We know that g(x) shows the percent of battery power on a laptop, and on the graph we can see that it becomes zero at x = 5 hours, so the laptop can stay on for 5 hours.
We also know that linear function f(x) shows the battery of a tablet, the function is:
f(x) = 0.75 - 0.125*x
The value will be zero when the tablet runs out of battery, so we can solve:
0 = 0.75 - 0.125*x
0.125*x = 0.75
x = 0.75/0.125= 6
So the tablet can stay on for 6 hours, we conclude that the tablet can stay on longer.
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Lera comes to the swimming pool once every 12 days. victor comes every 4 days and oksana comes every 10 days. last monday, all three were at the pool. in how many days will they all be at the pool again?
The three Lera, Victor and Oksana will meet in the pool again in 60 days
How to find the how many days will they all be at the pool again?The question is solved using the concept of Least common multiple: The Least common multiple refers to the least multiple that 12, 10, and 4 have in common
How to get the least common multiple LCMwe therefore solve the LCM as follows
2 | 12, 4, 10
2 | 6, 2, 5
3 | 3, 1, 5
5 | 1, 1, 5
| 1, 1, 1
= 2 * 2 * 3 * 5
= 60
From the calculation the numbers 4, 10, 12 have a least common multiple of 60. Therefore the Lera, Victor and Oksana will meet in the swimming pool 60 days.
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Starting at noon, Fatoumata observed the amount of snow on her lawn during a blizzard. She wrote an equation to represent ss, how many inches of snow were on the lawn: s=8+0.01xs=8+0.01x, where xx represents the number of minutes past noon. What is the meaning of the ss-value when x=1x=1?
The value of the inches of snow in 1 minute is 8.01 inches.
What is a expression?It should be noted that an expression is important to show the relationship between the variables.
In this case, the expression is given as:
s = 8 + 0.01x
where x = the number of minutes past noon.
s = inches of snow.
In this case, when x = 1, the value will be
s = 8 + 0.01x
s = 8 + 0.01(1)
s = 8.01
The snow is 8.01 inches.
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Answer:
Step-by-step explanation:
he value of the inches of snow in 1 minute is 8.01 inches.
What is a expression?
It should be noted that an expression is important to show the relationship between the variables.
In this case, the expression is given as:
s = 8 + 0.01x
where x = the number of minutes past noon.
s = inches of snow.
In this case, when x = 1, the value will be
s = 8 + 0.01x
s = 8 + 0.01(1)
s = 8.01
The snow is 8.01 inches.
help i need help ASAP pleeeeeeeeeeeeeeees
Answer:
Step-by-step explanation:
a linear equation of a line that is parallel to 2y-6x=6 and crosses through point (0,3)
evelyn won an election by a ratio of 6 to 5. if she received 7,230 votes, how many votes did her opponent receive?
6025 were the votes recieved by her opponent.
What is a ratio ?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
CalculationDivide the votes she received by the 6 parts of the ratio to find the value of one part of the ratio, that is
7230 ÷ 6 = 1205 ← value of 1 part of ratio
Her opponent received 5 parts, thus
votes received by opponent = 5× 1205 = 6,025
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find the missing number for 6hrs
Answer:
$51
Step-by-step explanation:
You just times $8.50 with 6
6x+5=8+6x
Please help me asap!
Answer:
This equation has no answer. Since both variables are the same
Step-by-step explanation:
6x + 5 = 8 + 6x
6x = 3 + 6x
if we subtract the 6x from eachother we get
0 ≠ 3 which is incorrect
Rewrite 15x^4y^3 - 45x^3y^4 using a common factor
help fast pls
Answer: 15x^3y^3 (x-3y)
Step-by-step explanation:
To get the greates common factor (or GCF) you
In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).
The number of times that each prime divides the original integer becomes its exponent in the final result.
In our example,
Prime number 3 to the power of 1 equals 3 .
The number of times that each prime divides the original integer becomes its exponent in the final result.
In our example,
Prime number 3 to the power of 2 equals 9.
Damian has a points card for a movie theater.
He receives 20 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs 195 points for a free movie ticket.
Which equation could be used to determine vv, the number of visits Damian must make to earn a free movie ticket? I need just the equation alright
The equation that could be used to determine v, the number of visits Damian must make to earn a free movie ticket is 20 + 12.5v = 195
How to calculate the equation?Based on the information, the following can be illustrated:
He receives 20 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs 195 points for a free movie ticket.
