Answer: Theorems About Roots of Polynomial Equations
Step-by-step explanation:
Theorems About Roots of Polynomial Equations
In the given case we can conclude that the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]
To create a polynomial with 4 terms, a degree of 6, a leading coefficient of -1, and a constant term of -5.5, we can use the general form of a polynomial:
A "polynomial" is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers, combined using addition and multiplication. Polynomials are fundamental objects in algebra and are used to represent a wide range of mathematical relationships, including functions, curves, and various mathematical concepts.
P(x) = [tex]ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g[/tex]
Plugging in the given values, we have:
P(x) = [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5[/tex]
Remember that the degree of a polynomial is determined by the highest exponent of x.
In this case, the degree is 6.
The leading coefficient is the coefficient of the term with the highest degree, which is -1. The constant term is -5.5.
So, the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]
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I need help is -2x=3/8 a literal equation?
The equation -2x=3/8 is not a literal equation.
What is a literal equation?A literal equation can be defined as an equation which primarily of letters.
It is an equation made up of several variables or letters.
Examples of literal equations are;
V = dts = ut + 1/2 at^2Area = πr²D = m/ vWe can see from the examples shown that the equations or formulas have several variables or letters that could be written in terms of other variables.
Given the equation;
-2x=3/8
We can see that there is only one variable to be worked out and hence, is not a literal equation.
Thus, the equation -2x=3/8 is not a literal equation.
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Paul's Bikes rents bikes for $11 plus $4 per hour. Amanda paid $31 to rent a bike. For how many hours did she rent the bike?.
As given Paul's Bikes rents bikes for $11 plus $4 per hour and Amanda paid $31 to rent a bike shows she rent the bike for 5hours.
As given in the question,
Let 'h' represents the number of hours
Paul's Bikes rents bikes for $11 plus $4 per hour
Amanda paid $31 to rent a bike
Required equation is:
31 = 11 + 4h
⇒4h = 20
⇒h = 5hours
Therefore, as given Paul's Bikes rents bikes for $11 plus $4 per hour and Amanda paid $31 to rent a bike shows she rent the bike for 5hours.
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Use the given information to find the unknown value. y varies inversely with the cube of x. when x=9, then y=1. find y when x=1. enter the exact answer.
When the value of x = 1, the value of y = 729.
What is inverse relation?An inverse relationship is one where the value of one parameter decreases as the value of the second parameter increases. It is frequently described as a bad relationship.
In other phrases, an inverse relationship, also recognized as a negative relationship, is a negative relationship between two variables that moves in the opposite direction. Like, we have two variables X and Y. As X increases, so does Y, and as Y increases, so does X.Now, as per the question.
y varies inversely with the cube of x.
y ∝ 1/x³
Removing inverse, a constant of proportionality will come (say k)
y = k/x³
k = x³y.
When x = 9 then y = 1. Substitute the values and find k.
k = 9³(1)
k = 729
Now, estimate the value of y when x = 1.
y = k/x³ ( put the value of k and x )
y = 729/1³
y = 729
Thus, the value of y when the value of x = 1 is 729.
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A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece . find the leg of each piece
One of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.
Here,
A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece .
We have to find the leg of each piece.
What is Length, Width and height?
The length, width and height of an object are the different dimensions in linear units. length is the longest side of a shape, width is the shorter side, and height is the vertical dimension of the shape.
Now,
If you're going to cut the 72 inch board into two pieces, you can call one of the pieces x units long.
And, since the other piece is 12 inches longer than your first piece, its length is x + 12.
And, when you place these two pieces back together, their lengths should add up to be 72 inches.
You can write this last statement about adding the two pieces together to get a 72 inch piece
In equation form as:
x + (x+12) = 72
2x + 12 = 72
To solve this begin by subtracting 12 from both sides;
2x = 60
Now just divide both sides by 2 to find that:
x = 30
So, one of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.
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how do i solve this equation
Answer:
[tex]\frac{9b}{a^{2} }[/tex]
Step-by-step explanation:
[tex]\frac{a^{2} }{b}(\frac{3b}{a^{2} })^{2}[/tex]
[tex]\frac{9a^{2}b^{2} }{a^{4}b }[/tex]
[tex]\frac{9b}{a^{2} }[/tex]
Could someone help me? The problems (see image attached) are about whether or not a decimal can be written as a question and why or why not.
Answer:
yes it can be bc it is repeating
Find the area of the shaded figure.
OF
80 mm 120 mm
PLS HELP
Answer: 2000π mm^2
Step-by-step explanation:
A=area of entire circle. B=Area of Inside circle. C=Area of shaded region
A-B=C
π(120/2)^2 -π(80/2)^2=
π(60)^2 -π(40)^2=
3600π-1600π=2000π mm^2
Which expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power?
