Use the remainder theorem to find P(-1) for P(x) = −x³ – 2x² −9. Specifically, give the quotient and the remainder for the associated division and the value of P(-1).
Answers
Using remainder theorem, Quotient = x-9 and Remainder = x² - x.
According to the remainder theorem, the remainder equals f when a polynomial, p(x), is divided by (x - a) (a). Euclid's Division Lemma can be used to demonstrate this. Using this, p(x) = q(x) (x - a) + r, where q(x) is the quotient and 'r' is the remainder.Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.P(x) = −x³ – 2x² −9
P(-1) = −(-1)³ – (-1)x² −9
P(-1) = −(-1) – 2(1) −9
= 1 -2 -9
= -10
Remainder of P(-1) = −(-1)³ – (-1)x² −9 is -10.
Remainder of P(x+1)
= −x³ – 2x² −9 / x+1
Quotient = x-9 and Remainder = x² - x
Hence, using remainder theorem, Quotient = x-9 and Remainder = x² - x.
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Related Questions
What is the answer to this question?
Answers
Answer:
0,-24,-3/4
You have to substitute the values for x and y to get the other output. When I put 0 into the equations I get back 0
A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in field positive after the 3 plays. Then find and interpret the change in position.
Answers
The total spots moved, after the 3 plays is 15 spots to the left.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the football team lost 5 yards on each 3 plays.
Assume that a number line to be able to see how far in the field did they lost in 3 games.
Therefore,
1 : 5 (1 game is to 5 yards)
3 : 15 (3 games is to 15 yards )
After the first play, we would move to the left on the line 5 spots (to simulate 5 yards lost) and then make a dot to show your new position.
The total spots moved, after the 3 plays is 15 spots to the left.
Hence, All they lost 15 yards in 3 games.
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1/2v + 8 = 3 – 1/3v plss
Answers
Answer:
v = -6
Step-by-step explanation:
½v + 8 = 3 - ⅓v
Collect like terms
½v + ⅓v = 3 - 8
⅚v = -5
Divide both sides by ⅚
⅚v/⅚ = -5/⅚
v = -5 × 6/5
v = -30/5
v = -6
the distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. a sample size of 40 is drawn randomly. find the probability that the sum of the 40 values is greater than 7,450. (round your answer to four decimal places.)
Answers
The probability that the sum of the 40 values is greater than 7,450 is 0.0239
Define Normal Distribution.
A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.Formula of Normal Distribution isZ = (x - μ ) / (σ / √n )
We have given following info,
mean μ = 180
Standard deviation σ = 20
n = 40
σ(mean of x) = σ / √ n
= 20 / √40
= 3.16
Sample average (mean of x) = 7450 / 40
= 186.25
P(x > 186.25) = 1 - P(x < 186.25)
= 1 - P( (x - μ ) / σ(mean of x) ) < ( [186.25 - 180] / 3.16) )
= 1 - P( Z < 1.98)
Using Normal distribution table,
= 1 - 0.9761
P(x > 186.25) = 0.0239
Therefore,the probability that the sum of the 40 values is greater than 7,450 is 0.0239
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You have $8.50 and you need to make copies of a flyer at a store that charges
$0.35 per copy. Find the inequality that represents the number of copies you can
make. Use x as the variable.
What is the maximum number of copies you can afford to make?
copies
Answers
The required number maximum number of copies can be afforded x < 24.28.
Given that,
We have $8.50 and you need to make copies of a flyer at a store that charges $0.35 per copy.
Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of copies be x,
According to the question,
0.35x < 8.50
x < 8.50 / 0.35
x < 24.28
Thus, the required number maximum number of copies can be afforded x < 24.28.
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if the probability of a is 0.45 and the probability of the intersection of a and b is 0.15, then the probability that b will occur given that a has occurred is:
Answers
The probability that b will occur given that a has occurred is 2/5 as the probability of a is 0.45 and the probability of the intersection of a and b is 0.15.