The equation will be:
20 + (12.5 × v) = 195
20 + 12.5v = 195
where v = number of visit
The equation is 20 + 12.5x = 195
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Because of the high cost of living, Kathlego, Tessa, and Zane each hold down two jobs, but no
two have the same occupation. The occupations are doctor, engineer, teacher, lawyer, writer
and painter
Kathlego, Tessa, and Zane all work two jobs to make ends meet due to the high cost of living.
The attorney and painter is Kathlego.
Tessa is a doctor and an engineer.
The educator and author is named Zane.
Given that,
Kathlego, Tessa, and Zane all work two jobs to make ends meet due to the high cost of living, however there are both work in the same field. Doctor, engineer, teacher, lawyer, painter, and writer are among the professions.
As soon as we realize that Zane "is not the doctor," we immediately rule off that possibility and move on to the other professions.
Given that "Zane beat Tessa and the painter at tennis," we can infer that Tessa and the painter are no longer together, which makes Kathlego the Painter.
We currently have.
Kathlego is an painter.
We can now go on to "The painter was engaged by the doctor to do the task." The fact that Zane is not the doctor and we know the painter is Kathlego gives us a huge hint. Tessa is therefore unquestionably a doctor.
We currently have:
A painter, Kathlego.
Tessa is a engineer.
We may now infer that the person is one and the same because we have "The teacher and the writer went fishing with Kathlego." We can rule out Kathlego and Tessa as the teacher and writer because they each have two jobs. Thus, we are left to assume that Zane is the instructor and author.
We currently have:
A painter, Kathlego.
Tessa is a engineer.
Both a writer and a teacher, Zane.
Consequently, the lawyer, Kathlego, is the last task left for us to complete.
Therefore,
The attorney and painter is Kathlego.
Tessa is a doctor and an engineer.
The educator and author is named Zane.
Complete question: 3. *Because of the high cost of living, Kimberly, Terry,and Otis each hold down two jobs, but no
two have the same occupation. The occupations are doctor, engineer, teacher, lawyer, writer,
and painter. Given the following information, determine the occupations of each individual:
a.) The doctor had lunch with the teacher.
b.) The teacher went fishing with Kimberly, who is not the writer.
c.) The painter is related to the engineer.
d.) The doctor hired the painter to do a job.
e.) Terry lives next door to the writer.
f.) Otis beat Terry and the painter at tennis.
g.) Otis is not the doctor
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please help me with this !
(A) Table of values
x y
1 22
2 29
3 36
4 43
5 50
6 57
(C) The function which represents the statement is y(x) = 7x + 15 where x is the number of weeks.
Anthony has $15 and wants to save $7 per week.
Let the number of weeks be x and the amount he saved be y.
Then, the function that represents the situation is:
y = 7x + 15
Therefore,
y(1) = 7(1) + 15 = 22
y(2) = 7(2) + 15 = 14 + 15 = 29
y(3) = 7(3) + 15 = 21 + 15 = 36
y(4) = 7(4) + 15 = 28 + 15 = 43
y(5) = 7(5) + 15 = 35 + 15 = 50
y(6) = 7(6) + 15 = 42 + 15 = 57
So, the table of values is:
x y(x) = 7x + 15
1 22
2 29
3 36
4 43
5 50
6 57
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Please help meee!! Like ASAP
Answer:
Step-by-step explanation:
x=30 is false.
x=y is false.
x+z=90 is true.
x+y+z=180 is false.
Answer: x=30 TRUE, x=y FALSE, y+z=90 TRUE, x+y+z=180 FALSE
Step-by-step explanation:
X=30 is true because each side is 90 degrees, and we already are given two values, 20 and 40. So to find x you do
90-(20+40) or 90-60.
This equals 30.
X=Y is false because we just saw that x is 30 degrees, and y looks to be 45 degrees. [tex]30 \neq 45[/tex]
Y+Z=90 is true because each side of the line is equal to 90 degrees and since there are two values y and z, we can do:
90/2=45.
This means that both y and z are 45 degrees and 45+45 is 90.
X+Y+Z is false because we have all of the values of them and when we add all of them together:
30 + 45 + 45
we get 120.
[tex]120 \neq 180[/tex]
Please mark Brainliest!
Find the 60th term of the arithmetic sequence -29, -49, -69,
The 60th term of the arithmetic sequence - 29, - 49, - 69 is - 1209.
An ordered collection of objects that allows repetitions is referred to as a sequence.
Consider the arithmetic sequence,
- 29, - 49, - 69
The common difference of the sequence is:
d = - 49 - ( - 29 ) = - 49 + 29 = - 20
The first term of the sequence is a = - 29.
The nth term of an arithmetic sequence is given as:
aₙ = a + ( n - 1 )d where n is the number of term.
Therefore, the 60th term of the sequence will be:
aₙ = a + ( n - 1 )d
a₆₀ = - 29 + ( 60 - 1 ) × - 20
a₆₀ = - 29 + 59 × - 20
a₆₀ = - 29 + 59 × - 20
a₆₀ = - 29 - 1180
a₆₀ = - 1209
Hence, the 60th term of the arithmetic sequence is - 1209.
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willie buys a hot rod magazine for $7 and intends to stock up on pork rinds at 2$ a bag. he bought $15 write and inequality that represents how many bags of pork rinds willie can buy algebra
3. What is the variance of the following set of data?
4, 44, 404, 244, 4, 74, 84, 64
Use 82 =
Σ(x₁ - x)²
(N-1)
O139
O130
O19,298
16,886
Answer:
16,886
Step-by-step explanation:
The last answer! Pls mark me brainly!
P is the center of the circle.
Identify three congruent triangles and explain how to show
that they are congruent.
The three congruent triangles in this problem are given as follows:
LPN, MPL and PLN.
What are congruent triangles?When triangles have the same side lengths, they are called congruent.
For a circle, we need to know that:
The radius of the circle is the distance of the center to any point in the circumference of the circle.The diameter of the circle is the length of a line through the center that touches two points on the circumference of the circle.Hence, for this triangle, we have that:
The following segments represent the radius: PL, PN and MP.These following segments represent the diameter: LN, MN and ML.The three triangles in this problem are given as follows:
LPN, MPL and PLN.
Since each triangle is composed by two segments that represent the radius of the circle and one segment representing the diameter, they have the same side lengths, hence they are congruent triangles.
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difference of 4 and 23/100
Answer:
4-0.23=3.77
Step-by-step explanation:
Find the measure of angle b.
b
43°
We conclude that the measure of angle ∠b is 43°.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles.So, a measure of angle b:
Let us name the other angle as c:
∠c = 43°As we can clearly observe that ∠c and ∠b are vertically opposite angles.
Then, ∠c = ∠b.Hence, ∠b = 43°.
Therefore, the measure of angle ∠b is 43°.
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In the figure below, m3=44°. Find mZ1, m2, and m/ 4.
Check the picture below.
crud matrices are created by creating a matrix that lists the classes across the top and down the side. group of answer choices true false
The given statement is true.
What is matrices ?
A matrix is a collection of numbers that are arranged in rows and columns to create a rectangular array. The elements of the matrix, also known as the entries, are the integers. Matrices are used extensively in many fields of mathematics as well as in engineering, physics, economics, and statistics.
Here ,
Create, Read or Reference, Update, and Delete are all parts of the acronym CRUD. These four interactions between classes in a system are feasible. In order to find possible partners while developing a communication diagram, an analyst would establish a CRUD matrix.
Here the CRUD matrices are created by lists the classes across the top and down of the side.
Hence the given statement is TRUE.
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What is the angles of these letters?
In the picture there is a diagram with angles. By supplementary and alternative angles we get the angles are ∠a=∠e=112°,∠b=∠c=∠d=68°.
Given that,
In the picture there is a diagram with angles,
We have to find the angles of the given diagram.
The one angle is given as 68°.
The angle a is
By supplementary,
∠a+68°=180°
∠a=180°-68°
∠a=112°
The angle b as
Alternative angles are equal
∠b=68°
We take the interial angle of triangle as x.
By alternative angles,
∠a=∠x
∠x=112°
The angle e is
By alternative angle,
∠e=∠x
∠e=112°
The angle d as
By supplementary,
∠d+∠e=180°
∠d+112°+180°
∠d=180°-112°
∠d=68°
The angle c as
By alternative angle,
∠d=∠c
∠c=68°
Therefore, the angles are ∠a=∠e=112°,∠b=∠c=∠d=68°.