Using exponent properties, the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
What is the equivalent expression?The original expression is:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2}[/tex]
When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2} = [y^{-3 - 6}z^{5 - (-4)}]^{-2} = [y^{-9}z^9]^{-2}[/tex]
The negative exponent at the numerator goes to the denominator, hence:
[tex][y^{-9}z^9]^{-2} = \left[\frac{z^9}{y^9}\right]^{-2}[/tex]
The negative outer exponent means that we have to exchange the numerator and denominator, hence:
[tex]\left[\frac{z^9}{y^9}\right]^{-2} = \left[\frac{y^9}{z^9}\right]^{2}[/tex]
Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
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Answer:
y^18/x^18
Step-by-step explanation:
An engineer is estimating the weight of a steel beam. the actual weight of the beam is 286 pounds. the engineer's estimate is 300 pounds.
find the absolute error and the percent error of the engineer's estimate. if necessary, round your answers to the nearest tenth.
The Absolute error of the engineer's estimate is 14 pounds and the percent error is 4.89 % .
Absolute Error is defined as the difference between The Actual value and the estimated value .
Percent Error is defined as the difference between The Actual value and the estimated value in comparison to actual value expressed in percent .
[tex]Percent Error=\frac{|Estimated Value-Actual value|}{Actual Value} *100[/tex]
Given that the Estimated value =300 pounds
Actual Value=286 pounds
Absolute Error=300-286=14 pounds
Percent Error=[tex]\frac{|300-286|}{286} *100[/tex]
=[tex]\frac{14}{286} *100=4.89[/tex]%
Therefore , The Absolute error of the engineer's estimate is 14 pounds and the percent error is 4.89 % .
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If the radius of a circle is 16 inches find the diameter area and circumference
diamater:
[tex]d=2r \\\\d=2 \cdot 16 \\\\d=32[/tex]
circumference:
[tex]C=2 \pi r \\\\C=2 \cdot \p \cdot 16 \\\\C=32 \cdot \pi \\\\C \approx 100.48[/tex]
Hope that I helped you!
In the figure below, m1= (x+24)° and m2=5x°,
Find the angle measures.
12
Measure of angle 1 is 50° and that of angle 2 is 130°
The sum of all the angles on a straight line is equal to 180°.
Here, we are given two angles ∠1 and ∠2
Also, we are given that
m∠1 = (x+24)°
and m∠2 = 5x°
As we can see from the given figure, ∠1 and ∠2 lie on a straight line
⇒ m∠1 + m∠2 = 180
⇒ (x+24) + 5x = 180
x + 24 + 5x = 180
x + 5x + 24 = 180
6x + 24 = 180
6x = 180 - 24
6x = 156
x = 156/ 6
x = 26
Therefore,
m∠1 = 26 + 24
= 50
and m∠2 = 5(26)
= 130
Thus, the measure of the two angles is 50° and 130°
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Your question was incomplete. Check for the missing figure below.
900 students attend Ridgewood Junior High School. 4% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
Line RQ bisects line DE at S. If DS = 10 + 3x and ES = -2 + 6x, what is DE
The equation for DE is [tex]8+9x[/tex]
According to the question statement, Line RQ bisects line DE at S. If DS = 10 + 3x and ES = -2 + 6x. We are supposed to find DE.
For solving this we need to know about Linear Equations and Bisector of a line.
Given that, DS = 10 + 3x and ES = -2 + 6x.
S is mid point of line DE as RQ bisects it.
So DS = SE
And DE = DS + SE
Hence, DE = [tex]10 + 3x + (-2 + 6x)[/tex]
DE = [tex]10 + 3x -2 + 6x[/tex]
DE = [tex]10 -2 +3x+6x[/tex]
DE = [tex]8+9x[/tex]
Hence equation of DE is 8+9x.
Linear Equation: The equation whose graph is always a straight line.Bisector of a line: The line or a point which divides it in two equal portions i.e., bisects it.To learn more about linear equations, click the link given below
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A snail moves at a pace of 2 ft/min. how fast does the snail move in inches/hour?
The snail move at the pace in 1440in/hr.
Speed:
Speed is measured as the ratio of distance to the time in which the distance was covered.
Speed is a scalar quantity as it has only direction and no magnitude.
Given,
A snail moves at a pace of 2 ft/min.
Here we need to find how fast does the snail move in inches/hour.
We know that,
1 ft/min = 720.00 in/h
So, here we have 2 feet/minute.
That is equal to
=> 2 x 720.00 in/h
When we multiply it then we get the value of,
=> 1440 in/hr
Therefore, the snail move at the pace in 1440in/hr.
