In graph theory, a 2-factor is a subgraph of a given graph that includes every vertex of the original graph and has the property that every vertex has even degree (i.e. degree is a multiple of 2).
The term "2-factor" is used because it is a factor of the original graph that is made up of edges and every vertex has degree 2.
A 2-factor can also be defined as a set of cycles that cover all vertices of the graph. In other words, it is a collection of cycles such that every vertex belongs to exactly one cycle. A 2-factor can also be thought of as a cycle cover of a graph.
A graph that has a 2-factor is called a 2-factorizable graph. Not all graphs are 2-factorizable, for example a graph with an odd number of vertices can't have a 2-factor.
2-factors have many applications in various fields such as scheduling, coding theory, and computer science. They are also used to study the connectivity and robustness of graphs.
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an object is moving at the constant rate of 32 feet per second. how many yards will it travel in one minute?
The object will travel 639.36 yards in one minute.
Formula: Yards = Feet x 0.3333
The question is asking how many yards an object will travel in one minute when it is moving at a constant rate of 32 feet per second.
We can use the formula above to calculate the number of yards the object will travel in one minute. We know that the object is traveling at a rate of 32 feet per second. To find the number of yards traveled in one minute, we need to multiply 10.6667 yards per second by 60 seconds in a minute. Therefore, in one minute (60 seconds), the object will travel 32 x 60 = 1920 feet. We can now use the formula to convert this to yards: Yards = 1920 x 0.3333 = 639.36 yards. Therefore, the object will travel 639.36 yards in one minute.
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please help me find the answer if u can thanks
Answer:
y = 4/3x - 1
Step-by-step explanation:
(3, 3) and (0, -1)
m = -1-3 / 0-3
m = -4/-3
m = 4/3
y = 4/3x + b
-1 = 4/3(0) + b
-1 = 0 + b
b = -1
y = 4/3x - 1
how long must a driver take to drive the last 50 miles of a 120 mile trip if he wants to average 50 mph for the entire trip and it took 90 minutes to drive the first 70 miles?
Therefore , the solution of the given problem of speed comes out to be
he needs to drive at 77.77 mph.
Specify the speed.How quickly something is traveling is determined by its speed from a distance. How far an object moves in a certain length of time depends on its speed. Speed is calculated as follows: velocity = range x time. The most used units for expressing speed are meters per second (m/s), kilometers per hour (km/h), and kilometers per second (mph) (mph).
Here,
70 + 50 = 120 miles is indeed the total distance.
You would need 2.4 hours to travel the 120 miles at such an approximate speed of 50 mph.
However, you are already on the road for 1.5 hours, so you must finish the trip in 0.9 hours.
You need to travel at a speed of 77.77 mph to complete the final 70 miles approximately 0.9 hours.
Therefore , the solution of the given problem of speed comes out to be
he needs to drive at 77.77 mph.
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18. If 5 men can erect 2 cottages in 21days, how many more men, working at the same rate will be needed to erect 2 cottages in the same period?
The number of extra men required to erect 2 additional cottages is; 5 men
How to solve proportion problems?Let us use;
M = men
D = Days
C = Cottages
Thus;
5M * 21D = 2C
105MD = 2C
To erect 2 cottages in 21days, 5 men are required
To erect 2 more cottages or 4 cottages in 21 days;
(4 * 5)/2 = 10 men
Thus, we conclude that is the number of men required to erect 2 additional cottages which is 5 extra men
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an automobile manufacturer claims that their jeep has a 34.9 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this jeep. after testing 16 jeeps they found a mean mpg of 34.6 with a standard deviation of 2.0. is there sufficient evidence at the 0.025 level that the jeeps underperform the manufacturer's mpg rating? assume the population distribution is approximately normal. step 1 of 5 : state the null and alternative hypotheses.
Null Hypothesis: The jeeps have an mpg rating of 34.9
Alternative Hypothesis: The jeeps have an mpg rating that is less than 34.9
Calculate the test statistic.