What is probability?It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
P(A)=0.45
P(A∩B)=0.15
P(A∪B)=1
P(B)=1-(0.45+0.15)
=1-0.60
=0.4
=2/5
With a probability of 0.45 and a and b's intersection having a 0.15 probability each, the likelihood that b will happen given that a has happened is 2/5.
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What is the slope of the line that passes through the points (-6, -6) and (-9, -5)? Write your answer in the simplest form.
Answers
Answer: -1/3
Step-by-step explanation:
The formula for slope =y1-y2/x1-x2. You first subtract the numbers for the y coordinate which is -6-(-5), and thats -1. Then you subtract the x coordinates. -6-(-9)=3. So the slope is -1/3
which of the following is part of the solution of the system?
y-x<=-5, y-2x>-5
a) (0,1)
b) (-1,-6)
Answers
Answer:
Neither of them are solutions unless you had a typo in the question.
Step-by-step explanation:
1) plug in the known values into both of the equations
First Coordinate:
y-x[tex]\leq[/tex]-5
(1)-(0)[tex]\leq[/tex]-5
1[tex]\leq[/tex]-5 which is not true.
In this case, we do not need to plug in (0,1) into both of the equations because the coordinate cannot be a solution unless the coordinate works in BOTH of the equations.
Second Coordinate:
1) y-x[tex]\leq[/tex]-5
(-6)-(-1)[tex]\leq[/tex]-5
(-6)+1[tex]\leq[/tex]-5 --> It becomes a +1 because two negatives make a positive
-5 [tex]\leq[/tex]-5 - -> which means this is true because -5 is less than or equal to -5
2) y-2x>-5
(-6)-2(-1)>-5
-6(2)>-5
-12>-5 NOT TRUE
ANSWER: Neither of them are solutions unless you had a typo in the question.
probability works not by compensating for imbalances but by overwhelming them. suppose that the first 1010 tosses of a coin give 1010 tails and that tosses after that are exactly half heads and half tails. (exact balance is unlikely, but the example illustrates how the first 1010 outcomes are swamped by later outcomes.) (use decimal notation. give your answers as exact numbers.) what is the proportion of heads after the first 10 tosses?
Answers
The proportion of heads after the first 10 tosses of a coin is zero i.e 0/10 = 0
A probability is a number that reflects the likelihood or probability that a particular event will occur. Probabilities can be expressed as percentages ranging from 0 to 1, and can also be expressed as percentages ranging from 0% to 100%. A probability of 0 indicates that the particular event is unlikely to occur, and a probability of 1 indicates that the event will definitely occur.
Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes.
We have given the following points ,
A coin is tossed 10 times and it comes with tail in each time of first 10 tosses.
When a coin is toosed , there two possibilities either it comes with head or tail. Both can't be come at once.
As we see first ten tosses of a coin gives tails as a result . Then, there is no chance of occurrence head in first 10 tosses.
So, there in no heads in first 10 tosses. The probability or proportion of heads after the first 10 tosses is 0/10 = 0..
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#Complete Question:
Probability works not by compensating for imbalances but by overwhelming them. Suppose that the first 10 tosses of a coin give 10 tails and that tosses after that are exactly half heads and half tails. (Exact balance is unlikely, but the example illustrates how the first 10 outcomes are swamped by later outcomes.) (Use decimal notation. Give your answers as exact numbers.) What is the proportion of heads after the first 10 tosses?
A golf ball is manufactured so that if it is dropped from A feet above the ground onto a hard surface, the maximum height of each bounce will be one half of the height of the previous bounce.
a. Find an exponential equation that gives the height h the ball will attain during the nth bounce.
h =
b. If the ball is dropped from 13 feet above the ground onto hard a surface, how high will it bounce on the 5th
bounce?
On the 5th bounce, the ball will reach a height of ____feet.
Answers
The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
A golf ball is fabricated so that assuming it is dropped from A feet over the ground onto a hard surface, the most extreme level of each skip will be one portion of the level of the past bob.
