We want to find a polynomial given that we know its roots and a point on the graph.
We will find the polynomial:
p(x) = (183/280)*(x - 1)*(x - 1)*(x + 2)*x
We know that for a polynomial with roots {x₁, x₂, ..., xₙ} and a leading coefficient a, we can write the polynomial equation as:
p(x) = a*(x - x₁)*(x - x₂)...*(x - xₙ)
Here we know that the roots are:
x = 1 (two times)x = 0x = -2Then the roots are: {1, 1, 0, -2}
We can write the polynomial as:
p(x) = a*(x - 1)*(x - 1)(x - 0)*(x - (-2))
p(x) = a*(x - 1)*(x - 1)*(x + 2)*x
We also know that this polynomial goes through the point (5, 336).
This means that:
p(5) = 336
Then we can solve:
336 = a*(5 - 1)*(5 - 1)*(5 + 2)*5
336 = a*(4)*(4)*(7)*5
336 = a*560
366/560 = a = 183/280
Then the polynomial is:
p(x) = (183/280)*(x - 1)*(x - 1)*(x + 2)*x
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Determine which of the following is a geometric sequence.
A. 2, 5, 8, 11
B. 2, -6, -18, -24
C. 3, -6, 12, -24
D. 3, 6, 18, 36
Step-by-step explanation:
A is in geometric sequence as 3 is added in the number,
2 + 3 = 5, 5 + 3 = 8, 8 + 3 = 11
hope this answer helps you dear...take care and may u have a great day ahead!
Suppose the sum of two integers is negative. Must both be negative
Answer: Not necessarily. There are many ways to write a basic equation with a negative answer. For example, -3-4 = -7.
Step-by-step explanation:
there are 3 factors in the equation 5 x 3 x 2 = 30 true or false
Answer:
true
Step-by-step explanation:
the factors are simply what is being multiplied together. We can see there are 3 because we have 5,3,and 2. 30 is not a factor because that is the answer. I hope this helps!
help me make a apple account and put the user and password please
A circle on the coordinate plane has a diameter
with endpoints at (6, 8) and (15, 8).
a. What are the coordinates of the center of the
circle?
b. What is the diameter of the circle?
C. What is the radius of the circle?
d. Identify the coordinates of another point
on the circle. Explain how you found
your answer.
9514 1404 393
Answer:
a. (10.5, 8)
b. 9
c. 4.5
d. (10.5, 12.5)
Step-by-step explanation:
a. The center of the circle is the midpoint of the diameter. Its coordinates are the average of the end point coordinates.
C = ((6,8) +(15, 8))/2 = (21, 16)/2 = (10.5, 8) . . . circle center
__
b. The diameter lies on the horizontal line y=8, so its length is the difference of the x-coordinates of the end points: 15 -6 = 9 . . . circle diameter
__
c. The radius is half the diameter: 9/2 = 4.5 . . . circle radius
__
d. Another point on the circle will be 4.5 units from the center on the same vertical line: (10.5, 8) +(0, 4.5) = (10.5, 12.5) . . . another point on the circle
First calculate the Subsets for set, then calculate the number of proper subsets {10,19,5,0}
The subsets of {10, 19, 5, 0} are
{ } - the empty set, or 1 subset of size 0
{10}, {19}, {5}, {0} - 4 subsets of size 1
{10, 19}, {10, 5}, {10, 0}, {19, 5}, {19, 0}, {5, 0} - 6 subsets of size 2
{10, 19, 5}, {10, 19, 0}, {10, 5, 0}, {19, 5, 0} - 4 subsets of size 3
{10, 19, 5, 0} - 1 subset of size 4
A proper subset of a set is any subset of that set that is not equal to that set. The only subset that is not a proper subset is {10, 19, 5, 0}, since that's the set itself. So there are 15 proper subsets.
In general, a set of size n has a total of 2ⁿ subsets, and 2ⁿ - 1 proper subsets.
Please solve this in under 15 minutes! It’s due in 20 minutes!
Answer:
i think that it would be the second one
Write the equation of a line that
goes through the points (3,7) and
(-3,5).