Test Statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)
Test Statistic = (34.6 - 34.9) / (2.0 / √16)
Test Statistic = -1.5 / 0.5
Test Statistic = -3
Calculate the critical value.
Critical Value = -2.960 Compare the test statistic with the critical value
Test Statistic = -3
Critical Value = -2.960
Since the test statistic is lower than the critical value, we reject the null hypothesis.
Make a conclusion The jeeps have an mpg rating that is less than 34.9
At the 0.025 level, there is enough proof to conclude that Jeeps do not get the claimed mpg.
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let f(x, y) = 1/√x^2 + y^2. Compute a) ∇f(x, y).
On solving the provided question, we can say that the value of the function is f(x) = => f(x) = vf(x,y) = (x² + y²) = (x² + y²),
What is function?fThe subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here, the function is f(x) =
f(x) =
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Complete the following statement. Use the integers that are closest to the number in the
middle.
<-√14<
The completed statement using the integers that are closest to the number in the middle is 3<-√14<4
The statement: <-√14< can be interpreted as the set of all real numbers that are less than the square root of 14, which is approximately 3.74166.
The integers closest to this number are 3 and 4, so the set of integers that are closest to the number in the middle can be represented as:
(-∞, 3) U (4, ∞)
The statement says that the value of the square root of 14, when multiplied by -1 (the square root of a negative number), is between 3 and 4. The closest integers to the value of the square root of 14 are -3 and -4.
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Use this number line to get the value of the given point
Answer:
1. Pt. A: -6 3. Pt. C: 3 5. Pt. E: 0
2. Pt. B: -2 4. Pt. D: 5
Step-by-step explanation:
By looking at the number line, you can see that a few points are labled from letter A to letter E.
In order to know the value of each point, you just have to look at their placement in the number line. For example, we can see that Point B is plotted at -2 on the number line, this means that the value of Point B is -2.
I hope this helps! :)
The population of a town is 345,000. The function
f(t) = 345,000(1.2)^t gives the predicted population of the
town in t years. Approximately what will the population be
in 3 years?
Answer:
600,000
Step-by-step explanation:
The mathematical concept demonstrated in this question is the process of exponential growth. Exponential growth demonstrates an increase in quantity by a percentage or factor over time. It is represented by the general formula [tex]f(x) = a(1+r)^{x}[/tex] where a is the initial amount, r is the growth rate, and x is the time interval expressed as an integer.
For this problem, we can see that the initial population of the town is 345,000, and it increases by a rate of 20% each year. We can determine that the growth rate is 20% because 1 + r = 1.2, so r must be equal to .20 (or 20%). We are given that t = 3, so we can plug that value in to the function given.
f(3) = 345,000(1.2)³f(3) = 345,000(1.728)f(3) = 596,160We calculate the population in 3 years to be 596,160. This can be approximated to 600,000.
Consider the two equations below. Explain completely the similarities and differences in how you would solve each equation. Be clear and complete.
3^x=12 and x^3=12
The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:
x = log3(12)
The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:
x = ∛12
How does the equation compare?The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.
The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.
As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.
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find the area of the surface. z = 2 3 x3/2 + y3/2 , 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
The area of the surface is S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]
Now, According to the question:
The given equation is:
[tex]z = \frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2} )[/tex],
0 ≤ x ≤ 1 , 0 ≤ y ≤ 1
Let's know:
Surface Area:
To surface area of a solid E, defined by z = f(x , y) can be found by integrating[tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex] where R is the rectangular region
[0,1] × [0, 1] and [tex]z_x,z_y[/tex] corresponds to the partials of z w.r.t x and y.
