based on the polynomial remainder theorem, what is the value of the function when x=10? f(x)=x^4-2x^3+5x^2-7x+4
Answers
Based on the polynomial remainder theorem, the value of the function when x = 10 is 8434.
What is Polynomial Remainder Theorem?Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder. This remainder that has been obtained is actually a value of P(x) at x = a, specifically P(a). So basically, x -a is the divisor of P(x) if and only if P(a) = 0. It is applied to factorize polynomials of each degree in an elegant manner.
Putting x = 10 into the function f(x)=x^4-2x^3+5x^2-7x+4
f(10) = \(10^{4} - 2(10)^{2} + 5(10)^{2} - 7(10) + 4\)
f(10) = 10000 - 2(1000) + 5(100) - 70 + 4
f(10) = 10000 - 2000 + 500 - 66
f(10) = 8000 + 434
f(10) = 8434
Thus, the remainder is 8434.
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Related Questions
PLEASE HELP ME ON QUESTION ASAP!!
IF YOU HAVE A TOPIC LIST IN YOUR EXAMS AND IT SAYS AVERAGES AND THE RANGE ARE YOU GOING TO BE HAVING MEAN AND RANGE IN YOUR TEST OR MEAN, RANGE MODE, MIDPOINT BASICALLY ALL OF IT ? IF ANSWERS CORRECT ILL RATE YOU FIVE STARS, GIVE YOU A THANKS AND MAYBE EVEN BRAINLIEST (sorry for caps)
Answers
Answer:
Step-by-step explanation:
Typically yes you need to know
Mean
Median
Mode
and Range
Mean = average, add all numbers then divide by how many
Median = midpoint, middle number. Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers
Mode = numbers that occurs the most in the list of numbers
Range = This is the largest number minus the smallest number.
A certain type of kickboard scooter comes in silver, red, 2
or purple with wheel sizes of 125 millimeters or 180
millimeters. Determine the total number of color-wheel size combinations.
(This is probability and I’m having such a hell of a time figuring it out pls help)
Answers
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.
Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:
Total combinations = Number of color options × Number of wheel size options
Total combinations = 4 colors × 2 wheel sizes
Total combinations = 8
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
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A customer at a local sub shop spent $22 on food for himself and his family. If small subs are $2.50 and larger subs are $4.00, how many of each did he purchase?
Answers
Graph the inequality on a number line
Answers
Hope this helps :)
Solve for r.
r= __ ?
Answers
r= \frac{q^{2} }{p^{3}} +1
Super is a ride-sharing company. The Chief of Operations wants the revenue (output value) to be seven times the cost of service operations (input cost). Suppose that each regular car earns a value of $1500 per month and premium cars earn $2500 per unit per month. The monthly cost of operating a regular car is $100 per month and $500 per premium car. Super currently has 19 regular cars. How many premium cars do they need to achieve a productivity ratio of 7? (Enter your response rounded to whole number.)
Answers
Super would need 2 premium cars to achieve a productivity ratio of 7.
How to find the productivity ratio?Let's call the number of premium cars "x".
The total revenue from the regular cars would be $1500 * 19 = $28,500 per month.
The total revenue from the premium cars would be $2500 * x.
The total cost of the regular cars would be $100 * 19 = $1900 per month.
The total cost of the premium cars would be $500 * x.
The Chief of Operations wants the revenue to be 7 times the cost of service operations, so we can write the following equation:
($28,500 + $2500x) / ($1900 + $500x) = 7
Expanding and simplifying the equation, we get:
$2500x + $28,500 = 7($1900 + $500x)
$2500x + $28,500 = $13,300 + 7$500x
$11,200 = 6$500x
$11,200 / $6,500 = x
x = 1.723
Rounding up, Super would need 2 premium cars to achieve a productivity ratio of 7.
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PLEASE HELP!!!!!!
WILL GIVE BRIANLIEST!!!
Answers
Answer:
\(r = \sqrt{ \frac{3v}{\pi \: h} } \)
3.15cm
Answer:
hellos :)
Step-by-step explanation:
i do dis so my fren here can have brainliest
:))) by for now <3
Please help quick!!!!!
Isolate for y
3y=4x +1
Answers
Divide both sides by 3
Single discount rate equavalent to a series of discounts 20% and 25% is
Answers
Answer:
The single discount rate equavalent is a discount of 40%.
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
The multiplier for a decrease of b% is 1 - b/100.