Then the equation is given as,
h = a (1/2)ˣ
Where 'a' is the initial height.
The exponential equation that gives the height h the ball will attain during the nth bounce will be given as,
h = a (1/2)ⁿ
If the ball is dropped from 13 feet above the ground onto hard a surface. Then the height on the 5th bounce will be given as,
h = 13 (1/2)⁵
h = 13 x 1 / 32
h = 0.40625 feet
The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.
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How do you create a polynomial function from a word problem?
Attached below is the problem that I am stuck on.
Answers
Considering the volume of the rectangular prism given the dimensions, it is found that:
The expression is: V = w³ - 8w² + 15w.The degree is of 3, the number of terms is of 3, and the leading coefficient is of 1.How to obtain the volume of a rectangular prism?The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width w, the height h and the length l, that is:
V = l x w x h.
In this problem, the dimensions are given as follows:
Width w.Length w - 5.Height w - 3.Hence the polynomial expression for the volume of the prism is given as follows:
V = w(w - 5)(w - 3)
V = w(w² - 8w + 15)
V = w³ - 8w² + 15w.
The features of the polynomial function are given as follows:
Degree of 3, as the highest exponent of the function is of 3.Number of terms of 3, which are w³, 8w² and 15w.The leading coefficient is of 1, as it is the term multiplying w³.More can be learned about the volume of a rectangular prism at https://brainly.com/question/22070273
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Jayden has two jobs. One week his paycheck was the same for both jobs. As a server
he earned $9.64 per hour plus $82.35 in tips. Working at a jewelry store he earned
$14.86 per hour plus $17.10 in sales bonuses. Write an equation that can be used to
determine the number of hours, h, that Jayden worked the week his paycheck was the
same for both jobs.
Create an equation
Answers
The equation for Jayden's paycheck is,
$9.64h+ 82.35= $14.86h+ $17.10
How to construct an algebraic equation?
STEPS TO CONSTRUCT AN ALGEBRAIC EQUATION---
Identify the inquiry being made.Simple statements should be used to record pertinent information.Assign symbols to values that are still unknown.Calculate the mathematical relationships between the assertions.let the number of hours Jayden works be h hours.
so, Jayden has got the total from the jewelry store is,,$9.64h+ 82.35
Jayden has got the total from the sales bonuses is, $14.86h+ $17.10
so, the total paycheck from the jewelry store is,,$9.64h+ 82.35
and from the sales bonuses is $14.86h+ $17.10.
as they are equal, the equation is, $9.64h+ 82.35= $14.86h+ $17.10
Hence, the equation is,$9.64h+ 82.35= $14.86h+ $17.10
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help meeeeeeeeeeeeeee pleaseee
Answers
Answer:
719.412
Step-by-step explanation:
S(x)=-.228x^2+8.154x-8.3 x=7 feet
Plug in 7 for x, you'll convert to inches at the end
S(x)=.228(7^2) +8.154(7)-8.3
S=49(.228)+8.154(7)-8.3
S=11.173+57.078-8.3
S=59.951
Multiply by 12 to get inches
719.412
(If this answer doesn't work then you probably need to convert to inches before plugging in for x. 7 x 12=84 so plug that in.)
what is the 5th letter of the alphabet
Answers
The 5th letter of the alphabet is E.
What is an alphabet?An alphabet is a standardized collection of basic written symbols or graphemes that represent the phonemes of different spoken languages.
The letter a begins the English alphabet and ends with the letter z. The alphabet is always written in the same order: a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z. A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z. This is known as "alphabetical order."
The set of 26 symbols represents sounds used in speech and writing. Each character in a syllabary, for example, represents a syllable, whereas characters in logographic systems represent words, morphemes, or other semantic units. In this case, E is the 5th letter.
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In a garden club, 90% i ladie. The number of ladie i 12 more than 3 time the number of gentlemen. How many ladie and how many gentlemen are in the club. (Note et up a a rational equation and olve)
Answers
In the garden club there are 18 ladies and 2 gentlemen.
