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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Sarah's grandmother has a square blanket that covers an area of 25 square feet. Sarah wants to put a string of pearls around the sides of the blanket. How many feet long will the string of pearls have to be for Sarah to complete the job?
Answer:
20 ft
Step-by-step explanation:
area of square = (side)^2
area of square = 25 ft^2
(side)^2 = 25 ft^2
side = 5 ft since (5 ft)^2 = 25 ft^2
The side of the square measures 5 ft.
All around the square is the perimeter.
perimeter = 4 * side
perimeter = 4 * 5 ft
perimeter = 20 ft
Answer: 20 ft
-2 as a decimal
Help if you can ik it’s simple I’m just very tired :)
NEED HELP FOR REAL 69 points!!!!!!!!!!!!!! ASAP
The physicist from the last problem lets the particle fall another 100 times, and finds that the average travel time is now 16 sec. Remember that when running the simulation many times it took 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. What does she conclude and why?
Martina runs 3 miles in 25 minutes. At the same rate, how many miles would she run in 20 minutes?
Answer:
2 and a half mile
Step-by-step explanation:
As she runs three miles in 25 minutes so she can run 2 and a half miles in 20 minutes because she needs five minutes to complete the third mile
Ey pls help me anyone pls
Answer:
we cant read the whole question so I cant help you.
Step-by-step explanation:
Answer:
I will do 1-4 and explain because I dont have the time to do all of this.
1=130 2=130 3=134? 4=63 Just add up the numbers and subtract them from either 90 180 or 360, how to know which number to add up to is easy, just see if the sum of the numbers added makes a number above one of those numbers, for example if you find one that the sum is larger then 90 but smaller then 180 then subtract the sum from 180.
Step-by-step explanation:
Can anyone help me with this?
it does not show the question
An election is over and a new student body president has been elected. The new president received 3 votes for every vote received by his opponent. The new president received 2193 votes. How many votes did his opponent receive?
can someone plz help me with this
Answer:
option D .....11
Option c 36
A+B + C = 180
A= 36
What is x
Answer:
which is x here
please write complete question
A phone company offers two monthly plans. Plan A costs $10 plus an additional $0.12 for each minute of calls. Plan B costs $15 plus an additional $0.10 for
each minute of calls.
For what amount of calling do the two plans cost the
Same?
Answer:
250 minutes
Step-by-step explanation:
10 + 0.12x = 15 + 0.10x
0.02x + 10 = 15
0.02x = 5
x = 250
Your welcome!
Kayden Kohl
8th Grade Student
9% out of 432 kids want to be lawyers. How many kids did not want to be lawyers?
Answer:
393.12 kids. This is technically impossible, as you can't have 0.12 of a kid, so I will round down to 393 kids.
Step-by-step explanation:
9% = 0.09
x = amount of kids who want to be lawyers
y = amount of kids who do not want to be lawyers
x = 0.09(432)
x = 38.88
y = 432 - 38.88
y = 393.12
Right triangle CDE has its right angle at vertex
D. The length of DE is 8 feet and the length of
CE is 17 feet. What is the length, in feet, of CD?
A) 11
B) 12
C) 14
D) 15
The length of the side CD which is the base of the right triangle CDE is 15 feet which is option D.
We have,
We can use the Pythagorean theorem to solve for the length of the height CD in the right triangle CDE.
Where CE is the hypotenuse and De is the base.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have:
CD² + DE² = CE²
Plugging in the given lengths:
CD² + 8² = 17²
CD² + 64 = 289
CD² = 289 - 64
CD² = 225
CD = √225
CD = √15²
CD = 15
Thus,
The length of the side CD which is the base of the right triangle CDE is D. 15 feet.
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If f(1) = 160 and
f(n)=1/2f(n-1) what is f(5)?
Answer:
10
Step-by-step explanation:
[tex]f(n) = \frac{160}{ {2}^{(n - 1)} } [/tex]
Answer:
This is 10
f(5) = 5f
Alyssa purchased 3 pounds of peanuts for $8.25. Write an equation that shows the relationship between the cost and the number of pounds purchased
Answer:$8.25 ÷ 3= x or 3·x =8.25
Step-by-step explanation:
3*x=8.25
Write a three digit number that gives same answer when rounded to the nearest ten and to the nearest hundred .explain
Answer:
Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, the nearest million, and so on. All the numbers to the right of the place you are rounding to become zeros. Rounded numbers are easier to remember and easier to use.
PLEASEEE!! HEPPPP!!
It takes Shonda of an hour to dry one load of laundry in her dryer. How many hours will it take her to dry 4 loads of laundry?
A. 1/5
B. 1 3/5
C. 3 1/5
D. 4/5
No of hours
[tex]\\ \sf\longmapsto 4(1)[/tex]
[tex]\\ \sf\longmapsto 4 hours[/tex]
None of the above
what does n equal in 4n − 2n = 4
Answer:
Step-by-step explanation:
4 = 2
What is the vertical change from Point A to Point B?