Discount of 20%:
20% decrease:
1 - (20/100) = 1 - 0.2 = 0.8
Discount of 25%:
1 - (25/100) = 1 - 0.25 = 0.75
Series of discounts(20% and 25%):
0.8*0.75 = 0.6
1 - 0.6 = 0.4
The single discount rate equavalent is a discount of 40%.
Andre was trying to write 7⁴/7⁻³ with a single exponent and wrote 7⁴/7⁻³=7⁴⁻³. Explain to Andre what his mistake was.
Answers
Answer:
see explanation
Step-by-step explanation:
Using the rule of exponents
\(\frac{a^{m} }{a^{n} }\) = \(a^{(m-n)}\), then
\(\frac{7^{4} }{7^{-3} }\) = \(7^{4-(-3)}\)
His mistake was in subtracting 3 rather than - 3
Andre's mistake was that he was not subtracting the power correctly.
The given expression is,
\(\frac{7^4}{7^{-3}}\)
As we know according to the exponent law:
\(\frac{a^m}{a^n} =a^{m-n}\)
Now, applying the above law into the given expression we get,
\(\frac{7^4}{7^{-3}}=7^{4-(-3)}\\ =7^{4+3}\\=7^7\)
Hence, Andre's mistake was that he was not subtracting the power correctly.
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The table shows the number of families staying at a campsite in 2015.
Questionnaires are sent to 60 families.
The sample of size 60 is stratified by type of unit and area.
Area
a) How many families who
Woods Fields Clifftop
stayed in a Tent in the
Woods are sent a
Caravan 25
20
35 questionnaire?
Type of unit Tent
15
30
b) How many families who
45
stayed in a Caravan
Motorhome 60
are sent a questionnaire?
50
20
Total
100
100
100
Answers
Answer:
a) = 3 b)=16
Step-by-step explanation:
60/300= 1/5
a) 1/5 x 15=3
b)25 + 20 +35=80
1/5 x 80= 16
(correct on mathswatch)
I Need Help please!!
Slope of one of the dotted lines:
Slope of the line of reflection:
Answers
Answer:
see explanation
Step-by-step explanation:
calculate slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
consider the middle dotted line
with
(x₁, y₁ ) = (- 5, - 3) and (x₂, y₂ ) = (6, 8) ← 2 points on the line
m = \(\frac{8-(-3)}{6-(-5)}\) = \(\frac{8+3}{6+5}\) = \(\frac{11}{11}\) = 1
consider the line of reflection ( the solid line )
with
(x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (- 1, 4) ← 2 points on the line
m = \(\frac{4-3}{-1-0}\) = \(\frac{1}{-1}\) = - 1
2. Patricia, Luca and Dauda shared an amount of money such that, Patricia had twice as much
as Dauda and Luca had GH¢600.00 more than Dauda. If Patricia had GH¢2,000.00, what
was the average share, to the nearest GH¢?
Answers
Answer:
GH¢1533
Step-by-step explanation:
Let d represent the amount of Dauda's share in GH¢. Then the problem statement tells us ...
Patricia's share is 2d = 2000
Luca's share is d+600
From Patricia's share, we know Dauda's share is ...
d = 2000/2 = 1000
and Luca's share is ...
1000 +600 = 1600
__
The average share is the sum of these, divided by three:
(2000 +1000 +1600)/3 = 4600/3 = 1533.33
To the nearest GH¢, the average share is GH¢1533.
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).
Answers
Answer: \(\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV\) = 1087.5
Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = \(\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]\)\(\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]\)
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
\(a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0\)
Then, replacing with point P and normal vector n:
\(36(x-5) + 20(y-0) + 45(z-0) = 0\)
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
\(z = \frac{180-36x-20y}{45}\)
When z = 0:
\(y = 9 + \frac{-9x}{5}\)
When z=0 and y=0:
x = 5
Then, triple integral is:
\(\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx\)
Calculating:
\(\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx\)
\(\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx\)
\(\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx\)
\(\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx\)
\(\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx\)
\(\frac{1}{45} [30375-60750+118462.5-39150]\)
\(\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx\) = 1087.5
The volume of the tetrahedon is 1087.5 cubic units.
The tripple integration will be \(\int\limits^a_E \int\limits^a_E \int\limits^a_E {xy} \, dV\) = 1087.5
What is triple integration?The triple integration is used to identify the volumes of the objects or for analyzing three dimension of the object.