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Add:
4⁄6 + 2⁄4 + 3⁄5 =
Answer:
Step-by-step explanation:
[tex]\frac{4}{6} + \frac{2}{4} + \frac{3}{5} = \frac{80}{120} + \frac{60}{120} + \frac{72}{120} = \frac{212}{120}[/tex]
simplest form : [tex]\frac{53}{30}[/tex]
Solve the given initial-value problem. the de is a bernoulli equation. y1/2 dy dx y3/2 = 1, y(0) = 9
A differential equation with some initial conditions is used to solve an initial value problem.
The required particular solution is given by the relation:
[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]
What is meant by an initial-value problem?An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.
Let the given equation be [tex]$y^{1/2} dy\ dx y^{3/2} = 1[/tex], y(0) = 9
[tex]$(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1[/tex] …..(1)
Divide the given equation (1) by [tex]$\sqrt{ y} $[/tex] giving
[tex]$y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$[/tex], which is in Bernoulli's form.
Put [tex]$u=y^{(1+1 / 2)}=y^{(3 / 2)}$[/tex]
Then [tex]$(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$[/tex].
Multiply (2) by [tex]$\sqrt{ } y$[/tex] and we get
[tex]y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1[/tex]
(2/3) [tex]u^{\prime}+u=1$[/tex] or [tex]$u^{\prime}+(3 / 2) y=3 / 2$[/tex],
which is a first order linear equation with an integrating factor
exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is
[tex]u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$[/tex] or
[tex]\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}[/tex]
To obtain the particular solution satisfying y(0) = 4,
put x = 0, y = 4, then
8 = (9/4) + c
c = (23/4)
Hence, the required particular solution is given by the relation:
[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]
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please help with this question. n refers to the number of sides.
Answer:
n = 18
Step-by-step explanation:
The sides in a regular polygon are equal in length.
⇒ BC = CD
If BC = CD then ΔDCB is an isosceles triangle.
As the base angles of an isosceles triangles are equal:
⇒ ∠DBC = ∠BDC = 10°
Interior angles in a triangle sum to 180°.
⇒ ∠DBC +∠BDC + ∠DCB = 180°
⇒ 10° + 10° + ∠DCB = 180°
⇒ 20° + ∠DCB = 180°
⇒ ∠DCB = 180° - 20°
⇒ ∠DCB = 160°
Therefore, the interior angle of the regular polygon is 160°.
The interior angles of a regular polygon are equal in size.
[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Interior angle of a polygon}\\\\$\dfrac{(n-2) \times 180^{\circ}}{n}$\\\\where $n$ is the number of sides.\\ \end{minipage}}[/tex]
To find the number of sides, equate the formula to the found value of the interior angle and solve for n:
[tex]\begin{aligned}\implies\dfrac{(n-2) \times 180^{\circ}}{n} & =160^{\circ}\\(n-2) \times 180^{\circ} & =n \times 160^{\circ}\\ 180(n-2) & = 160n\\180n-360 & = 160n\\180n & = 160n+360\\180n-160n & = 360\\20n & = 360\\n &= \dfrac{360}{20}\\n & =18\\\end{aligned}[/tex]
Therefore, the regular polygon has 18 sides.
Assignment Active
Solve and write about ratios.
Students voted for a new class president and the results What does the ratio 344:109 represent?
are shown in the table.
O Jocelyn's votes to total votes
O Rosalia's votes to Danny's votes
O total votes to Jocelyn's votes
O total votes to Danny's votes
Assignment
Candidate
Rosalia
Jocelyn
Danny
Intro
Votes
124
109
111
Who votes to who’s votes
The answer to this question is:
Ratio 344:109 represents the ratio of the total votes to Jocelyn's votes.
A ratio in mathematics shows how frequently one number is contained in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of orange to lemon is eight to six (that is, 8:6, which is equal to the ratio of 4:3).
According to the question,
No. of votes Rosalia got = 124
No. of votes Jocelyn got = 109
No. of votes Danny got = 111
No. of votes received by all candidates =
= 124 + 109 + 111
= 344
So, the ratio 344:109 is the ratio of the total votes to Jocelyn's votes.
Therefore, Ratio 344:109 represents the ratio of the total votes to Jocelyn's votes.
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how many seconds are in 10 1/2 minutes
Answer:
630 seconds
Step-by-step explanation:
1 minute = 60 seconds
Number of minutes × Number of seconds per minute = Number of seconds in total
60 × 10 ½ = 630 seconds
Hope this helped! ^^
Use the Segment Addition Postulate to solve the problem below.
Point E is the midpoint of line segment YT.
line segment YT = 14
line segment YE = 3x + 1
What is the value of x?
Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.
