I NEED HELP!!!! Use the graph of the polynomial equation y=x^4-10x² + 16 to describe its concavity. How many points of inflection does this curve have?
Answers
Points of inflection does this curve have is:
Concave Up: [tex]$\left(-\infty,-\sqrt{\frac{5}{3}}\right),\left(\sqrt{\frac{5}{3}}, \infty\right)$[/tex]
Concave Down: [tex]$\left(-\sqrt{\frac{5}{3}}, \sqrt{\frac{5}{3}}\right)$[/tex]
Points of Inflection: [tex]$(-1.2910,2.1111),(1.2910,2.1111)$[/tex]
To find the concavity of a function?
We need to take the second derivative.
y' = 4x^3 - 20x
y'' = 12x^2 - 20
Finding the points of inflection involves setting the second derivative equal to 0. Add 20 over, divide by 12, and take the square root. The positive and negative square roots of 5/3 are the potential points of inflection.
Setting up a number line can help to determine concavity. Let's plug in -2 into the second derivative. From this, we have found that from negative infinity to the negative square root of 5/3, the graph is concave up, as f''(-2) > 0. f''(0) < 0, so from the negative square root of 5/3 to the positive square root of 5/3, the graph is concave down. f''(2) is also > 0, and therefore from the positive square root of 5/3 to infinity, the graph is concave up.
Since the graph shifted direction at both potential points of inflection, they are both actually points of inflection. To find the y-values for each point of inflection, plug the x-value back into the original polynomial equation.
To learn more about polynomial equation visit:https://brainly.com/question/25958000
#SPJ1
Related Questions
Evaluate. Remember Order of
Operations! (PEMDAS)
4-(7+2)÷3= [?]
Answers
Answer: 1
Yessssssssssssssss
Write a rule for the glide reflection that maps ABC with vertices A(-4,-2), B(-2, 6).
and C(4, 4) to A'B'C' with vertices A'(4, -2), B(6, -6), and C'(12,-4).
Answers
The glide reflection that maps ABC to A'B'C' is given as follows:
Reflection over the line y = x - 9.Translation right 8 units.What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.
The midpoint of segment A'B' is given as follows:
x = (4 + 6)/2 = 5.y = (-2 - 6)/2 = -4.The slope of this segment is given as follows:
m = (-6 - (-2))/(6 - 4) = -1.
Then the slope of the reflection line is of:
m = 1.
(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).
Then:
y = x + b.
When x = 5, y = -4, then the intercept b is calculated as follows:
-4 = 5 + b
b = -9.
Thus the reflection line is of:
y = x - 9.
Then the translation is given subtracting the coordinates of one of the vertices, as follows:
4 - (-4) = 4 + 4 = 8 units right.-2 - (-2) = -2 + 2 = 0 units vertically.More can be learned about glide reflections at https://brainly.com/question/5612016
#SPJ1
find the domain of the function
Answers
The domain of the function is { (x, y) ∈ R² | x² + y² ≥ 1 }
What is Domain of function?
A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0. Special functions with more constrained domains can also be defined.
According to question
⇒ [tex]z = e^{\sqrt{x^{2}+ y^{2} -1 } }[/tex]
⇒ x² + y² - 1 ≥ 0
⇒ x² + y² ≥ 1
Hence, the Domain of f(x, y) is { (x, y) ∈ R² | x² + y² ≥ 1 }
To learn more about Domain , check out
https://brainly.com/question/28135761
#SPJ1
Which relationships have the same constant of proportionality between yyy and xxx as the following table?
x y
7 24.5
9 31.5
Choose 3 answers
Answers
Answer:
A,D,E
Step-by-step explanation:
A:
14/4 = 3.5
D:
7/2 = 3.5
E: 14/4 = 3.5
The constant of proportionality for the table is 3.5. Any other table that satisfies the equations x/y = 3.5 will have the same constant of proportionality.
Explanation:To find the constant of proportionality, we can divide the y-values by the corresponding x-values and see if they are the same for all given points. In this case, if we divide 24.5 by 7, we get approximately 3.5. If we divide 31.5 by 9, we also get approximately 3.5. Therefore, the constant of proportionality is 3.5 for this table.
Now, we need to find the relationships that have the same constant of proportionality.
For example, if we have a table with the following values:
x1 y1
x2 y2
x3 y3
and the constant of proportionality is k, then we have the following equations:
x1/ y1 = k
x2/ y2 = k
x3/ y3 = k
So, any other table that satisfies these equations will have the same constant of proportionality as the given table.
Learn more about Mathematics here:https://brainly.com/question/26854035
#SPJ2
Two angles form complements. One angle measure is eight more than twice the other. Find both angles measures.
Answers
Answer:
41° and 49°
Step-by-step explanation:
Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:
2x + 8 = 90
Solving for x, we get:
2x = 82
x = 41
Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.
Therefore, the two angles have measures of 41 and 49 degrees.
please help meee!!!!
Answers
The value of x and z are x° = 6.71°, z° = 75.26° simulataneously,
What is the linear pair angles?
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
We have,
Angles:
6x° + 35°
z°
8x° + 51°
To find the values of x and z
from the given figure
Linear pair angles:
6x° + 35° + 8x° + 51° = 180
14x° + 86° = 180
14x° = 180° - 86°
14x° = 94°
x° = 94°/14°
x° = 6.71°
Vertically opposites angles are equal
6x° + 35° = z°
z° = 6( 6.71°)° + 35
z° = 40.26 + 35
z° = 75.26°
Hence, the value of x and z are x° = 6.71°, z° = 75.26° simulataneously.
To learn more about linear pair angles visit,
https://brainly.com/question/1757859
#SPJ1
let g be a polynomial function of x where g(x) = 2x^3 + 5x^2 - 28x - 15 Given (x - 3) is a factor of g, what is the reminder of g(x) + (x - 3)?
Answers
The remainder of polynomial g(x) divides (x - 3) that is g(x) / (x - 3) is 0.
What is polynomial?
A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.
Given: g(x) = 2x^3 + 5x^2 - 28x - 15
(x - 3) is a factor of g(x).
We have to find the remainder of g(x) / (x - 3).
Consider,
2x^2 + 11x + 5
[tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]
- 2x^3 -6x^2
____________________________
11x^2 - 28x
- 11x^2 - 33x
____________________________
5x - 15
- 5x - 15
_______________________________
0
Hence, the remainder of polynomial g(x) divides (x - 3) that is
g(x) / (x - 3) is 0.
To know more about polynomial, click on the link
https://brainly.com/question/2833285
#SPJ1
arianna collected data from a random sample of 600 people in her city asking whether or not they bike to work. based on the results, she reports that 44% of the people in her state bike to work. why is this statistic misleading?
Answers
Sample is biased. Based on her findings, Arianna revealed the percentage in her state after polling 600 residents of her city. Thus, the sample fails to accurately reflect the population. Option (4) is correct.
When some members of a population are systematically more likely to be chosen in a sample than others, this is known as sampling bias. What makes sampling bias significant? Sampling bias poses a risk to external validity since it restricts the applicability of your findings to a larger population. When some population members have a higher or lower sampling probability than others, the sample is biased.
This includes choosing or sampling people according to their hobbies, gender, or age. Therefore, a fair or impartial sample must be representative of the entire population under investigation. When a research study design fails to gather a representative sample of a target population, the phenomenon known as sampling bias takes place. This usually happens as a result of the respondents' selection criteria not capturing a broad enough sampling frame to include all points of view.
To learn more about biased sample Visit : brainly.com/question/313246
#SPJ4
Correct Question:
Arianna collected data from a random sample of 600 people in her city asking whether or not they bike to work. Based on the results, she reports that 44% of the people in her state bike to work. Why is this statistic misleading?
Select the correct answer below:
1. The statistic contains a calculation error.
2. The sample is self-selected.
3. The data contains an outlier.
4. The sample is biased.
A speed skater goes around a turn with a 25 m radius. The skater has a velocity of 15 m/s and experiences a centripetal force of 720 N. What is the mass of the skater?
Answers
Answer:
80 kg
Step-by-step explanation:
To find the mass of the skater, you can use the formula for centripetal force:
F_centripetal = m * v^2 / r
Where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
Plugging in the values you know, you get:
720 N = m * (15 m/s)^2 / 25 m
Solving for m, you find that the mass of the skater is:
m = 720 N * 25 m / (15 m/s)^2
= 720 N * 25 m / 225 m^2/s^2
= 80 kg
So the mass of the skater is approximately 80 kilograms.
10 points if you answer his question
Answers
This is because 8•3 is 24, and 24 divided by 4 is 6
For a sample size of 85 and a population parameter of 0.2, what is the standard error of the sampling distribution?