To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedron is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = \(\left[\begin{array}{ccc}i&j&k\\5&-9&-0\\0&9&-4\end{array}\right] \left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]\)
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
\(a(x-x_o)+b(y-y_o)+c(z-z_o)=0\)
Then, replacing with point P and normal vector n:
\(36(x-5)+20(y-0)+45(z-0)=0\)
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
\(z=\dfrac{180-36x-20y}{45}\)
When z = 0:
\(y=9+\dfrac{-9x}{5}\)
When z=0 and y=0:
x = 5
Then, triple integral is:
\(\int\limits^5_0 \int\int xy\ dzdydx\)
Calculating:
\(\int\limits^5_0 \int\int xy\ dzdydx\)
\(\int\limits^5_0 \int\int xy\ (\dfrac{180-36x-20y}{45}-0)dydx\)
\(\dfrac{1}{45}\int\limits^5_0 \int \ 180xy-36x^2y-20xy^2dydx\)
\(\dfrac{1}{45}\int\limits^5_0 \int \ 90xy^2-18x^2y^2-\dfrac{20}{3}xy^3dydx\)
\(\dfrac{1}{45}\int\limits^5_0 \int \ 2430x-1458x^2+\dfrac{94770}{125}x^3-\dfrac{23490}{375}x^4dx\)
\(\dfrac{1}{45} [30375-60750+118462.5-39150]\)
\(\int\limits^5_0 \int\int xy\ dzdydx=1087.5\)
The volume of the tetrahedron is 1087.5 cubic units.
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Winston found $3.75 for in change on the beach with
his metal detector over the course of 3 1/3 hours. Write
a unit rate that describes this situation,
Answers
Answer:
Winston can find $1.125 dollars every 1 hour.
Step-by-step explanation:
I got this by dividing 3.75 by 3 1/3.
3.75 ÷ 3 1/3 = 1.125
Hope this helps! :)
how many miles per hour does it take to go 160 miles in 4.5 hours
Answers
Que es un Monomi i un Polinomi?
Answers
Answer: Traducción Española
Polynomi es un término matemático que muestra la suma de monomios. Monomi es un problema matemático donde las variables y constantes pueden estar solas o multiplicarse.
Step-by-step explanation:
English translation:
Polynomi is a mathematical term that shows the sum of monomials. Monomi is a mathematical problem where variables and constants can stand alone or multiply.
Question 5 If 25% of x is 120. What is the value of x?
Answers
25% × × = 120
2. 0.25× = 120
Divide both sides
3.x=120/0.25
Divide both sides
4. × = 480
The answer is X=480
The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per
year since.
Find the population at the beginning of 1994. Round to the nearest person.
Answers
Answer:
37356
Step-by-step explanation:
HALP! EASY MATH (not for me obviously)
show work plz
halp!
Answers
Answer:
Infinitely many solutions
Step-by-step explanation:
Solve y = 3x+1 for y
y = 3x+1
Substitute 3x+1 for y in -6x+2y = 2
−6x+2y = 2
−6x+2(3x+1) = 2
2=2
2+−2=2+−2
0=0
F 2,826 m2
CONSTRUCTED RESPONSE
9. A wheel has a radius of 9 inches and
travels as it spins. How far does the
wheel travel in one revolution? Show your
work. Use 3.14 for n and round to the
nearest inch,
Answers
Answer:
57inches
Step-by-step explanation:
In order to determine how far the wheel travels, we will have to find the circumference of the wheel. This is expressed as;
Circumference of the wheel = 2πr
r is the radius of the wheel = 9in
Substitute
Circumference of the wheel = 2(3.14)(9)
Circumference of the wheel = 56.52inches
Hence the wheel travels 57inches to the nearest inch
What is the area of the triangle?
Answers
9514 1404 393
Answer:
7 square units
Step-by-step explanation:
There are several ways the area of triangle EBD can be found.
find the lengths EB, BD, DE and use Heron's formula (messy due to roots of roots being involved).define point G at the lower left corner and subtract the areas of ∆DEG and BCD from trapezoid BCGE.figure the area from the coordinates of the vertices.use Pick's theorem and count the dots.We choose the latter.
__
Pick's theorem says the area of a polygon can be found as ...
A = i + b/2 -1
where i is the number of grid intersection points interior to the polygon, b is the number of grid points intersected by the border.
The attached figure shows the lines EB, BD, and DE intersect one point in addition to the vertices. So, b=4. A count of the red dots reveals 6 interior points (i=6). So, the area is ...
A = 6 + (4/2) -1 = 7
The area of ∆EBD is 7 square units.
If sec 0 = √2, find 0 and identify all angles 0° < 0 < 360° that are co-terminal with the
given angle.