What is the numerical value of x?A midpoint is simply a point that divides a segment into two equal halves.
Given the data in the question;
Point E is the midpoint of line segment YTLine segment YT = 14Line segment YE = 3x + 1Numerical value of x = ?Point E is the midpoint of line segment YT, YT is divided into two equal halves. Hence, Two times Line segment YE equals to YT.
2( Line segment YE ) = Line segment YT
Plug in the given values and solve for x.
2( Line segment YE ) = Line segment YT
2( 3x + 1 ) = 14
Expand using distributive property
2 × 3x + 2 × 1 = 14
6x + 2 = 14
Collect like terms
6x = 14 - 2
6x = 12
6x/6 = 12/6
x = 12/6
x = 2
Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.
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1. Which of the following points are on the circle centered at the origin with 2 = 89 ?
A) (25,64)
B) (5, -8)
C) (-3,-9)
D) (√89, √89)
The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).
Which of the following points are on the circle centered at the origin with r² = 89?It follows from the task content that the circle in discuss has a center at the origin, (0,0).
Hence, the since the square of the radius is; = 89.
It follows that the point which fits into the equation of the circle; x² + y² = r² is;
Choice C; (5)² + (-8)² = 25 + 64 = 89.
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The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).
Which of the following points are on the circle centered at the origin with r² = 89?It follows from the task content that the circle in discuss has a center at the origin, (0,0).
Hence, the since the square of the radius is; = 89.
It follows that the point which fits into the equation of the circle; x² + y² = r² is;
Choice C; (5)² + (-8)² = 25 + 64 = 89.
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If a person drives 360 miles at an average of 35 miles per hour, then their distance d from the destination (in miles) is a function of the number of hours h driven.
The required function is d = 360 - 35h, 0 ≤ h ≤ 10.29.
We know that distance travelled is equalled to speed multiplied by time.
Let d be the distance from the destination.
Let d₁ be the distance travelled in h hour.
And h be the number of hours driven.
Given that the average speed is 35 miles per hour.
Therefore, we have d₁ = 35h
And the initial distance from the destination is 360 miles.
Note at time h= 0 the distance from the destination is the maximum which is 360 miles.
Therefore, we have d₁ = 35h
Distance from the destination is 360 - d₁.
⇒ d = 360 - d₁
⇒ d = 360 - 35h
Time taken to reach destination = d/v = 360/35 = 10.29 hours
Therefore the required function is d = 360 - 35h, 0 ≤ h ≤ 10.29
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12^-2 in simplest form
Answer:
Step-by-step explanation:
1/144
hope this helps :)
what following is (are)the solution to(x-3)=7x-4
Answer:
Step-by-step explanation:
The X is equal to 1/6.
Meaning that the X is 1/6.
Answer:
x = 1/6
Step-by-step explanation:
(x - 3) = 7x - 4
x = 7x -1
-6x = -1
-x = -1/6
x = 1/6
A coordinate plane with a horizontal line passing through (negative 3, negative 3), (negative 3, 0) and (negative 3, 3).
Which is true of the standard form of the equation of the line graphed?
Answer:
x = - 3Step-by-step explanation:
GivenThe line passes through the points:
(-3, -3,), (-3, 0) and (-3, 3)Since all x- coordinates are same, the line is vertical and its equation is:
x = - 3Find the sum of all multiple 3 between 5 and 64
Answer:
The multiple of 3 between 5 and 64 are 6+9+12+15+18+21+24+27+30+33+36+39+42+ 45+48+51+54+57+60+63
=690
Brian invests £2300 into his bank account.
He receives 10% per year simple interest.
How much will Brian have after 2 years?
Give your answer to the nearest penny where appropriate.
Here is a liner equation in two variables 2x + 4y - 31 = 123 determine whether each statement is true or false. the equation solved for x is x = 154 - 4y true or false ?
the equation solved for y is y = 77-x- 2 true or false ?
Answer:
Both sentences are false.
Step-by-step explanation:
Let's solve for x:
2x + 4y - 31 = 123
2x = 123 - 4y + 31
2x = 154 - 4y
x = 77 - 2y
Let's solve for y:
x = 77 - 2y
2y = 77 - x
y = 38.5 - 0.5x
a guest total is $5.45 and they give you $10 how much change do you owe them
Answer: $4.55
Step-by-step explanation:
Just subtract $10.00 from $5.45 and you will get $4.55
Answer:
$4.55
Step-by-step explanation:
To find the change, we have to subtract the money they give you ($10) with the guest total ($5.45).
10 - 5.45
= $4.55
$4.55 is your answer.
Take care and have a lovely rest of your day! :)
help please !!! example is not needed :)
Answer:
b
Step-by-step explanation:
