Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros of multiplicity 2) and (multiplicity 1) and with f(0) = 15. f(x) = Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -2 (multiplicity 1), 3 (multiplicity 2), and with f(0) = -54. f (x) = 0 Write a polynomial f(x) that satisfies the given conditions. Degree 3 polynomial with integer coefficients with zeros 7i and 8 5 f (x) = 0
Answers
Here are the polynomials that satisfy the given conditions:a. Polynomial of lowest degree with zeros of multiplicity 2 and multiplicity 1 and with f(0) = 15To create a polynomial of degree two with a zero of multiplicity 2 and another zero of multiplicity 1, we must have a quadratic of the following form:(x - a)(x - a)b = x^2 - (2a) x + a^2.
We should have another factor of the form (x - b), so the quadratic can be multiplied by this linear factor, giving a cubic function:f(x) = k(x - a)^2 (x - b)We are told that the function passes through the point (0, 15), so we can use this information to figure out the value of k. f(0) = 15k(a)(-b) = 15Then the cubic polynomial with zeros of multiplicity 2 and 1 and with f(0) = 15 is: f(x) = 5x^3 - 25x^2 + 0x + 0b. Polynomial of lowest degree with zeros of -2 (multiplicity 1), 3 (multiplicity 2), and with f(0) = -54 . Similar to the first case, let us create a quadratic first: (x + 2)(x - 3)^2Then multiplying the quadratic by (x - b).
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Related Questions
5. An inequality is shown.
-1/3x+ 1/2< 3.5
What is the solution to the inequality?
A X > -12
B. x < -12
C. X > -9
D. x < -9
Help!!
Answers
Answer:
x>−9
Step-by-step explanation:
Hope this helps.
9. The value of a book is $258 and decreases at a rate of 8% per year. Find the value of the book after 11 years.
2 S5698
h $159. 05
c. $101. 38
d. S103. 11
Answers
The value of the book after 11 years is $101.38. Therefore, the correct option is C.
Find the value of the book after 11 years with an initial value of $258 and a decrease rate of 8% per year as follows.
1. Convert the percentage decrease to a decimal by dividing it by 100:
8% / 100 = 0.08
2. Subtract the decimal from 1 to represent the remaining value each year:
1 - 0.08 = 0.92
3. Raise the remaining value (0.92) to the power of the number of years (11):
0.92^11 ≈ 0.39197
4. Multiply the initial value of the book ($258) by the calculated remaining value (0.39197):
$258 × 0.39197 ≈ $101.07
Therefore, after 11 years, the value of the book is approximately $101.07, which is closest to option C, $101.38.
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Write a unit rate for the situation. Round to the nearest hundredth if necessary. 210 heartbeats in 3 minutes
Answers
Answer:
70 heartbeats per second
Step-by-step explanation:
Given f(x)=4x^2+9x+9, find f(−1)
Answers
The value of the function f(-1) is -4
What is a function?A function is simply described as an equation that explains the relationship between the independent variable and the dependent variable.
From the information given, we have the function;
f(x)=4x^2+9x+9
To determine the value of f(-1)
substitute the value of x as- 1, we get;
f(-1) = 4(-1)² + 9(-1) + 9
expand the bracket, we get;
f(-1) = -4 -9 + 9
Add or subtract the values, we have;
f(-1) = -4
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additive inverse of 1 3/4.
Answers
Answer: I think its -1 3/4
Step-by-step explanation:
54Find the exact value of x.
Answers
5/x = x/ 9
Cross-multiply
x² =45
Take the square root of both-side
x = 3√5 or 6.7082039325
the size of a television screen is given as the length of the diagonal. if a television is advertised as having a 30-inch screen and a height of 18 inches, what is the width of the television?
Answers
The width of the television is 24 inches.
To find the width of the television, we can use the Pythagorean theorem, which relates the length of the diagonal (hypotenuse) to the height and width (legs) of a right-angled triangle.
Let's denote the width of the television as w, the height as h, and the diagonal as d.
According to the Pythagorean theorem, we have:
\(d^2 = w^2 + h^2\)
In this case, we know that the diagonal (d) is 30 inches, and the height (h) is 18 inches. We want to find the width (w).
Substituting the known values into the equation, we get:
\(d^2 = w^2 + h^2\)
\(900 = w^2 + 324\)
Rearranging the equation to isolate w, we have:
\(w^2 = 900 - 324\)
\(w^2 = 576\)
Taking the square root of both sides to solve for w:
\(w =\sqrt{576}\)
\(w = 24\)
Therefore, the width of the television is 24 inches.