Now,
[tex]\sqrt{(z_x)^2+(z_y)^2+1}[/tex] = [tex]\sqrt{1+(\sqrt{x} )^2+(\sqrt{y} )^2}[/tex] = [tex]\sqrt{1+x+y}[/tex]
S = [tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex]
= [tex]\int\limits^1_0\int\limits^1_0 \sqrt{x+y+1}dy dx[/tex]
[Integrate with respect to y ]
= [tex]\int\limits^1_0 (\frac{2}{3}(x + y + 1)^\frac{3}{2} )|^1_0 dx[/tex]
= [tex]\int\limits^1_0 (\frac{2}{3}(x + (1) + 1)^\frac{3}{2}-\frac{2}{3}(x + (0) + 1)^\frac{3}{2} )dx[/tex]
= [tex]\int\limits^1_0 ((\frac{2}{3}(x +2)^\frac{3}{2} ) - (\frac{2}{3}(x +1)^\frac{3}{2} ) , dx[/tex]
= [tex]\int\limits^1_0 (\frac{2}{3}((x +2)^\frac{3}{2} - (x +1)^\frac{3}{2} )) , dx[/tex]
[Integrate with respect to x ]
= [tex]\frac{2}{3} (\frac{2}{5}(x + 2)^\frac{5}{2} - \frac{2}{5}(x +1)^\frac{5}{2} )|^1_0[/tex]
= [tex]\frac{2}{3}(\frac{2}{5}((1)+2 )^\frac{5}{2}-\frac{2}{5}((1)+1)^\frac{5}{2})-\frac{2}{3}(\frac{2}{5}((0)+2 )^\frac{5}{2} -\frac{2}{5}((0)+1)^\frac{5}{2}[/tex]
= [tex]\frac{2}{3}(\frac{18\sqrt{3}}{5} -\frac{8\sqrt{2} }{5} )-\frac{2}{3} (\frac{8\sqrt{2} }{5} -\frac{2}{5} )[/tex]
= [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]
Hence, The area of the surface is S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]
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$36\%$ of the letters in pythagoras's alphabet soup are vowels, and $33\frac13\%$ of those vowels are os. if pythagoras removes all the os from his soup, then $x\%$ of the original letters remain. what is $x$?
The value of x is: x=88.
Here, given that, 36% of the letters in Pythagoras's alphabet soup are vowels.
33 1/3% of those vowels are "os."
To calculate the percentage of letters that are "os," we first need to find 33 1/3% of 36%.
33 1/3% is equivalent to 1/3. So, we can calculate the percentage of "os" as follows:
Percentage of "os" = (36% * 1/3) = 12%
Now, we know that 12% of the letters in the soup are "os."
Next, Pythagoras removes all the "os" from his soup.
This means that what remains are the non-"os" letters, which are the remaining vowels and consonants.
To calculate the percentage of the original letters that remain, we need to subtract the percentage of "os" from 100%:
Percentage of original letters remaining = 100% - Percentage of "os"
Percentage of original letters remaining = 100% - 12% = 88%
Therefore, x% of the original letters remain, and x is equal to 88.
Hence, The value of x is: x=88.
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What are the 5 system components?
System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.
1. Algebra: This is the study of equations and their solutions, as well as the manipulation of symbols and operations.
2. geometry: This involves the study of shapes and the properties of space, such as angles and distances.
3. Calculus: This involves understanding the rate of change of a function and the area under a curve.
4. Trigonometry: This involves the study of angles and their relationships to one another and to other types of measurements.
5. Number Theory: This involves the study of the properties of numbers, such as divisibility, primes, and multiplicative functions.
System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.
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Answer This Question Please!!!!!
Answer:
Step-by-step explanation:
none of these the corrct answer is 5
problem 2 the losing team of each game is eliminated from the tournament. if sixteen teams compete, how many games will be played to determine the winner?
If sixteen teams compete, the winner will be decided after 15 games.
Since there are 16 teams and each team is playing with some of the other, there are 16/2 =8 pairs
Out of each pair only one team will move on.
So, there are 8 teams left after the first round.
