Determine an nth degree polynomial that satisfies the aforementioned conditions.
Answers
The polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.
Given that,
An nth degree polynomial p meets the requirements listed below:
p is of degree 3.
-3 is a multiplicity 1 zero of p.
-4 is a zero, with multiplicity 1, of p.
3 is a root, with multiplicity 1, of p.
p(-2)=-40
We have to determine an nth degree polynomial that satisfier the conditions.
Let the polynomial be p(x) whose zero are -3,-4 and 3.
a be the coefficient.
p(x)=a(x+3)(x+4)(x-3)
p(x)=a(x²-3²)(x+4)
p(x)=a(x²-9)(x+4)
p(x)=a(x³+4x²-9x-36)
Now, take x=-2
p(-2)=a((-2)³+4(-2)²-(-2)-36)
-40=a(-8+16+2-36)
-40=a(-26)
a=-40/-26
a=40/26
a=20/13
We get,
p(x)=20/13((x+3)(x+4)(x-3))
p(x)=20/13(x³+4x²-9x-36)
Therefore, the polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.
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Related Questions
A line intersects the points
(8, -4) and (-6, 10).
m = -1
Write an equation in point-slope form
using the point (8, -4).
-
y + 4 = [?] (x −
Enter
Answers
Answer:
y + 4 = -(x - 8)
Step-by-step explanation:
The point-slope form equation is y - y1 = m(x - x1)
Since we're given m and since they use the 4 from (8, -4) as y - (-4) = y+4, we simply need to plug in 8 into the RHS of the equation and you can check the math.
If you substitute 8 and -4 for y and x, you have:
-4 + 4 = -1(8 - 8)
0 = -1 * 0
0 = 0
You'd get -2 on both sides if you used -6 and 10, but having an equal equation means our math is true/accurate.
A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer.
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line x = 0 is an asymptote of the graph.
The point (0,30) contains the x-intercept.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
The asymptote indicates that there were never more than 800 mice in existence.
Answers
Answer:
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
Step-by-step explanation:
Took the test
Solve for a : a+4/5= 1/ 1/2
Answers
[tex]a=\frac{6}{5}[/tex].
Step-by-step explanation:1. Write the expression.[tex]a+\frac{4}{5} =\frac{1}{\frac{1}{2} }[/tex]
2. Convert the right hand side of the equation (check attached image 1).[tex]a+\frac{4}{5} =1*\frac{2}{1} \\ \\a+\frac{4}{5} =2[/tex]
3. Subtract 4/5 from both sides of the equation.[tex]a+\frac{4}{5}-\frac{4}{5} =2-\frac{4}{5}\\ \\a=\frac{2}{1}-\frac{4}{5}\\\\a=\frac{2*5}{1*5}-\frac{4}{5}\\ \\a=\frac{10}{5}-\frac{4}{5}\\ \\a=\frac{10-4}{5} \\ \\a=\frac{6}{5}[/tex]
4. Verify your answer.[tex](\frac{6}{5} )+\frac{4}{5} =\frac{1}{\frac{1}{2} }\\ \\\frac{10}{5} =2\\ \\2=2[/tex]
5. Conclude.[tex]a=\frac{6}{5}[/tex].
2 3/5 divided by 9 3/5
Answers
Answer:
as decimal
0.27083333333
Answer:
2 3/5 divided by 9 3/5 is 32
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?
Answer the questions to solve this problem using a system of equations.
1. Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read. (1 point)
2. Write an equation to represent the number of pages Jesse has read.
Using x, the number of days Amir has been reading, write an expression to represent the number of days Jesse has been reading. Remember that Jesse started reading one day before Amir. Use this expression to write an equation for the number of pages Jesse has read. Let y represent the number of pages read. (1 point)
3. Write the system of equations using your answers from questions 1 and 2.
(2 points)
5. Solve the system of equations. Show your work. (2 points)
6. Interpret your solution. How many days does it take Amir to catch Jesse? At that time, how many pages have they read? (2 points)
Answers
1. An equation representing the number of days Amir has been reading and the number of pages he has read is y = 35x.
2. An equation representing the number of days Jesse has been reading and the number of pages she has read is y = 30 + 30x.