Answers
Answer:
0.043
Step-by-step explanation:
I hope this helps you! Let me know if you have any questions! :)
find the value of y² when y=-9
Answers
Answer:
81
Step-by-step explanation:
y = -9
y² = (-9)² = 81
Multiple
Solution
Y=-81
Mark Brainly pls
Work out:
(1.2 × 10′²) × (2 × 10ª)/3 x 10-5
Give your answer in standard
form.
Answers
The standard form of the expression is [tex]0.000286 \times 10^a[/tex].
What is a standard form?
A standard form is a document that contains predetermined information in a specific format, such as a contract or agreement. Standard forms are often used to ensure uniformity and efficiency among different parties. Standard forms may include a variety of information, including contact details, payment information, and other important details related to a transaction. By utilizing a standard form, individuals and organizations are able to save time and effort when completing administrative tasks. Standard forms can also be used to ensure that all parties involved in a transaction are aware of the terms and conditions.
The given expression is
[tex]=(1.2 \times 10^2) \times \frac{(2 \times 10^a)}{3} \times 10^{-5}\\\\=129 \times\frac{2}{3}\times\frac{10^a}{3}\times0.00001\\\\=0.000286 \times 10^a[/tex]
Hence, the standard form of the expression is [tex]0.000286 \times 10^a[/tex].
To learn more about the standard form, visit:
https://brainly.com/question/19169731
#SPJ1
what is equilvalent to the square root of -2.
Answers
Answer:
1.4142135623730951i
Step-by-step explanation:
Did it help pls make me the brainliest and you can round your answer to how you want it and if not that's you answer thank you.
what is the square root of 1476
Answers
Answer : 6√41
Look at the triangles shown below.
5
Which statement is TRUE?
Answers
Answer: B
Step-by-step explanation:
vertical angles are =
Which one. Multiple choice.
Answers
In the given relation, 1 is not a domain.
What is domain?The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.
All the values that go into a function. The output values are called the range.
The domain of a function is the set of all possible inputs for the function.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.
Given that, a function,
{(5, 1), (4, -3), (3, -1)}
We know, a domain is the set of all "x" values.
Therefore, domain of the function are, 5, 4 and 3
But, if we see, 1 is one of the values of y.
Hence, 1 is not a domain.
For more references on domain, click,
https://brainly.com/question/28135761
#SPJ1
The expression - 270 +18.3y represents a submarine that began at a depth of 270 feet below sea level and ascended at a rate of 18.3 féet par minute. What was the depth
of the submarine after 8 minutes?
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. The submarine ___ was feet below sea level after 8 minutes.
(Type an integer or a decimal:)
B. The submarine will have reached sea level after 8 minutes.
Answers
The depth of the submarine after 8 minutes is -123.6 feet below sea level.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Depth of the submarine after y minutes.
= -270 + 18.3y
The depth of the submarine after 8 minutes.
= -270 + 18.3 x 8
= -270 + 146.4
= -123.6
Thus,
The submarine is at -123.6 feet below sea level.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs $0.91. There are 3.8 liters in one gallon. How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
Answers
Answer: One gallon of gas in Toronto would cost approximately $3.43. To find this, first convert the price of gasoline in Buffalo to liters. Since there are 3.8 liters in one gallon, one gallon of gas in Buffalo costs $2.29 * 3.8 liters = $8.69. Next, divide the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.91 / 3.8 liters/gallon = $0.24/liter. Finally, multiply the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.24/liter * 3.8 liters/gallon = $0.91/gallon. Round this to the nearest cent to find that one gallon of gas in Toronto costs $0.91/gallon = $<<0.91/gallon=0.91>>0.91.
Triana is on a 120-mile four-day bike ride. On the first day she travels 24 miles. She would like to travel equal amounts over the remaining three days. How far will she travel on each of those three days? Write and solve an equation of the form px+q=r. Then write a sentence to explain your answer.
Answers
Explanation:
x = amount she travels on each of those three remaining days
3x = total amount traveled over those three remaining days
3x+24 = total amount traveled over the four days
3x+24 = 120 miles total
This equation is in the form px+q = r where:
p = 3q = 24r = 120Let's solve for x. We follow PEMDAS in reverse to undo what's happening to x, so we can isolate it.
3x+24 = 120
3x+24-24 = 120-24 .... subtract 24 from both sides
3x = 96
3x/3 = 96/3 .... divide both sides by 3
x = 32
Triana must travel 32 miles per day for those remaining three days.
Doing so means she travels 3x = 3*32 = 96 miles over those three remaining days. Then add on those 24 miles traveled on the first day to get 96+24 = 120 miles total. This helps confirm the answer.