Given, In a garden club, 90% is ladies.
The number of ladies is 12 more than 3 times the number of gentlemen.
Let the total members be, x
the number of ladies be, l and the number of gentlemen be, g
according to the question,
l = 90x/100
l = 9x/10
also, l = 12 + 3g
g = (l - 12)/3
as, l + g = x
9x/10 + (9x/10 - 12)/3 = x
9x/10 + 9x/30 - 4 = x
36x/30 - 4 = x
6x/30 = 4
x = 20
so, ladies be, l = 9x/10 = 18
and gentlemen be, g = 20 - 18 = 2
Hence, in the garden club there are 18 ladies and 2 gentlemen.
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in a one-period binomial model of an option value, the probabilities of an up-move and a down-move are:
Answers
In a one-period binomial model of an option value, the probabilities of an up-move and a down-move are "calculated from the model inputs."
What is binomial model?The number of survivors, x, in n independent tests is described by a binomial model. The number of tests must be predetermined, the results—success or failure—must be statistically independent for each test, and the survival probability—p—must be constant throughout the tests. When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of observing a specified number of "successes."
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If the price of gas was $3.12 on the first day of school and $3.55 on the fifth day, what was the rate of change in the price of gas per day)
Answers
it's a easy question I think you can solve it
The total measure of two adjacent angles is 153°. if one of the adjacent angles measures 104.7°, determine the measure of the other adjacent angle. 194.7° 257.7° 48.3° 75.3°
Answers
One of the unknown adjacent angle measures 48.3 degrees.
The adjacent angles are next to each other and hence are calculated by performing addition of the constituent angles. Let us assume the unknown adjacent angle be x.
Forming the equation based on x, adjacent angles and it's sum
104.7 + x = 153
Rewriting the equation as per the x
x = 153 - 104.7
Performing subtraction on Right Hand Side of the equation to find the value of x
x = 48.3 degrees
Thus, the measure of the adjacent angle is 48.3 degrees.
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Answer: its 48.3
Step-by-step explanation:
x+104.7= 153 -104.7 -104.7 =48.3
This rectangular design is made from 6 squares. there are 2 small squares surrounded by 4 larger squares. the area of each small square of 1sq.cmwhat is the total area of the design?
Answers
The total Area the design is 8 square cm.
Area of rectangular design is product of length and breadth of rectangular design.
In the given question we have,
Rectangular design is made up from 6 squares .
there is 2 small squares surrounded by 4 large squares.
Area of each small square = 1 sq.cm
let the length of rectangular design be l cm
and breadth is b cm.
Area of rectangular design= l×b sq.cm
from the given statement, we can see that side of small square is 1 cm and small squares surrounded by 4 large squares i.e side of large square is sum of side of small squares or 2cm .
Also , length of rectangular design is sum of sides of two large squares and breadth is same as side of one large square.
so, length of rectangular design= 4 cm
breadth of rectangular design= 2cm
Area of rectangular design= 4×2 = 8sq. cm
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simplify by using order of operations 22 - (8 x 1) divided by (6 - 4) - 2
Answers
The value of the expression 22 - (8 x 1) divided by (6 - 4) - 2 is 0.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
The expression given is:
22 - (8 x 1) divided by (6 - 4) - 2
= 22 - (8 x 1) ÷ (6 - 4) - 2
= [22 - 8] ÷ [2 - 2]
= 14 ÷ 0
= 0
The value is 0.
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Give the domain and range of the relationship. List items from least to greatest. Do not include duplicates. Determine whether or not the relationship is a function.
Answers
Answer:
Domain: {7, 8, 9} Range: {2, 3, 4, 5}
Step-by-step explanation:
This relationship is not a function because one input (7) gave two different outputs (2 and 4)
A bake sale committee wants to raise $162 for a donation to a local charity. They set aside $12 of their profit at the end of each day. How many days will it take them to raise enough money for the whole donation
Answers
Answer:
It would take them 13.5 days to raise enough money.