3. The system of equations from 1 and 2 is y = 35x and y = 30 + 30x.
4. At the end of Friday, after solving the equations, both Jesse and Amir read 210 pages each, with Jesse spending 7 days and Amir 6 days.
5. For Jesse and Amir, the equation solutions are y is 210 pages and x is 6 days.
6. After solving the equations, it will take Amir 6 days to catch up with Jesse and each person must have read 210 pages or a total of 420 pages.
What is a system of equations?A system of equations involves using more than one equation solved simultaneously.
Jesse's reading rate per day = 30 pages
Amir's reading rate per day = 35 pages
The number of pages read by Jesse, y = 30 + 30x
The number of pages read by Amir, y = 35x
Where x = the number of days they have been reading
Solving the equations:y = 30 + 30x and y = 35x
35x = 30 + 30x
35x - 30x = 30
5x = 30
x = 6 (30/5)
Jesse:y = 30 + 30x
y = 30 + 30(6)
y = 210
Amir:y = 35x
y = 35(6)
y = 210
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Complete the number sentence. Must show your work. Please help! I’m confused
Answers
Answer:
2 + (-10) = 12
Step-by-step explanation:
The great answers. Thank you. I hope for help to you.
-9 + (-13) = -22
-25 + 16 = -9
-16 + (-13) = -29
Word problem involving the Pythagorean Theorem
A kite is flying 8 ft off the ground. Its line is pulled taut and casts a 6-ft shadow. Find the length of the line. If necessary, round your answer to the nearest
tenth.
6
0f
x 5
Answers
The length of the line is 10ft
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse in familiar algebraic notation, a2 + b2 = c2
Given that A kite is flying 8 ft off the ground. Its line is pulled taut and casts a 6-ft shadow
We have to find a third side
By using Pythagoras' theorem. a^2+b^2=c^2
8^2+6^2=c^2
64 +36 = c^2
c^2= 100
c^2= 10
Therefore the length of the line is 10ft
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17 Solve the inequality. Graph the solution. 4.2y ≤ -12.6 The solution is and then where it goes on thr number line
Answers
The solution to this inequality in interval notation is {-∞, -3} and it goes to the left on the number line.
What is an inequality?In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data such as integers, and variables in an equation based on any of the following inequality symbols:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).From the information provided, we have the following inequality:
4.2y ≤ -12.6
Dividing both sides of the inequality by 4.2, we have the following:
y ≤ -12.6/4.2
y ≤ -3
In conclusion, a solution to this inequality is equal to {-∞, -3} as shown in the number line (graph) attached below.
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could you describe the expression 2(3+4) as a product of two factors explain
Answers
The expression 2(3+4) can be expressed as 2×7
What are factors?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
For example the factors of 8 are 1,2,4,8. i.e 1×8=8, 2×4= 8
considering the expression 2(3+4), the value is 2(7)= 14
Therefore the expression can be expressed as product of two factors (2 and 7) as 2×7.
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The function f(x) is graphed below. How many points on the graph
represent a relative extreme value?
Answers
From the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).
As given in the question,
For the given graph of a function,
Number of points represented on the graph are 5
Points are a, b, c, d, e
Point a, c, e are on the x-axis.
Relative extreme value representing the maximum and minimum value of the graphed function.
For the given graph,
Maximum value represented by point d.
Minimum value represented by point b.
Number of points representing relative extreme values are 2 ( b and d).
Therefore, from the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).
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HELP ME PLEASE
not sure what to do
Answers
Since we are give the area, the length, and the width, we could put it in a formula.