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according to the smcre model presenters have the most control over the source variable beause they cn control of their appearance. True or false?
Answers
False. According to the SMCRE model, which stands for Source, Message, Channel, Receiver, and Environment, presenters do not have the most control over the source variable.
According to the SMCRE model, which stands for Source, Message, Channel, Receiver, and Environment, presenters do not have the most control over the source variable. In this model, the source variable refers to the information being presented or communicated. While presenters can influence the source through their choice of content and delivery, they do not have complete control over it. The source variable can also include factors such as the underlying research, data, or ideas being conveyed, which may not be directly controlled by the presenter. Other variables, such as the message, channel, receiver, and environment, also play significant roles in the overall communication process.
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find the velocity, acceleration, and speed of a particle with the given position function. r(t) = (− 1/2^t2, 2t)v (t) =a (t) =|v (t)| =
Answers
Particle's velocity, acceleration, and speed are found by differentiating its position function r(t) = (-1/2t^2, 2t) and calculating the magnitude of its velocity vector. Velocity: (-t, 2), acceleration: (-1, 0), and speed: sqrt(t^2 + 4).
To find the velocity, acceleration, and speed of a particle with the given position function r(t) = (-1/2t^2, 2t), we'll follow these steps:
1: Find the velocity (v(t)) by taking the derivative of r(t).
v(t) = (dr/dt) = (-d(1/2t^2)/dt, d(2t)/dt)
2: Calculate the derivatives.
v(t) = (-t, 2)
3: Find the acceleration (a(t)) by taking the derivative of v(t).
a(t) = (dv/dt) = (d(-t)/dt, d(2)/dt)
4: Calculate the derivatives.
a(t) = (-1, 0)
5: Find the speed |v(t)| by calculating the magnitude of the velocity vector.
|v(t)| = sqrt((-t)^2 + (2)^2)
|v(t)| = sqrt(t^2 + 4)
In conclusion, the velocity v(t) of the particle is (-t, 2), the acceleration a(t) is (-1, 0), and the speed |v(t)| is sqrt(t^2 + 4).
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What do you mean by 184x9302
Answers
Answer:
1711568
Step-by-step explanation:
184*9302 = 1711568
Use a calculator to check your work
Graph the following inequalitiesy < 2/5x - 3
Answers
Given the following question:
\(y<\frac{2}{5}x-3\)The following inequality is graphed as followed:
if in one batch of cookies, you use 6 cups of dough and 2 cups of chocolate chips
how many cups of chocolate chips will you need to make two batches of cookies
Answers
Answer:
4cups of chocolate chips
Hope I helped
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
2 cups times two recipes
2x2=4
The equation of a line is 5x – 3y = 6. Which is the y-intercept of the line?
A)
y = 2
B)
y = 1
C)
ya
=
wiu
D)
y = -2
Answers
Answer:
y-intercept = -2
Step-by-step explanation:
The given equation of line is :
5x – 3y = 6 ...(1)
The general equation of line is given by :
y = mx +c ...(2)
Where
m is slope
c is y-intercept
Equation (1) can be written as :
-3y = 6-5x
\(y=\dfrac{6}{-3}-\dfrac{5x}{(-3)}\\\\y=-2+\dfrac{5x}{3}\\\\y=\dfrac{5x}{3}+(-2)\) ..(3)
Comparing equation (1) and (3).
y-intercept = -2
Hence, this is the required solution.
What is the pattern in the values as the exponents increase?
Powers of 2
Value
2 Superscript negative 5
StartFraction 1 Over 32 EndFraction
2 Superscript negative 4
StartFraction 1 Over 16 EndFraction
2 Superscript negative 3
StartFraction 1 Over 8 EndFraction
2 Superscript negative 2
One-fourth
2 Superscript negative 1
One-half
2 Superscript 0
1
add StartFraction 1 Over 16 EndFraction to the previous value
subtract StartFraction 1 Over 16 EndFraction from the previous value
divide the previous value by 2
multiply the previous value by 2
Answers
The pattern in the values as the exponents increase is multiply the previous value by 2.
