Answer:
I'd be happy to help!
a. From the picture of the window, we can identify the following quadrilaterals:
Rectangle: ABCD (all angles are right angles and opposite sides are parallel and congruent)
Parallelogram: EFGH (opposite sides are parallel and congruent)
Trapezoid: BCGH (at least one pair of opposite sides are parallel)
b. To identify the parallelograms in the picture, we would need to know the following properties of parallelograms:
Opposite sides are parallel and congruent
Opposite angles are congruent
Diagonals bisect each other
Using these properties, we can identify the following parallelograms in the picture:
Parallelogram EFGH: Opposite sides EF and GH are parallel and congruent, and opposite sides EG and FH are also parallel and congruent. Additionally, angles E and G are congruent, and angles F and H are congruent.
Rectangle ABCD: Opposite sides AB and CD are parallel and congruent, and opposite sides AD and BC are also parallel and congruent. Additionally, angles A and C are congruent, and angles B and D are congruent. The diagonals AC and BD bisect each other, meaning that they intersect at their midpoints.
Step-by-step explanation:
generally, cold fronts move fast er than warm fronts generally, cold fronts have steeper slopes generally, precipitation cover s a much broader area with a cold front especially in winter, cumuliform clouds are more often associated with cold fronts
Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.
On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.
With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.
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In an effort to figure out why application rates are slipping, your college decides to set up an experiment to determine why students who are interested in the college decide to enroll or not. The college decides to send out a questionnaire to everyone who submitted an application to the college in 2017. What's the population for this study, and what's the sample?
A. The population is all college students everywhere, and the sample is all college students interested in your school.
B. The population is all college students everywhere, and the sample is the individuals who responded to the survey.
C. The population is all students who applied to your college, and the sample is the individuals who responded to the survey.
D. The population is all college students interested in your school, and the sample is everyone who decided to enroll.
The population of interest is the group of students who submitted an application to the college in 2017.
What is sample?A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.
According to question:The correct answer is C.
The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.
Option A is incorrect because the population is not all college students everywhere, only those who applied to the college in question.Option B is incorrect because the sample is not just the individuals who responded to the survey, but rather all students who submitted an application in 2017.Option D is incorrect because the sample is not just everyone who decided to enroll, but rather all students who submitted an application, regardless of whether they enrolled or not.To know more about sample visit:
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of the following people, who would be included in the survey conducted by the bureau of labor statistics?
The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).
The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.
The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:
(i) Worked at least one hour as paid employees
(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise
(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.
⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.
⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.
⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.
Therefore, all the options are correct , which is Option(d).
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The given question is incomplete, the complete question is
Who of the following are included in the Bureau of Labor Statistics "employed" category?
(a) certain unpaid workers
(b) part-time workers
(c) workers on vacation
(d) All of the above are correct.
-51+((-5+(-4)) all calculation
Answer:
the answer to that is -31
can you help me to solve these two questions?
Case 1: The constant c of the piecewise function is equal to 1 / 7.
Case 2: The value of the constant b of the piecewise function with the greater absolute value is equal to 20.
How to determine the value of a variable such that a piecewise function is continuous
A piecewise function is function formed by two or more functions relative to intervals. A piecewise function is continuous if they do not have any jump on graph. For two functions, we must solve the following equation for the case of a piecewise function formed by two functions:
g(a) = h(a)
Case 1 - g(y) = c · y + 3, h(y) = c · y² - 3, a = 7
c · a + 3 = c · a² - 3
c · (a² - a) = 6
c = 6 / (a² - a)
c = 6 / (7² - 7)
c = 6 / 42
c = 1 / 7
The value of the constant c is equal to 1 / 7.