Another way to confirm the answer is to plug x = 32 into 3x+24 = 120. After simplifying both sides, you should get 120 = 120 which is a true statement.
Select the correct answer from each drop-down menu.
In a particular year, the population of Dallas, TX, was approximately 1 × 10^6 people. If the population of Los Angeles, CA, was approximately three times that of Dallas, there were about ______ x _______ ^6 people living in Los Angeles that year.
The population of Pittsburgh, PA, was approximately 3 × 10^5 people during the same year, which was about ______times that of Dallas.
Answers
Answer:
Step-by-step explanation:
Dallas = 1 x 10^6
Los Angeles = 3 times Dallas = 3 [ 1 x 10^6] = 3 x 10^6
Pittsburgh / Dallas = [ 3 x 10^5 ] / [ 1 x 10^6] = 3 / 10 that of Dallas
What is the slope of y = − 5 + 4x
Answers
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
Answers
The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.
What is a sphere?
The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.
Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.
The radius of a sphere is the half of its diameter.
The radius of the bottom ball is 3/2 feet =1.5 feet
The radius of the middle ball is 2/2 feet = 1 feet.
The radius of the top ball is 1/2 feet = 0.5 feet.
The volume of a sphere is 4/3 × ∏r³.
The volume of bottom ball is 4/3 × ∏ × (1.5)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (1)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (0.5)³ cubic foot.
The total amount of snow is
4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³
= 4/3 × ∏ [1.5³ +1³ + 0.5³ ]
= 4/3 × ∏× 4.5
= 18.84
≈ 19 cubic foot
To learn the volume of a sphere, click on below link:
https://brainly.com/question/7473395
#SPJ1
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
Answers
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
Learn more about area of similar figures on:
https://brainly.com/question/17132861
#SPJ1
a car manufacturer wants to learn more about the brand preferences of electric car owners. there are millions of electric car owners in the world. who should the company survey? 1 point the entire population of electric car owners a sample of car owners who have owned more than one electric car a sample of all electric car owners a sample of car owners who most recently bought an electric car
Answers
A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.
What is Survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.
As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.
To know more about Survey:
https://brainly.com/question/17373064
#SPJ1
Triangle A'B'C' is a reflection of triangle ABC across line BC. Prove that ray BC is the angle bisector of angle ABA'.
Answers
Proof of ray BC is the angle bisector of angle ABA' is given.
What are angle bisectors?Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.
A graph will move exactly to the other side of an axis, such as the x-axis, as if it were a mirror when it is reflected along that axis.
Because it is symmetrical, each point is as far from the axis of reflection as its mirror counterpart.
Triangle A'B'C' is a mirror of triangle ABC over line BC, as shown by the provided issue.
Therefore, <A'B'C' = <ABC
by virtue of congruent triangles' characteristics. Means that if the sides' lengths are equal, the angles' measures are equal, and they may be overlaid.
Therefore, the ray BC is the angle, bisector of angle ABA'.
Learn more about angle bisector here;
https://brainly.com/question/12896755
#SPJ1
Kiera's lemon cookie recipe calls for 5 cups of sugar. How much sugar would Kiera use to make 3 5/8 batches of cookies?
Answers
Answer:18 1/8
Step-by-step explanation:
5x3=15
5x5/8=25/8=3 1/8
15+3 1/8=18 1/8
Harry owns a rare baseball card that is valued at $13.00. If he originally purchased the card for $5.00, by what percentage has its value increased?
Answers
The value of baseball card has increased by 160(%) percentage.
What is the percentage?
A number or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word per cent means. The letter "%" stands for it.
Increase = New Number - Original Number
Then: we divide the increased number by the original number and multiply by 100.
Therefore, % increase = (Increase ÷ Original Number)× 100.
Given, the new price of a baseball card = $13
The original price of a baseball card = $5
Then from the above definition,
Increase = 13-5 = 8
% increase = (8/5)*100 = 160%
Hence, its value has increased by 160 percentage.
To learn more about a percentage
https://brainly.com/question/24877689
#SPJ1
Given: segment BD bisects angle ABC and segment BD bisects angle ADC. Prove: segment AD is congruent to segment CD
Answers
If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.
What is bisector of an angle?
In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..
Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.
Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.
AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.
Consider △ABD and △DBC:
∠ABD = ∠DBC
∠ADB = ∠BDC
Therefore, △ABD ≅ △DBC
According to CPCT, AD ≅ CD.
To learn more about congruent triangle, click on below link:
https://brainly.com/question/15064982
#SPJ1
Geometry is hard help