2592=(16)(12)h
Multiply 16 x 12= 192
So now the formula is 2592= 192h
lastly, we divide 192 from 2592
h= 13.5 mm
−18 < 9x
how to solve and answer
Answers
Answer:
x> 2
Step-by-step explanation:
18< 9x Divide both sides by 9
2<x or x > 2 All the numbers greater than 2 is a solution.
Suppose you earned a $710,000 bonus this year and invested it at 8.25% per year. how much could you withdraw at the end of each of the next 20 years? select the correct answer.
Answers
Withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]
What do you mean by simple interest and compound interest?
Simple interest can be defined as the amount that is paid back using borrowed money over a period of time.
simple interest:
Simple interest can be defined as the principal of a loan or deposit that an individual puts into a bank account.
Compound interest:
Compound interest is interest that accrues on the principal and accrues interest.
Given:
Principal, P = $710000
Rate of interest, r = 8.25%
Time period, t = 20 years
withdrawal at the end of 20 years , A = [tex]P(1+r)^{t}[/tex]
A = [tex]710000(1+8.25/100)^{20}[/tex] = [tex]710000(1+0.0825)^{20}=710000(1.0825)^{20}[/tex]
Therefore, withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]
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The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
Answers
Answer:
Step-by-step explanation:
The maximum that the company can expect for returned items is C. $5972.65
How to calculate the value?
From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The maximum the company can expect for returned items will be:
= (15% + 4%) × Profit
= 19% × $31,435
= 0.19 × $31,435
= $5972.65
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A bag has 2 red, 3 green, and 6 orange balls. If a ball is randomly selected from the bag, what is the theoretical probability
that it is the color specified in parts (a) through (d).
a) green
b) not green
c) orange
d) not orange
***
Answers
Using theoretical probability, the probability of selecting green ball is 3/11, not selecting green ball is 8/11, selecting orange ball is 6/11 and not selecting orange ball is 5/11.
In the given question,
A bag has 2 red, 3 green, and 6 orange balls.
So total number of balls = 2+3+6 = 11
We have to find the theoretical probability.
(a) We have to find the theoretical probability of selecting green ball.
P(G) = Total number of green balls/Total number of balls
P(G) = 3/11
Hence, the probability of selecting green ball is 3/11.
(b) Now we have to find the theoretical probability of not selecting green ball.
Except green ball there is having red and orange i.e.
Total remaining balls except green = 2+6 = 8
P(G) = Total number of balls except green balls/Total number of balls
P(G) = 8/11
Hence, the probability of not selecting green ball is 8/11.
(c) Now we have to find the theoretical probability of selecting orange ball.
P(G) = Total number of orange balls/Total number of balls
P(G) = 6/11
Hence, the probability of selecting green ball is 6/11.
(d) Now we have to find the theoretical probability of not selecting orange ball.
Except orange ball there is having red and green balls i.e.
Total remaining balls except orange = 2+3 = 5
P(G) = Total number of balls except orange balls/Total number of balls
P(G) = 5/11
Hence, the probability of not selecting orange ball is 5/11.
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Melinda needed to mail a package. She used .02 stamps and .10 stamps to mail the package. If she used 15 stamps worth .78 how many of each type of stamp did she use
Answers
The number of each type of stamp used is as follows:
9 of 0.02 stamps6 of 0.1 stampsHow to find how many of each type of stamp used?Melinda needed to mail a package. She used .02 stamps and .10 stamps to mail the package. She used 15 stamps worth 0.78. The number of each type of stamp she used can be calculated as follows:
let
x = number of 0.02 stamp
y = number of 0.10 stamp
Using system of equation,
x + y = 15
0.02x + 0.10y = 0.78
multiply equation(ii) by 50
x + y = 15
x + 5y = 39
4y = 24
y = 24 / 4
y = 6
Hence,
x = 15 - 6
x = 9
Therefore, the number of 0.02 stamps is 9 and the number of 0.10 stamp is 6.