What is exponents and powers?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
Given:
Powers of 2 Values
\(2^{-5}\) 1/32
\(2^{-4}\) 1/16
\(2^{-3}\) 1/8
\(2^{-2}\) 1/4
\(2^{-1}\) 1/2
As, from the given data we can see that negative powers of 2 reducing by 1.
as, 2^-5 * 2= 2^-4
Hence, multiply the previous value by 2 to obtain the next value.
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The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12. 5 years and the standard deviation is 2. 4 years.
Use the empirical rule (68-95-99. 7%) to estimate the probability of a lion living more than 10. 1 years.
Answers
The probability of a lion living more than 10.1 years is approximately 1 - 0.1587 = 0.8413, or 84.13% (rounded to the nearest hundredth).
To use the empirical rule, we first need to convert the value of 10.1 years into a z-score:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
z = (10.1 - 12.5) / 2.4
z = -1.00
Using the empirical rule, we know that approximately:
68% of the data falls within one standard deviation of the mean
95% of the data falls within two standard deviations of the mean
99.7% of the data falls within three standard deviations of the mean
Since we want to estimate the probability of a lion living more than 10.1 years, we need to find the area under the normal curve to the right of this value. This is equivalent to finding the area to the left of the z-score of -1.00 (since the standard normal distribution is symmetric).
From a standard normal distribution table or calculator, we can find that the area to the left of z = -1.00 is approximately 0.1587.
Therefore, the probability of a lion living more than 10.1 years is approximately 1 - 0.1587 = 0.8413, or 84.13% (rounded to the nearest hundredth).
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please help it's due by the end of class
Answers
Answer:
350, 420, 8, 700
Step-by-step explanation:
i dont know the bottom part.
PLEASE HELP MEEE
Write a linear function that related y to x
Answers
Answer:
\(y = \frac{x}{ - 4} \)
Besides being simple for its own sake, what other advantage do simple models usually have?
a) Higher accuracy
b) Greater complexity
c) Easier interpretation
d) More detailed predictions
Answers
The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.
This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.
Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.
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(-28-32r-x+ 1)(x-2)
multiply and combine like terms to determine product of polynomials.
Answers
Answer:
−25x+54−32rx+64r−x^2
Step-by-step explanation:
(−28−32r−x+1)(x−2)
Add −28 and 1 to get −27.
(−27−32r−x)(x−2)
Apply the distributive property by multiplying each term of −27−32r−x by each term of x−2.
−27x+54−32rx+64r−x^2+2x
Combine −27x and 2x to get −25x.
−25x+54−32rx+64r−x^2
find the sum. 2/5 + 1/2
Answers
4+5 / 10 • look for the LCD of 5 and 2
which is 10 then 5 goes 2
times into 10 the multiply by 2
= 4. Then 2 goes 5 times into
10 then multiply by 1 = 5.
Therefore the sum of 2/5 + 1/2 =9/10
Answer:
9/10 NINE OVER 10
Step-by-step explanation:
To add two fractions they must be over a common denominator, which for this problem is 10. To put each fraction over a common denominator we must multiply each fraction by the appropriate form of 1. 2/5 + 1/2 ( 2/2 X 2/5 ) + (5/5 X 1/2 ) --> 4/10 + 5/10
We can now add the numerators of the two fractions over the common denominator: 4/10 + 5/10 ---> 4+5/10 ---> 9/10.
Hope this helps! I know what does though, marking me brainliest.
A one-year Treasury bill yields 4.5% and the expected inflation
rate is 3%. Calculate, approximately, the expected real rate of
interest.
Answers
The approximate expected real rate of interest is find by subtracting the approximate expected inflation rate from the yield of the Treasury bill. In this case, the approximate expected real rate of interest is around 1.5%.
To calculate the approximate expected real rate of interest, we can use a simplified formula that involves subtracting the approximate expected inflation rate from the nominal interest rate. In this scenario, the nominal interest rate is 4.5%, and the expected inflation rate is 3%.
Using the simplified formula, we subtract the approximate expected inflation rate of 3% from the nominal interest rate of 4.5% to get an approximate expected real rate of interest of 1.5%.
It's important to note that this calculation provides an approximation of the expected real rate of interest and may not account for all factors and variations in inflation. For a more precise calculation, additional considerations and data would be required.
Therefore, the approximate expected real rate of interest in this case is around 1.5%. This suggests that after adjusting for an expected inflation rate of 3%, the investor can anticipate an approximate real return of 1.5% on their investment in the one-year Treasury bill.
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A carriage on a carnival ride can hold up to 4 people. How many carriages are needed for a group of 22 people to ride?