Answer:
[tex]y = mx + c \\ 7 = 3m + c \\ 5= - 3m + c \\ 2c = 12 \\ c = 6 \\ 7 = 3m + 6 \\ 3m = 1 \\ m = \frac{1}{3} \\ y = \frac{1}{3} x + 6[/tex]
What time is 13 hours past 1:00 am
Answer:
2 pm
Step-by-step explanation:
Answer:
I'm guessing it's 1:00pm? Or 2, not really sure, sorry
Hello, need help on this (:
The answer is attached below
Answer:
he anwersed so hello
Step-by-step explanation:
Someone help me pls, this is a distance time graph
Answer:
it's b
Step-by-step explanation:
just took the test
The Scientific Method Which of these is the best reason for doing more background research after making an observation and before forming a hypothesis? to find the answer without having to do an experiment to prevent making the same mistakes made in a prior experiment to fill the space in your lab report to make your data agree with prior experiments
Answer:
Step-by-step explanation:
The best reason for doing more background research after making an observation and before forming a hypothesis is to prevent making the same mistakes made in a prior experiment. It is to make sure that you are able to see the problems of a research and make an experimental design that will minimize the errors?
I keep getting it wrong help
what is 13q - 9q + 5 = 17
the answer is: q=3
start by combining like terms (13q - 9q) which would leave you with 4q + 5 = 17. subtract 5 from both sides and you're left with 4q = 12. divide by 4 on both side and you get q = 3
Answer:
q=3
Step-by-step explanation:
13q - 9q + 5 = 17
13q - 9q = 17 - 5
4q = 12
4q/4 = 12/4
q = 3
What is an equation of the line that passes through the point (-5,-6) and is parallel to the line x+5y=25x+5y=25?
Answer:
[tex]y = - \frac{1}{5} x - 7[/tex]
Step-by-step explanation:
let's rewrite the equation
[tex]x + 5y = 25 \\ 5y = - x + 25 \\ y = - \frac{1}{5} x + 5[/tex]
Now let's use the given point and substitute it to find the y-intercept
[tex] - 6 = - \frac{1}{5} ( - 5) + b \\ - 6 = 1 + b \\ b = - 7[/tex]
The required solution of the given equation of the line that passes through the point (-5,-6) and is parallel to the line x+5y=25 is
[tex]y=\frac{-1x}{5} -7[/tex].
What is slope?Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it.
Given:
The point is (-5,-6) and is parallel to the line x+5y=25.
According to given question we have
By use of slope we get
x+5y=25
5y=25-x
Divide both sides 5 we get,
y=-1/5x+5
Where m= -1/5
Now you can find the equation of the parallel line using
[tex](y-y_{0} )=m(x-x_{0})[/tex]
Put the given point as (-5,-6) we have,
[tex](y+6)=\frac{-1}{5} (x+5)\\\\y=\frac{-1x}{5} -1-6\\\\y=\frac{-1x}{5} -7[/tex]
Therefore, the required solution of the given equation of the line that passes through the point (-5,-6) and is parallel to the line x+5y=25 is
[tex]y=\frac{-1x}{5} -7[/tex].
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Which of the functions below could have created this graph?
A. F(x) = x2 + x2+x+1
B. F(x)= x2 +5
F*+6
c. - *-+*
(-)y-
D
Answer:
only D is negative on the leading term
Suppose f(x) = x ^ 3 Find the graph of f(x + 3) Click on the correct answer
Answer:
f(x)=(x+3)^3, horizontal translation/shift of 3 units to the left.
Step-by-step explanation:
f(x)=x^3 is your given function. f(x+3) is a horizontal shift of 3 units to the left because the "+3" is inside the parentheses and it's a shift to the left instead of the right because x needs to equal -3 for the quantity to equal 0. Overall, the graph shifts 3 units to the left.
The school auditorium has 438 seats. There are 18 rows of seats. What is the best estimate for the number of each seats in each row?
Answer:
24
Step-by-step explanation:
Model and Solve the problem.
5x1/2 Please hurry!!
Answer:
2.5
Step-by-step explanation:
i just did 5 times 0.5 hope this helped.
and 2.5 is greater then 2.05
HURRY UP I NEED HELP
What is the slope of the line that passes through the points (−3, 1) and (1, −5)? 1/2 −2/3 −3/2 I don't know.
PLEASE HELP DUE AT 12:00 PM
Answer:
A) 5; B) 32; C) 3; D) 14; E) 1/3
Step-by-step explanation:
Answer:
1. 5
2. 42
3. 3
4. 14
5. 0.3333
Step-by-step explanation:
Third Grade:
8 x 5 = 40
8 + 42 = 40
21 ÷ 7 = 3
21 - 14 = 7
---------------------------21 • x = 7
Which can be written as:
21x = 7
To solve the equation above, we need to remove the 21 on the left side to make the x alone. To do that, we divide both sides by 21.