Case 2 - g(x) = b - 2 · x, h(x) = - 150 / (x - b), a = 5
b - 2 · a = - 150 / (a - b)
(b - 2 · a) · (a - b) = - 150
a · b - b² - 2 · a² + 2 · a · b = - 150
- b² + 3 · a · b - 2 · a² = - 150
b² - 3 · a · b + 2 · a² - 150 = 0
b² - 15 · b - 100 = 0
(b - 20) · (b + 5) = 0
b₁ = 20 or b₂ = - 5
The solution with the greater absolute value is b = 20.
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type the correct words in the blanks. two radicals are said to be radicals if they have the same and the radicand.
Two radicals are said to be radicals if they have the same indices and the radicand.
In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.
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Complete question:
Type the correct words in the blanks:
Two radicals are said to be radicals if they have the same and the radicand.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
What is probability?Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.
Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.
Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:
P(accurate order) = 1246 / 1300 = 0.958 for McDonald's
P(accurate order) = 1020 / 1100 = 0.927 Taco Bell
P(accurate order) = 708 / 800 = 0.885 for Burger King
P(accurate order) = 940 / 1000 = 0.94 for Wendy's
P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929
As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
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can anyone help me with this question triangles?
The missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Is this a quadrilateral, parallelogram, rectangle,rhombus,square or trapezoid 
As all the sides of the closed figure are equal to each other, the quadrilateral here is a square.
What is a square?A square is a closed, two-dimensional (2D), object with four corners. With four sides and four vertices, a quadrilateral is referred to as a square. All four sides of a square are equal and parallel.
In other words, a square is a polygon or quadrilateral with four sides. An equiangular quadrilateral is a shape in which all of the angles are of equal size.
Here in the given figure, we can see a quadrilateral is given.
We can see that all the sides of the quadrilateral are given to be equal to each other.
We can conclude from the observation that the quadrilateral is a square as the sides are all equal to each other.
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Consider two agents, Alice and Bob, who have utility functions 0.3x3 + 0.72A if xa > XB (0.314 +0.72B if XB > XA UA(2A, 2B) = UB(XA, XB) 4X A – 32B if XB > IA -0.32A + 1.3xB if x A > XB If Alice is the dictator in the dictator game with a $10 endowment, then she will offer Bob (A) $0; (B) $5; (C) $2; (D) $10.
The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.
Compare Alice's utility from each option and choose the one that maximizes her utility.
Let us consider each option,
If Alice offers Bob $0, her utility will be,
If XA > XB then
UA (XA , XB )= 0.3x3 + 0.72A
UA(10,0)
= 0.3(10)³ + 0.72(10)
= 307.2
If Alice offers Bob $5, Bob's utility will be,
UB(10,5)
= 0.314 + 0.72(5)
= 0.314 + 3.6
= 3.914
And Alice's utility will be,
UA(5,10)
= -0.32(5) + 1.3(10)
= 11.4
Total utility for both Alice and Bob will be,
UA(5,10) + UB(10,5)
= 11.4 + 3.914
= 15.314
If Alice offers Bob $2, Bob's utility will be,
UB(10,2)
= 0.314 + 0.72(2)
= 1.754
And Alice's utility will be,
UA(2,10)
= -0.32(2) + 1.3(10)
= 12.4
So the total utility for both Alice and Bob will be,
UA(2,10) + UB(10,2)
= 12.4 + 1.754
= 14.154
If Alice offers Bob $10, Bob's utility will be,
UB(10,10)
= 0.314 + 0.72(10)
= 7.514
And Alice's utility will be,
UA(10,10)
= 0.3(10)³ + 0.72(10)
= 307.2
So the total utility for both Alice and Bob will be,
UA(10,10) + UB(10,10)
= 307.2 + 7.514
= 314.714
Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.
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I need help with this
Answer:
D.
Step-by-step explanation:
Last years freshman class at big state university totaled 5,303 students
URGENT
The 1,262 students who received a merit scholarship, the amount they received varied per student and totaled an average of $3,458 ($454). That amount is 78.2% of the full tuition cost of $4,400.