These 8 teams pair up to have 8/2 =4 pairings
Continuing this process, we get the total number of games played to determine the winner is,
8+4+2+1=15
Each game's losing team gets eliminated from the tournament. If sixteen teams participate, the winner will be decided after 15 games.
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The equation _____ represents an additive relationship.
Given the formula for compound interest, calculate the amount of money Total in an account that pays 8% annual interest compounded quarterly and you invest $1200 for 5 years: ____A = P (1+r/n)mHow long will it take for the original amount of money to double to $2400?
A = P(1+r/n)(nt), where P is the original principal, r is the annual interest rate, n is the number of times the interest is compounded annually, and t is the number of years the money has been held, is the formula for compound interest.
To calculate the final amount of money in the account:
First, divide the 8% annual interest rate by 100 to get a decimal value: 0.08.
Find the number of times the interest is compounded annually. Since it is done quarterly, the answer is n = 4.
Put these values into the formula now, along with the $1200 principle sum and the number of years, 5, to complete it:
A = $1200(1+(0.08/4))^(4*5) = $2490.07
to determine how long it will take for the initial sum to double to $2400.
Divide the final sum by the starting sum: 2400/1200 = 2
Take the natural logarithm of 2: ln(2) = 0.693
Decimalize the result and divide it by the interest rate: 0.693 / 0.08 = 8.66 years
Therefore, the time it will take for the initial sum of money to double to $2400 is 8.66 years.
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Can you come up with the equation for the graph to the left in y = mx+ b form?
Answer:
y = 3x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (1, 4) ← 2 points on the line
m = [tex]\frac{4-1}{1-0}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 1 ) ⇒ c = 1
y = 3x + 1 ← equation of line
A pencil case contains 8 blue and 4 green
pens.
A pen is chosen at random and not
returned, and then a second pen is chosen
at random.
Copy and complete the tree diagram.
What is the probability that the first pen is
green and the second pen is blue?
Give your answer as a fraction in its
simplest form.
Help me with this question it’s bugging me
The probability is 8/33 is already in its simplest form as the numerator and denominator share no common factors.
What is probability and step by step explanation?Probability is a measure of the likelihood of an event occurring, represented as a decimal or fraction between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.(Probability of choosing a green pen on the first draw) x (Probability of choosing a blue pen on the second draw, given that a green pen was chosen on the first draw)= (4/12) * (8/11)= (1/3) * (8/11)= 8/33So the probability is 8/33. This is already in its simplest form as the numerator and denominator share no common factors.To learn more about probability refer:
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The probability is 8/33 is already in its simplest form as the numerator and denominator share no common factors.
What is probability and step by step explanation?Probability is a measure of the likelihood of an event occurring, represented as a decimal or fraction between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.
(Probability of choosing a green pen on the first draw) x (Probability of choosing a blue pen on the second draw, given that a green pen was chosen on the first draw)
= (4/12) * (8/11)
= (1/3) * (8/11)
= 8/33
So the probability is 8/33. This is already in its simplest form as the numerator and denominator share no common factors.
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Emma has been saving up to go on a big summer trip, visiting the United States and Russia. After working hard throughout the year, she has a total of £2500 in spending money.
The exchange rates are:
£ 1 = $ 1.28, and
$129.35 Rubles
Emma has also discovered that the maximum amount of money she can enter Russia with is 32 285 Rubles.
Assuming Emma wants as much cash as possible in Russia, how much should she spend while in the United States?
Emma has been saving up to go on a big summer trip, visiting the United States and Russia. Emma should spend $2951.46 while in the United States.
What is his savings?Generally, To maximize the amount of cash Emma has in Russia, she should spend all of her money in the United States before entering Russia. First, we convert the Ruble limit to USD:
32,285 Rubles / 129.35 =249.594 USD.
Next, we convert Emma's savings from pounds to USD:
£2500 x 1.28 = $3200.
Finally, we subtract the Ruble limit from Emma's total savings in USD: $3200 - $248.54 = $2951.46.
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Review the table of values.