What is the horizontal change from Point A to Point B?
What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth, if
necessary
Answer:
The vertical change is 1
The horizontal change is =2
The rate of change .5
Step-by-step explanation:
Point A is at (2,1)
Point B is at (4,2)
The vertical( up and down) change is (2-1) = 1
The horizontal ( left and right) change is (4-2) =2
The rate of change is vertical over horizontal (1/2) = .5
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
1. Vertical change :
[tex]2 - 1[/tex][tex]1[/tex]2. Horizontal change :
[tex]4 - 2[/tex][tex]2[/tex]3. Rate of change :
[tex] \dfrac{y_2 - y_1}{x_2 - x_1} [/tex][tex] \dfrac{2 - 1}{4 - 2} [/tex][tex] \dfrac{1}{2} [/tex][tex]0.5[/tex]4. Lincoln began his speech, “Four score and seven years ago....” How many years is four score and seven? (Hint: A score is 20 years.) Can someone help me?
Is it possible to construct a triangle with the side lengths of 6 cm 11cm and 13 cm why or why not?
Answer:
yes because....
Step-by-step explanation:
6 + 11 > 13
AAA help I need to do this for schoosleldkdk
Answer:
[tex] \frac{1}{8} [/tex]
Step-by-step explanation:
The total amount of cards is 8, and the stack have 4 even numbers, so the probability is
4/8 Simplify it and
1/2
Now, there are just 6 cars bigger than 6, so:
2/8. Simplify it
1/4
Now you have to multiply the two values:
1/2×1/4 = 1/8
look at the pictuse below i would copy and paste but I can't copy a picture
Answer:
I can't really see it so i don't know I'm sorry
Answer:
15
Step-by-step explanation:
find the value of a square + b square when a+b = 6 a_b = 4
Answer:
a+b=6
a-b =4
______subtract
(a-a)+(b-(-b))=6-4
0+2b = 2
b= 1
put the value of b at any equation
a+1 =6
then a=6-1=5
a square+b square= 25+1= 26
Martha Stewart has developed a new perfume. She decides to test its side effects by spraying the perfume in 31 randomly chosen houses. She records the level of antigens that create an allergic response. If the antigen level is high enough, the person will go into anaphylactic shock. The mean of her sample is a lot bigger than the median, but Martha hopes that a 90% confidence interval will contain zero. Her confidence interval is (0.116, 1.884). Disappointed, she offers you $144 to find an acceptable, realistic way to change the confidence interval to contain zero. What could you say to earn the money
The acceptable and realistic ways to to change the confidence interval to contain zero are;
Martha should decrease x-bar by providing medicine to treat shock to the perfume users.Decrease sample size than 30Increase the confidence level, till the interval contains zeroReasons:
The confidence interval is given by the following formula;
[tex]CI=\bar{x}\pm t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex]
When the mean, [tex]\overline x[/tex], is positive and large, both values, [tex]\bar{x}+ t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and [tex]\bar{x} -t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], will be positive.
Therefore, Martha has to either intervene to reduce the mean also known as x-bar
Increasing the confidence level will increase the allowable error such that [tex]\bar{x} < t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and the interval will contain zero
Therefore;
Martha should decrease x-bar, [tex]\overline x[/tex], by providing medicine to treat shock to the perfume usersUse a much smaller sample size, n, such that [tex]t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}} > \bar{x}[/tex]Increase the confidence level to 95% or 99%, thereby increasing the error boundLearn more here:
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Jessie made 15 sales calls yesterday. Clay made n calls. If clay made 3 times as many sales calls as jessie, choose the equation thats shows how many sales calls clay made yesterday
Answer:
n = (15)(3) = 45
Step-by-step explanation:
This problem is very simple, all we need to do is take the information we get and put it in equation form.
Jessie made 15 calls, Clay made 3 times as many as her. 15 times 3 is 45. Put in equation format it will look like:
n = (J) * (3)
n is how many calls Clay made, and J is how many calls Jessie made.
I need help ASAP! Is this linear increase decrease or exponential growth decay
Option B: Exponential growth
If for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.
Option A is incorrect because y is not decreasing
Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.
*EASY* I WILL GIVE BRAINLIST TO THE FIRST RIGHT ANWSER
Ruby is visiting San Francisco. From her hotel she walks 2 blocks east an 4 blocks north to a coffee shop. Then she walks 4 blocks west and 3 blocks north to a museum. Where is the museum in relation to her hotel?
here's the format for the answer if it helps : The museum is _ blocks _(West/East) and _ blocks _(South/North) of her hotel.
Answer:
Step-by-step explanation:
6. a + 6 < -2; a = -8
I
0. yes
P. no
Answer:
yes
Step-by-step explanation:
HELP !! Look at the photo please
No links just answer
Simplify
Answer:
first option _32\21 is the answer
Step-by-step explanation:
the answer will
-32/21
I'm indian just came in Canada
indians are very intelligent in maths