What is merit?Merit is a term used to describe the quality of something or someone that makes them worthy of recognition or respect. It is an indicator of worthiness and is usually based on a person's ability, effort, or accomplishments. Merit is often used when evaluating an individual or a group for a promotion, hiring, or award. Merit is subjective, as different people have different standards for what merits recognition.
Therefore, 21.8% of the students who received a merit scholarship did not receive enough to cover full tuition. Therefore, the percentage of students who received a merit scholarship and did not receive enough to cover full tuition is 21%.
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I am in my room (State 1). There is a 65% chance that I stay here and do my work like I am supposed to. There is a 35% chance I go get a snack and procrastinate (State 2). Once I have gone to get the snack, there is a 15% chance that I go back to work (go back to State 1), and there is an 85% chance that I get another snack and procrastinate further (stay in State 2).
Create a diagram and a transition matrix for this case.
Answer:
Here is a diagram and transition matrix for this case:
Diagram:
+---(0.65)---> State 1 (work)
|
Start ---+
|
+---(0.35)---> State 2 (procrastinate)
|
+---(0.15)---> State 1 (work)
|
+---(0.85)---> State 2 (procrastinate)
Transition matrix:
| State 1 | State 2 |
----------+-----------+-----------+
State 1 | 1.00 | 0.00 |
----------+-----------+-----------+
State 2 | 0.15 | 0.85 |
----------+-----------+-----------+
In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.
any point on the parabola can be labeled (x,y), as shown. a parabola goes through (negative 3, 3)
The correct standard form of the equation of the parabola is:
[tex]y = -x^2 - 1[/tex].
To find the standard form of the equation of the parabola that passes through the given points (-3, 3) and (1, -1), we can use the general form of the equation of a parabola:
[tex]y = ax^2 + bx + c[/tex] ___________(1)
Substituting the coordinates of the two given points into this equation, we get a system of two equations in three unknowns (a, b, and c):
[tex]3 = 9a - 3b + c[/tex]
[tex]-1 = a + b + c[/tex]
To solve for a, b, and c, we can eliminate one of the variables using subtraction or addition. Subtracting the second equation from the first, we get:
[tex]4 = 8a - 4b[/tex]
Simplifying this equation, we get:
[tex]2 = 4a - 2b[/tex]
Dividing both sides by 2, we get:
[tex]1 = 2a - b[/tex]___________(2)
Now we can substitute this expression for b into one of the earlier equations to eliminate b. Using the first equation, we get:
[tex]3 = 9a - 3(2a - 1) + c[/tex]
Simplifying this equation, we get:
[tex]3 = 6a + c + 3[/tex]
Subtracting 3 from both sides, we get:
[tex]0 = 6a + c[/tex]
Solving for c, we get:
c = -6a __________(3)
Substituting this expression for c into the second equation, we get:
[tex]-1 = a + (2a - 1) - 6a[/tex]
Simplifying this equation, we get:
[tex]-1 = -3a - 1[/tex]
Adding 1 to both sides, we get:
[tex]-3a =0[/tex]
Solving for a, we get:
[tex]a = 0[/tex]
Substituting this value of a into the equation(3) for c, we get:
c = 0
Substituting a = 0 into the equation(2) for b that we found earlier, we get:
[tex]1 = 0 - b[/tex]
Solving for b, we get:
[tex]b = -1[/tex]
Putting the values of a, b and c in (1), we get
[tex]y = -x^2 - 1[/tex]
Therefore, the equation of the parabola that passes through the given points (-3, 3) and (1, -1) is:
[tex]y = -x^2 - 1[/tex]
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Complete question:
A parabola goes through (-3, 3) & (1, -1). A point is below the parabola at (-3, 2). A line above the parabola goes through (-3, 4) & (0, 4). A point on the parabola is labeled (x, y).
What is the correct standard form of the equation of the parabola?
The figure is in the image attached below
What is the slope of the line passing through the points (-1, -7) and (-9, -2)?