Which description best fits the regression model for the data?
power model; y = 10.15x–0.68
exponential model; y = 12.80(0.78)x
logarithmic model; y = 9.98 – 3.85 ln x
quadratic model; y = 0.13x2 – 2.38x + 12.27
quadratic model; y = 0.13x2 – 2.38x + 12.27 is the best to fit the regression model for the data.
What is a Quadratic equation?ax2+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
For the given Dataset
Sum of X = 27
Sum of Y = 22
Mean X = 5.4
Mean Y = 4.4
Sum of squares (SSX) = 45.2
Sum of products (SP) = -42.3
Regression Equation = ŷ = bX + a
b = SP/SSX = -42.3/45.2 = -0.93584
a = MY - bMX = 4.4 - (-0.94*5.4) = 9.45354
ŷ = -0.93584X + 9.45354
Thus Given linear Equation is not the best fit
Since the graph is decreasing Option b and c are also not possible
Therefore, the best to fit the regression model for the data is the quadratic model; y = 0.13x2 – 2.38x + 12.27.
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Match the following vector fields with the verbal descriptions of the level curves or level surfaces to which they are perpendicular by putting the letter of the verbal description to the left of the number of the vector field.
Nonvisual language is used to describe the visual world verbally. It can lead people around a museum, help an audience member find their way around an artwork, or provide them access to the visual elements of a performance.
It was in 1981 when Dr. Margaret Pfanstiehl, founder and president of The Metropolitan Washington Ear Inc., and her husband Cody perfected the art and practice of verbal description.
Standard information found on a label, such as an artist's name, nationality, the title of the artwork, date, dimensions or size of the piece, media, and method, can be found in a spoken description as well. In addition, a vocal description can offer a broad overview of the work's subject matter and structural elements.
1. Lines
2. Planes
3. Hyperboloids
4. Lines
5. Spheres
6. Ellipsoids
7. Paraboloids
8. Hyperbolas
9. Ellipses
10. Hyperbolas
11. Circles
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a researcher designs an experiment to test memory. he will test three groups of participants. group 1 will listen to a list of words. group 2 will read a list of words printed on paper. lastly, group 3 will hear and read the words. the researcher then tests the participants' memories to see how many words the members of each group can recall. to reduce experimenter and participant bias, what procedure must be used when choosing groups? deception naturalistic observation random assignment random sampling research accountability
Random mean assignment involves randomly assigning participants to different groups, so that each group is similar in terms of characteristics such as age, gender, race, etc. This ensures that the groups are as similar as possible, reducing the chance of bias in the experiment.
Random mean assignment is an important procedure used in experiments to reduce experimenter and participant bias. This involves randomly assigning participants to different groups in the experiment, so that the groups are as similar as possible in terms of characteristics such as age, gender, race, etc. This ensures that any differences observed in the results are due to the experimental variables, rather than any pre-existing differences between the groups. Random assignment also ensures that any experimenter bias is minimized, as the experimenter is not able to select which participants go into which group. Random assignment is therefore a key procedure used to reduce the chance of bias in experiments, and ensure that the results are more reliable and valid.
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Determine zα for the following. (Round your answers to two decimal places.)
(a) α = 0.0089
(b) α = 0.09
(c) α = 0.707
Please explain where and how you got the answer.
Thank you.
The value of zα for the following is :
(a) α = 0.0089 is 2.37
(b) α = 0.09 is 1.34
(c) α = 0.707 is -0.545
zα is the inverse function of the standard normal CDF.
(a) Central limit c= 1-α
for α = 0.0089 , c=1-0.0089
∴ c=0.9911
Hence confidence level in percentage= 99.5%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.9911)
zα =2.37
(b) Central limit c= 1-α
for α = 0.09 , c=1-0.09
∴ c=0.91
Hence confidence level in percentage= 91%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.91)
zα=1.34
(c) Central limit c= 1-α
for α = 0.707 , c=1-0.707
∴ c=0.293
Hence confidence level in percentage= 29.3%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.707)
zα= -0.545
Therefore zα value for 0.0089 is 2.37, for 0.09 is 1.34 and for 0.707 it is -0.545.