Step-by-step explanation:
In order to find the answer, you just have to take the amount of money they want to raise, which is $162, and divide it by the amount of money they save each day, or $12. In this case that would be dividing 162/12 giving you an answer of 13.5 days.
select function or not a function
Answers
Answer:
The graph is a function.
Step-by-step explanation:
a pollster decides to poll every 10th person that comes out of a store. this alternative to random sampling is called
Answers
The alternative to random sampling is called as systematic sampling which is accepted by a pollster to poll every 10th person that comes out of a store.
Systematic sampling is a probability sampling technique where researchers choose individuals from the population at predetermined intervals (or k).
This method will provide you with a representative sample that can be used to make generalizations about the population if the order of the population is random or random-appearing (for example, alphabetical).
Simple random sampling has numerous advantages over systematic sampling in terms of randomization, but systematic sampling is a little bit simpler to carry out.
Similar to basic random sampling, systematic sampling can be used with a list of the complete population. Contrary to basic random sampling, one can still utilize this technique if you don't have access to a list of the population beforehand.
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NAME
DATE
Topic Representing Linear Relationships
PERIOD
4. A mountain road is 5 miles long and gains elevation at a constant rate.
After 2 miles, the elevation is 5,500 feet above sea level.
After 4 miles, the elevation is 6,200 feet above sea level. (Lesson 3-6)
a. Find the elevation of the road at the point where the road begins.
Answers
The elevation of the road is 4800 feet.
From the question, we have
y = mx + b
where m is the rate of change, b is the initial value of y and y, x are variables.
Let y represent the elevation of the road after x miles.
After 2 miles, the elevation is 5500 feet above sea level.
5500 = 2m + b (1)
After 4 miles, the elevation is 6200 feet above sea level.
6200 = 4m + b (2)
Solving equation 1 and 2, we get
m = 350, b = 4800
The elevation of the road 4800 feet.
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers. The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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will give you brainliest!! ASAP
Answers
Answer:
686 cm^2
Step-by-step explanation:
4(7)=28
7(7)=49
49 x 28= 1372
1372/2=686
hopes this helps
Number of factors of 10 in 10²
Answers
Answer:
24
Step-by-step explanation:
give me brainliest pls
A rectangle has width 2x + 0.6 and width x -0.4. The perimeter of the rectangle is
51.4 cm. What are the length and width of the rectangle?
Answers
Answer:notsure
Step-by-step explanation:
If f(x) = 10 - 200 and g(x) = 25x2 + 90, the value of f (4) - g (2) is:
Answers
As function f(x) is not completely right i assume it to be like f(x)= 10x-200.
Acc. to which the answer is -350.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.
Main Body:
f(x)= 10x-200
f(4)= 10*4-200
= 40-200
=-160
g(x)= 25[tex]x^{2}[/tex]+90
g(2)= 25*(2)² +90
= 25*4+90
=190
So, f(4)-g(2) = -160-190
= -350
Therefore the answer is -350.
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a sum of money was shareed between aziz and ahmad in the ratio of 4:7. aziz reeceived 21 dollars less than ahmad. find the total sum of money shareed by both of them
Answers
The total sum of money is 77 dollars .
Let the total sum of money be x .
⇒ Aziz's share = 4x / 11
Ahmad's share = 7x / 11
Given : Aziz received 21 dollars less than Ahmad
⇒ 4x / 11 = ( 7x / 11 ) - 21
Solving the above linear equation in one variable ,
( 7x - 4x ) / 11 = 21 ( taking like terms together )
3x = 21 * 11
x = 7 * 11
x = 77
Aziz's share = ( 4 / 11 ) * 77 = 28
Ahmad's share = ( 7 / 11 ) * 77 = 49
Total Sum of money = 28 + 49 = 77 dollars .
Hence , the total sum of money = 77 dollars .
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