Answer:
m = -5/8
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-1, -7) (-9, -2)
We see the y increase by 5 and the x decrease by 8, so the slope is
m = -5/8
There are two types of trees to plant in the yard type A trees are 36 inches tall and grows 8 inches per year type B are 18 inches tall but grow 10 inches per year when will the trees be the same height
As a result, both varieties of trees will be the same height after 9 years. We can change both equations to a = 9 to verify this: Height of the type A tree is 36 + 8(9) or 36 + 72 inches, whereas the height of the type B tree is 18 + 10(9) or 18 + 90 inches.
What function do height and distance serve in everyday life?Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It utilised to compute height of towers, structures, mountains, etc., and distance between any two objects such celestial bodies others. ,sys,s tos.as to .... and.
Let's use "a" to denote the number of years after planting the trees.
A type A tree will reach the following height after "a" years:
Height of type A tree = 36 + 8a
After "a" years, the height of a type B tree will be:
Height of type B tree = 18 + 10a
We must set the two types of trees' heights equal to one another and solve for "a" to determine when they will reach the same height:
36 + 8a = 18 + 10a
Subtracting 8a from both sides, we get:
36 = 18 + 2a
Subtracting 18 from both sides, we get:
18 = 2a
Dividing both sides by 2, we get:
a = 9
Therefore, after 9 years, both types of trees will be the same height.
To check this, we can substitute a = 9 into both equations:
Height of type A tree = 36 + 8(9) = 36 + 72 = 108 inches
Height of type B tree = 18 + 10(9) = 18 + 90 = 108 inches
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Question:
You have two types of trees to plant in your yard: type A trees are 36 inches tall and grow 8 inches per year, while type B trees are 18 inches tall and grow 10 inches per year. At what point in time will the trees be the same height? How tall will the trees be at that time?
How do you find the slope of (-4, 8) and (4, 2)
To find the slope of a line that passes through two points, you can use the slope formula. The slope formula is:
Slope = (y2 - y1) / (x2 - x1)
Using the points given in your question, the slope formula to find the slope of the line is:
Slope = (2 - 8) / (4 - (-4))
Using the order of operations, the calculation of the slope formula is as follows:
Slope = -6 / 8
Therefore, the slope of the line passing through (-4, 8) and (4, 2) is -3/4.
help plssss explainnn!!
Answer:
[tex]xy^8[/tex]
Step-by-step explanation:
Notice if you have the same base you can ADD the exponent, for example:
[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]
[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]
so the answer is
[tex]xy^8[/tex]
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Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?
picture below
Question 6
One gallon of water weighs 8.34 lb. How much weight is added to a fire truck when its tank is filled
with 750 gal of water?
Question 7
1
Answer
6255 pounds
8.34×750=6255lbs
1. A living room measures 4.75 m by 5.2 m. a. What is the area of the living room? 24.7m b. The area of the game room is one and a half times that of the living room. Fi the living room and the game room.
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
What is area?Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.
The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².
To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.
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Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle? Please show your work.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%
What is Conditional probability?
Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.
The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:
(number of Plastic #4 bottles correctly placed) / (total number of bottles)
So the probability is:
5/20 = 1/4 = 0.25
Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.
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1. (Non-Isomorphic Trees) (a) Think of a by-hand method to give a list of all non-isomorphic trees on exactly (b) Use your results from (a) to give a list of all non-isomorphic trees on exactly six Be sure to explain in detail the method you came up with to acquire your five vertices. Display your results. vertices. Show you're results. lists in (a) and (b).
Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.
A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.
For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.
Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.
To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.
The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.
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Solve each proportion round to the nearest tenth
Answer:
[tex]v = \frac{7}{2}[/tex]
Step-by-step explanation:
Find any critical numbers of the function.