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Find a point-slope form for the line that satisfies the stated conditions. Slope 4, passing through (-8,1)
Answers
Answer: (y - 1) = 4(x + 8)
Step-by-step explanation:
The point-slope form is (y - y₁) = m(x - x₁), where:
m = slope = 4(x₁, y₁) = (-8, 1)So, the point-slope of this line would be (y - 1) = 4(x + 8).
PLEASE HELP ASAP! WILL GIVE BRAINLIEST AND FIVE STAR RATING FOR ACTUAL HELP! Describe the function‘s end behavior. f(x)=−10+6x^5+4x^3
as x→ ∞, f(x)→
as x→ −∞, f(x)→
Possible answers for both are:
-∞
∞
0
an asymptote
Answers
Answer: As x approaches infinity, f(x) approaches infinity.
As x approaches -infinity, f(x) also approaches - infinity.
Step-by-step explanation:
You can either graph this function on an online graphing (such as desmos. com) calculator to see the end behavior, or you can try inputting some numbers in. You could put in the number 1,2,3 and see that the graph will keep on increasing to positive infinity, and input the numbers -1,-2,-3 to see that the numbers will decrease to negative infinity.
In how many ways can the digits in the number 7,550,000 be arranged
Answers
The number of ways the digits of the given number can be arranged would be = 5,040
What is factorials?Factorials are mathematical expressions that are used to show the number of ways a variable can be arranged in a data set.
The number of digits found in the number 7,550,000 = 7
The number of ways the digits can be arranged would be the factorials of 7 (7!) ;
= 7×6×5×4×3×2×1
= 5,040
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The mean of 6 numbers is 8.
The numbers are in the ratio 1 : 1 : 2 : 2 : 3 : 3.
Find the range.
Answers
The range of six numbers is 8
According to the question,
Total number of Number = 6
Mean of number = 8
Ratio of numbers = 1 : 1 : 2 : 2 : 3 : 3
Let the common factor in numbers be "x"
Then , sum of number will be x + x + 2x + 2x + 3x +3x
=> 12x
Mean = sum of quantity / Number of quantity
8 = 12x / 6
Calculating the value of x,
12x = 48
=> x = 4
Substituting the value of x,
Number will be : 4 , 4 , 8 , 8, 12 , 12
Range = highest number - smallest number
Here , highest is 12 and smallest is 4
Therefore , Range = 12 - 4
=> 8
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Ling tried to solve an equation.
12=p+6.2
12 + 6.2 = p + 6.2- 6.2 Setting up
18.2 = P Calculating
Answers
Answer:
p = 5.8
Step-by-step explanation:
12 = p + 6.2 Subtract 6.2 from both sides. Ling subtracted 6.2 from the right, but added it to the left side.
5.8 = p
Graph the equation y= - 7/2 x + 2 on the coordinate plane
Answers
Refer to the attachment for your graph.
Consider the function f(x) = √ x+2 and g(x) = ax+b. Find a and b, if fog (1) = 2 and g (-1)=2.
Answers
The value of a and b in the function f(x) = √ x+2 and g(x) = ax + b , is a = 0 and b = 2 .
In the question ,
it is given that ,
the function f(x) = √(x+2) and the function g(x) = ax + b
also given that
fog(1) = 2
f(g(1)) = 2
f(a + b) = 2 .... because g(1) = a + b
√(a + b +2) = 2
Squaring both the sides
a + b + 2 = 4
a + b = 2 .......(1)
also given that
g(-1) = 2
a(-1) + b = 2
-a + b = 2 .....(2)
Adding equation (1) and (2) , we get
2b = 4
b = 2
Substituting b = 2 in the a + b = 2 , we get
a + 2 = 2
a = 2 - 2
a = 0
Therefore , The value of a and b in the function f(x) = √ x+2 and g(x) = ax + b , is a = 0 and b = 2 .
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Given the inequality 4(n − 5) < 3(n + 11), determine which integer makes the inequality false.