Answers
Answer:
Hello!
Let's simply divide our two numbers to find how many carriages we need.
22/4=5.5
The thing is, we cannot have 5.5 carriages. We can just have an extra carriage with only 2 people. This gives us 6 carriages.
Therefore, our answer is 6.
I hope this helps!
Six carriages are needed to move a group of 22 people.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
To find the number of carriages needed for a group of 22 people to ride, we need to divide the total number of people by the number of people each carriage can hold.
Each carriage can hold 4 people,
⇒ 22 / 4 = 5.5 carriages.
Since we cannot have half a carriage, we will need to round up to the nearest whole number, which means we will need 6 carriages.
Therefore, the number of carriages needed for a group of 22 people to ride is 6.
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A cylinder has a height of 16 inches. Its volume is 5,024 cubic inches. What is the radius of the cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
Using the volume formula, the radius of the cylinder is approximately 10 inches.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The formula for the volume of a cylinder is -
V = πr²h
where V is the volume, r is the radius, and h is the height.
In this problem, we know that the height of the cylinder is 16 inches and the volume is 5,024 cubic inches.
We can substitute these values into the formula and solve for the radius -
5,024 = 3.14r² × 16
Dividing both sides by (3.14 × 16), we get -
r² = 5,024 / (3.14 × 16) = 100
Taking the square root of both sides, we get -
r = √100 = 10
Therefore, the radius value is obtained as 10 inches (rounded to the nearest hundredth).
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Carlos had at most 7 hours to spend in an amusement park in which he uses 1 hour for lunch and the rest of the time on park rides. What is the maximum number of rides Carlos can comete if each ride takes 15 minutes?
Answers
Answer:
24
Step-by-step explanation:
7 hours = 420 mins (7×60)
420-60=360 (time taken for lunch)
15mins=one ride
360÷15=24 rides
A number line going from negative 5 to positive 5. From positive 2 to positive 5 is positive 3.
David added 2 and –3 using the number line tool. Which of the following errors did he make?
He started at 2 instead of zero.
He moved right 2 units for positive 2.
He moved right 3 units for negative 3.
He started at zero instead of 2.
Answers
The correct statement is :David started at 0 instead of 2
What is a number line in math?A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.
Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3
The right steps are
Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5
Thus 2+3=5 which is the required answer
but David addes 2-3=-1 which is incorrect.
Hence, David started at 0 instead of 2
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d = 6 m.
Calculate the circumference of the circle.
Answers
Step-by-step explanation:
circumference = 2 pi r = 2 r pi
= d pi
= 6 × 3.14 = 18.84
There are 4 buses for a field trip for 4th graders and each bus accommodates the same number of students. If there are 76 students going to a trip, how many are on each bus?
Answers
Answer:
19
Step-by-step explanation:
divide 76 by 4
Jamaar helped in the community garden for 21/10 hours this week. that was 2 4/5 equal-length shifts, because jamaar stopped early one day when it started to rain. what does 21/10 divided by 2 4/5 represent in this situation?
Answers
21/10 divided by 2 4/5 represents the time spent on a shift
How to determine what 21/10 divided by 2 4/5 represent in this situation?The given parameters are
Time = 21/10
Shifts = 2 4/5
This means that:
21/10 divided by 2 4/5 represents:
Time/Shift
i.e. time per shift
Hence, 21/10 divided by 2 4/5 represents the time spent on a shift
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Answer:
the lenght on each sift
Step-by-step explanation:
Eddie is twice as old as Michael. Michael's age is represented by a. Which
expression can be used to find Eddie's age?
A 2+a
B 2-a
C 2a
D 2a+2
Answers
________ probability represents the likelihood of a single event occurring by itself.
Answers
The probability that represents the likelihood of a single event occurring by itself is called marginal probability.
Marginal probability refers to the probability of an individual event happening independently without considering any other events. It focuses on a single variable or outcome without considering the relationship or dependencies with other variables.
To calculate marginal probability, you divide the number of times the specific event occurs by the total number of observations. For example, if you have a bag of marbles with different colors and you want to find the marginal probability of drawing a red marble, you would count the number of red marbles and divide it by the total number of marbles in the bag.
Marginal probability is often used when working with categorical variables or when studying the probability of a single event without considering any other variables or conditions. It provides a fundamental understanding of the likelihood of an event occurring in isolation, independent of any other factors.
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