21x/21 = 7/21
21x/21 is x and 7/21 is 0.3333 which means our equation will look like this:
x = 0.3333
Thus, the answer to "21 times what equals 7?" is 0.3333.
Which of the following graphs represents the equation −2 + = 10?
what’s 5 5/32 (as an mixed number ) as a decimal.
Answer:
Convert 5 5/32 to an improper fraction.
Step-by-step explanation:
Exact Form:
165/32
Decimal Form:
5.15625
Mixed Number Form:
5 5/32
Answer:
[tex]{ \tt{5 \frac{5}{32} = \frac{(32 \times 5) + 5}{32} }} \\ \\ = { \tt{ \frac{165}{32} }} \\ \\ = { \boxed{ \tt{5.15625}}}[/tex]
PLS HELP QUICK
Write an
equivalent expression (simplify): 14h + 12 - 8h - 3
Answer:
22h - 9
Step-by-step explanation:
14h + 12 - 8h - 3
14h + 8h + 12 - 3
22h + 12 - 3
22h + 9
Recibes un cierto embarque con la promesa de que no tiene más del 15% de ítems defectuosos. Si la proporción o porcentaje de ítems defectuosos es mayor queel15%,puedes solicitar una devolución. Tomas una muestra aleatoria de 10 ítems y encuentras 6ítems defectuosos. Ciertamente 6es más del 15% de la muestra.Presentas tu queja y te responden: el embarque tiene menos del 15% de ítems defectuosos. Si usted encontró 6 en su muestra, fue simplemente coincidencia o mala suerte, porque el embarque sí cumple con lo establecido.¿Cuál es la probabilidad de que realmente haya sido fruto de la coincidencia? ¿Cómo argumentarías para conseguir que te devuelvan el dinero?
Usando la distribución binomial, se encuentra que hay una probabilidad de 0.0012 = 0.12% que realmente haya sido fruto de la coincidencia. El argumento para conseguir que te devuelvan el dinero seria de que 6 ítems defectuosos es un resultado inusualmente alto.
Para cada ítem, solo hay dos resultados posibles. O está defectuoso o no lo es. La probabilidad de que un ítem sea defectuoso es independiente de cualquier otro ítem, lo que significa que se utiliza la distribución binomial para resolver esta cuestión.
Distribuición binomial:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
n es el número de ensayos.p es la probabilidad de éxito en un ensayo x es el número de éxitosLa media de la distribución binomial es:
[tex]E(X) = np[/tex]
La desviación estándar de la distribución binomial es:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Una medida se considera inusualmente alta si está más de 2.5 desviaciones estándar por encima de la media.
En este problema:
10 ítems, o sea, [tex]n = 10[/tex]15% defectuosos, o sea, [tex]p = 0.15[/tex].La probabilidad de que realmente haya sido fruto de la coincidencia es P(X = 6), o sea:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{10,6}.(0.15)^{6}.(0.85)^{4} = 0.0012[/tex]
Probabilidad de 0.0012 = 0.12% que realmente haya sido fruto de la coincidencia.
Para el argumento:
[tex]E(X) = np = 10(0.15) = 1.5[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10(0.15)(0.85)} = 1.13[/tex]
[tex]6 > 1.5 + 2(1.13)[/tex], o sea, el argumento para conseguir que te devuelvan el dinero seria de que 6 ítems defectuosos es un resultado inusualmente alto.
Un problema similar es dado en https://brainly.com/question/22304471
PLEASE HELP ITS MATH THANK YOUUUU
Please help fast brainly will be given
Answer:
1. 500 milligrams
2. 6450 grams
3. 50 oranges
4. 30 weeks
5. 1500 grams
To do this, all you basically need to do is convert grams, milligrams, etc.
You also need to do Multiplying, Dividing, Adding, and Subtratcing.
Please give me Brainliest!
What is the answer to number 4
Round $23.8763 to the nearest hundred
Answer: I would say 23.88
Step-by-step explanation:
Answer pls I don’t know.
Answer:
x < -5
Step-by-step explanation:
We have that The solution set for -the inequality 4x+10≥5x+55 is mathematically given as
From the question we are told
What is the solution set for -4x+10≥5x+55
Generally the equation for the Inequality is mathematically given as
Therefore
-4x + 10>5+55
-9x > 45
x < -5
The solution set for -the inequality 4x+10≥5x+55 is mathematically given as
Answer:
C
Step-by-step explanation:
1. subtract 5x on both sides
-9x+10>55
2. subtract 10 on both sides
-9x>45
3. divide both sides by 9
x<-5
(sorry I didn't have the less than or equal to & more than or equal to sign