Answer:
(1, 2) and (-1, -2). or. (±1, ±2)
Step-by-step explanation:
[tex]{ \sf{f(x) = \frac{4x}{ {x}^{2} + 1 } }} \\ [/tex]
- Simply, a critical number or critical point is gotten by differentiating the function.
From Quotient rule;
[tex]{ \sf{ {f}^{l}(x) = \frac{4( {x}^{2} + 1) - (2x)(4x)}{ {( {x}^{2} + 1)}^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{ {4x}^{2} + 4 - {8x}^{2} }{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{4(1 - {x}^{2}) }{ {( {x}^{2 } + 1) }^{2} } }}[/tex]
Then equate this derivative to zero;
[tex]{ \sf{0 = \frac{4(1 - {x}^{2} )}{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{4(1 - {x}^{2} ) = 0}} \\ \\ { \sf{4 - {4x}^{2} = 0}} \\ \\ { \sf{4 {x}^{2} = 4}} \\ \\ { \sf{x = \sqrt{1} }} \\ \\ { \sf{ \underline{ \: x = \pm 1 \: }}}[/tex]
Substitute for x in f(x)
For x = 1
[tex]{ \sf{f(1) = \frac{4(1)}{ {(1)}^{2} + 1} = \frac{4}{2} = 2 }} \\ [/tex]
For x = -1
[tex]{ \sf{f( - 1) = \frac{4( - 1)}{ {( - 1)}^{2} + 1 } = \frac{ - 4}{2} = - 2 }} \\ [/tex]
Therefore points are;
(1, 2) and (-1, -2)
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Answer:
if u want total price then,
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What is the smallest possible average of five distinct positive even integers?
A. 10
B. 8
C. 6
D. 4
E. 0
Answer:
The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:
2, 4, 6, 8, 10
The average of these five integers is:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.
1.
What is the average rate of change between
the points (3,9) and (5, 15)?
Therefore, the average rate of change between the points (3,9) and (5,15) is 3.
What is coordinates?Coordinates are a set of values that locate the position of a point in space. In mathematics, coordinates are used to represent the position of points on a plane or in space, using a set of numerical values that correspond to the distance along each axis from an origin point. In two-dimensional Cartesian coordinate systems, for example, a point is represented by two numbers (x, y) that indicate its position relative to the x and y axes. In three-dimensional Cartesian coordinate systems, a point is represented by three numbers (x, y, z) that indicate its position relative to the x, y, and z axes.
Here,
The average rate of change between the points (3,9) and (5,15) is the slope of the line passing through those two points. We can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (3,9) and (x2, y2) = (5,15).
slope = (15 - 9) / (5 - 3)
= 6 / 2
= 3
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If the gradient of the equation 2x-ay+2=0 is 1. Then find the value of a.
Step-by-step explanation:
2x + ay + 2 = 0
the gradient or slope of the line is the factor m of x in the form
y = mx + b
so let's transform the given equation into that form :
ay = -2x - 2
y = (-2/a)x - 2/a
we know that m = 1.
so,
-2/a = 1
-2 = a
Problem 2 (Vector and Matrix Refresh) Seven data points are arranged as columns of a data matrix X given as follows: 2 1 0 0 -1 0 -2 X = 2 0 1 0 0 -1 -2 a) Draw all data points on a 2D plane by hand. Properly label the two axes. Clearly provide important tick values to facilitate a precise graphical description of the data. b) Consider each point as a vector. Calculate the angle in between (2 27 and the five other points (excluding [0 07), respectively, using the inner/dot product formula that involves the angle. Note that the angle between two vectors can be negative. c) Calculate the matrix outer product for X, namely, R = XXT. Show the intermediate steps of calculating each element of the 2-by-2 matrix R. d) The matrix outer product can also be calculated via R =
a) The drawing of all data points on a 2D plane is illustrated below.
b) The angle in between the five other points is 27
c) The matrix outer product for X is R = XXT.
d) The matrix outer product can also be calculated via R is (2,27)
The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.
To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.
Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.
The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.
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