S:{4}
S:{11}
S:{53}
S:{−8}
Answers
Answer:
C
Step-by-step explanation:
4(n-5)<3(n+11)
4n-20<3n+33
4n-3n<33+20
n<53
n is not 53 but less than 53.
It takes 3.5 ounces of cocoa to make a cup of hot chocolate how much cocoa is needed to make 7 cups of hot chocolate
Answers
Answer: 24.5
Step-by-step explanation: 3.5 x 7 = 24.5
Answer: 24.5 ounces
Step-by-step explanation:
3.5 times 7 = 24.5 ounces
If you have trouble try
3.5 + 3.5 + 3.5 + 3.5 + 3.5 + 3.5 + 3.5
What is the slope of the
function below?
(4,4)
(3, 3)
Slope = [?]
Answers
Answer:
slope is m=1
Step-by-step explanation:
Answer: 1
Step-by-step explanation: use the slope formula to find the slope m
Write a linear function f with f(0)=7 and f(3)=1
y=mx+b
Answers
The linear function f with f(0) = 7 and f(3) = 1 is y = -2x + 7
How to represent linear equation?Linear equation can be represented in slope intercept form as follows:
y = mx + c
where
m = slopec = y-interceptTherefore,
f(0) = 7 and f(3) = 1
Using linear equation
7 = m(0) + b
b = 7
1 = m(3) + 7
1 - 7 = 3m
-6 = 3m
m = - 6 / 3
m = -2
Therefore, the linear function is y = -2x + 7
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c) ¿Cuántas combinaciones se pueden hacer en seleccionar los tres lugares ganadores de una carrera de 15
caballos?
Answers
Hay un total de 2730 combinaciones posibles.
¿Qué es permutación y combinación?Las permutaciones y combinaciones forman principios de conteo, que se aplican en muchas situaciones diferentes. Una permutación es el número de arreglos diferentes que se pueden hacer a partir de un conjunto dado. Cuando se trata de permutaciones, los detalles importan porque el orden o el orden importan. Este orden en el que escribe los nombres de los países es importante, ya que escribir los nombres de los tres países {EE. UU., Brasil, Australia} o {Australia, EE. UU., Brasil) o {Brasil, Australia, EE. UU.} es diferente. En combinación, los nombres de los tres países son solo un grupo, y el orden o secuencia no importa. Obtenga más información sobre permutaciones y combinaciones en el siguiente contenido. Las permutaciones y las combinaciones son métodos que se utilizan para contar el número de resultados posibles en diversas situaciones. Las permutaciones se entienden como arreglos y las combinaciones se entienden como alternativas. Siguiendo los principios básicos del conteo, hay reglas de suma y reglas de multiplicación para una fácil aplicación del conteo. Supongamos que hay 14 niños y 9 niñas. Al elegir un niño o una niña como maestro de salón, el maestro de salón puede elegir 1 de cada 14 niños y 1 de cada 9 niñas. Puede hacerlo en sus 14 + 9 = 23 maneras (usando la regla de la suma de conteo).Cálculoen carrera de 15 caballos si se consideran 3 posiciones
entonces número de combinaciones posibles = 15 * 14 * 13 = 2730 combinaciones posibles
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Write an equation for line L in point-slope form and slope-intercept form.
L is parallel to y = 5x.
-6
-4
-2
Ay = 5x
6-
4
2
-6
L
(3,2)
6
X
5
Answers
y-2=5x(x-3) - point slope form
y=5x-13 - slope intercept form
A store is having a sale on walnuts and chocolate chips. For 6 pounds of walnuts and 5 pounds of chocolate chips, the total cost is $28. For 2 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $14. Find the cost for each pound of walnuts and each pound of chocolate chips.
Answers
Answer:
chocolate- 2 dollars walnuts- 4
Step-by-step explanation:
2 x3=6. 14-6=8
8÷2=4