Answers
In the trigonometry relation the value of θ is 45 degrees and the coterminal angle between 0° < θ < 360° is 315 degrees
How to find conterminal of the angleCoterminal angles are angles that have the same terminal side in a given circle. They are angles that differ by a multiple of 360 degrees.
In other words, if two angles are coterminal, they have the same trigonometric functions, despite having different degrees.
If sec θ = √2
θ = arc sec (√2)
θ = arc cos (1/√2))
θ = 45 degrees
coterminal of angle 45 degrees between 0° < θ < 360°
360 - 45 = 315.
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Evaluate this expression.
3^-2
Answers
Answer:Exact Form: one over 9
1
9
Step-by-step explanation: ,..
9. A student received a 75% on an exam. If there were 20 questions on the exam,
which ratio would show the number of questions answered correctly to the total
number of questions?
Microsoft
Edge
O A. 20:5
O B. 20:15
O C. 15:20
Zoom
O D. 5:20
Answers
Answer:
The answer is C. 15:20
Step-by-step explanation:
hope that helps
Answer:
B
Step-by-step explanation:
Step 1: Take 20 and multiply by 0.75 to get the number of answers that were correct, which is 15.
Step 2: Put the number of correct questions and the total number of questions into a ratio form, 20:15
For Mean = 73.19, Mode = 79.56 and Variance = 16, the Karl Pearson's Coefficient of Skewness will be -0.0256 -1.64 0.0256 0
Answers
Answer:
To calculate Karl Pearson's coefficient of skewness, we need to use the formula:
Skewness = 3 * (Mean - Mode) / Standard Deviation
Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.
Standard Deviation = √Variance = √16 = 4
Now we can substitute the values into the formula:
Skewness = 3 * (73.19 - 79.56) / 4
Skewness = -6.37 / 4
Skewness = -1.5925
Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.
Prior to the Academy Awards ceremony in 2009, the United Kingdom bookmaker Ladbrokes reported the following odds for winning an Oscar in the category of best actress (The Wall Street Journal, February 20, 2009).
Best Actress Movie Odds
Anne Hathaway Rachel Getting Married 2:11
Angelina Jolie Changeling 1:20
Melissa Leo Frozen River 1:33
Meryl Streep Doubt 3:10
Kate Winslet The Reader 5:2
a. Express the odds for each actress winning as a probability. (Round your answers to 3 decimal places.)
Best Actress Probability
Anne Hathaway
Angelina Jolie
Melissa Leo
Meryl Streep
Kate Winslet
Answers
Answer:
Anne Hathaway: 0.154 = 15.4%
Angelina Jolie: 0.048 = 4.8%
Melissa Leo: 0.029 = 2.9%
Meryl Streep: 0.231 = 23.1%
Kate Winslet: 0.714 = 71.4%
Step-by-step explanation:
Odds to probability:
Odds of a:b
The probability is given by:
\(p = \frac{a}{a+b}\)
Anne Hathaway 2:11
So \(p = \frac{2}{2+11} = \frac{2}{13} = 0.154\)
Angelina Jolie 1:20
So \(p = \frac{1}{1+20} = \frac{1}{21} = 0.048\)
Melissa Leo 1:33
So \(p = \frac{1}{1+33} = \frac{1}{34} = 0.029\)
Meryl Streep 3:10
So \(p = \frac{3}{3+10} = \frac{3}{13} = 0.231\)
Kate Winslet 5:2
So \(p = \frac{5}{5+2} = \frac{5}{7} = 0.714\)
PLS HELP ME 25 POINTS
The roots of the equation x^2+bx+c=0 are −4 and 2. Find b.
Answers
x^2 + 2x - 8
a = 1
b = 2
c = -8
whats the mean and median of 13, 1, 17, 6, 2, 111, 3?
Answers
Answer:
111
Step-by-step explanation:
The mean is 21.9
Find the slope of identity function using points (0,0) and ( 3,3) then from two points (0,0) and (-3,-3). Is there any change in its slope?
Answers
There is no change in its slope as initial and final slope is 1.
What is slope?
In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.
Main body:
formula for slope with two points form is =
y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)
according to question ,
points are (0,0) and (3,3)
y - 0 = (3-0/3-0)(x -0)
y = 3/3 *x
y = x
hence slope of line is 1.
Now points are (0,0) and (-3,-3).
y - 0 = (-3-0/-3-0)(x -0)
y =- 3/-3 *x
y = x
hence slope of line is 1.
So there is no change in its slope.
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