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p(x)=1/2(x-2)(2x-3)(4x+7)
The simplified expression for the polynomial is 2y = 8x³− 14x²− 25x+ 42
A mathematical formula that uses integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).
A polynomial is an equation made up of exponents, constants, and variables that is combined using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable)The given function is p(x)=1/2(x-2)(2x-3)(4x+7)
The simplified form of the function can be written as
2y = 8x³− 14x²− 25x+ 42
Now we know that the roots of the equation are 2 ,3/2 and -7/4.
The graph of the function is attached below.
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please help me with this problem
Step-by-step explanation:
[tex]12^{9} / 12 ^{3} =[/tex]
When dividing exponential expressions with similar bases (in the problem, the base is 12), calculate the difference (this means subtract) between their exponents and keep the base:
so:
9 - 3 = 6
so the answer is : [tex]12^{6}[/tex]
A small fruit smoothie is 11 ounces while a large fruit smoothie is 13.86 ounces. The large fruit smoothie is ___% larger?
Answer:
23.0088% difference
Step-by-step explanation:
Calculate percentage difference
between V1 = 11 and V2 = 13.86
|V1−V2|[(V1+V2)2]×100=?
1) =|11−13.86|[(11+13.86)2]×100
2) =|−2.86|[24.862]×100
3) =2.8612.43×100
4) =0.230088×100
Answer: 23.0088% difference
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Answer: Brainly got this! 87 million
Step-by-step explanation:
20b - 16 Factor the expression completely
Answer:
4(5b-4)
Step-by-step explanation:
(20b-16)/4
4(5b-4)
Answer:
4(5b - 4)
Step-by-step explanation:
20b - 16 ← factor out 4 from each term
= 4(5b - 4)
need asap pleasee will give 30 points and brainiest if its correct
[tex]{ \sf{option(a)}}[/tex]
The statement For all real numbers a, b and c, if a = b, then a - c = b - c represents the subtraction property of equality.
What is the y-intercept of 5x+4y=−40 ?
Responses
A- (−10,0)
B- (0,−10)
C- (8,−10)
D- (0,8)
The y-intercept of 5x+4y=-40 is (0,-10 )
A quadratic equation is expressed in its standard form as y=ax2+bx+c, where x and y are variables and a, b, and c are well-known constants. Substitute 0 for x in a quadratic equation and solve to obtain the y-intercept. The value of c in the equation is always the value of the y-intercept.
Given equation :
5x+4y=-40
To find x-intercept substitute 0 in y and solve for x
5x+4(0)=-40
5x=-40
x=8
so the x intercepts = (8,0)
To find y-intercept substitute 0 in x and solve for y
5(0)+4y=-40
4y=-40
y=-10
here the y-intercepts = (0,-10)
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If f(1) = 1 and f(n) = 2f(n-1) then find the value of f(6).
The value of the function f (6) will be 32.
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The value of the function;
f (1) = 1
And, The function is;
f (n) = 2 f (n - 1)
Now, Find the value of the function f (6) as;
Since, The function is;
f (n) = 2 f (n - 1)
Substitute n = 2, we get;
f (n) = 2 f (n - 1)
f (2) = 2 f (2 - 1)
f (2) = 2 f (1)
f (2) = 2 x 1
f (2) = 2
And, Substitute n = 3, we get;
f (n) = 2 f (n - 1)
f (3) = 2 f (3 - 1)
f (3) = 2 f (2)
f (3) = 2 x 2
f (3) = 4
And, Substitute n = 4, we get;
f (n) = 2 f (n - 1)
f (4) = 2 f (4 - 1)
f (4) = 2 f (3)
f (4) = 2 x 4
f (4) = 8
And, Substitute n = 5, we get;
f (n) = 2 f (n - 1)
f (5) = 2 f (5 - 1)
f (5) = 2 f (4)
f (5) = 2 x 8
f (5) = 16
And, Substitute n = 6, we get;
f (n) = 2 f (n - 1)
f (6) = 2 f (6 - 1)
f (6) = 2 f (5)
f (6) = 2 x 16
f (6) = 32
Thus, The value of the function f (6) will be 32.
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