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What is an example of a ratio word problem?
John has 5 red balls and 8 blue balls. What is the ratio of red balls to blue balls? Answer: The ratio of red balls to blue balls is 5:8.
We can solve this problem by using a ratio. Ratios are two values that are compared to each other. In this case, we need to compare the number of red balls to the number of blue balls. We are given that there are 5 red balls and 8 blue balls. To find the ratio, we need to write the numbers as a fraction. The fraction for red balls is 5/8 and the fraction for blue balls is 8/5. We can then simplify the fractions to get the ratio of 5:8. This means that there is a ratio of 5 red balls to 8 blue balls.
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Keilantra has $660 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $488.20.
She buys 2 bicycle reflectors for $11.17 each and a pair of bike gloves for $19.05.
She plans to spend some or all of the money she has left to buy new biking outfits for $37.26 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Keilantra can purchase while staying within her budget.
a) An inequality that can determine x the number of outfits Keiland can purchase while staying within her total budget of $660 is 529.59 + 37.26x ≤ 660.
b) The inequality solution shows that x cannot be more than 3.
What is inequality?An inequality is a mathematical statement that two or more mathematical expressions are unequal or not equivalent.
Inequalities are depicted as follows:
Greater than (>)Greater than or equal to (≥)Less than (<)Less than or equal to (≤)Not equal to (≠).These inequality symbols are usually written between two numbers or algebraic expressions.
The total spending budget Keilantra has = $660
The cost of a new bicycle = $488.20
The cost of 2 reflectors = $22.34 ($11.17 x 2)
The cost of a pair of bike gloves = $19.05
The total costs for the above three items = $529.59
The unit cost of new biking outfits = $37.26
The number of outfits Keilantra can purchase = x
Inequality:529.59 + 37.26x ≤ 660
37.26x ≤ 660 - 529.59
37.26x ≤ 130.41
x ≤ 3.5
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In a trapezoid $ABCD$ with $AB$ parallel to $CD$, the diagonals $AC$ and $BD$ intersect at $E$. If the area of triangle $ABE$ is 50 square units, and the area of triangle $ADE$ is 20 square units, what is the area of trapezoid $ABCD$
The area of trapezoid ABCD is 98 square units.
How to find the area of trapezoid ABCD?Based on the data given, The area of ΔDBA = area of ΔADE + area of ΔABE = 20 + 50 = 70. So
area of Δ DBA = 0.5 sin DBA (AB x DB) = 70
sin DBA = 140 / ( AB x DB)
sin DBA = sin CDB
The area of ΔCDB would be 0.5 sin (DBA) (DB x DC)
The area of ΔCDB = 0.5 (140 / [(AB x DB] ) (DB x DC)
The area of ΔCDB = 70 (DC/AB) = 70 ( DE /BE)
The area of ΔAEB would be 0.5 sin AEB ( AE * BE)
The area of ΔAEB = 50 (1)
Area Δ ADE would be 0.5 sin DEA (AE * DE)
Area Δ ADE = 20 (2)
Because of angle AEB is supplemental to angle DEA, their sines are equal. So
sin AEB = sin DEA
Let rearranging (1), (2). So we will have
sin AEB = sin DEA
100 / [ AE * BE] = 40 / [ AE * DE ]
DE / BE = 40/100 = 2/5
Since area of ΔCDB equal to 70 (DE / BE) then
ΔCDB = 70 (2/5) = 28
So...area of trapezoid ABCD = area of ΔDBA + area of ΔCDB
area of trapezoid ABCD = 70 + 28 = 98
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A scale drawing of a rectangular park had a scale of 1 cm = 60 m
What is the actual perimeter of the park in meters?
5. A binary operation is defined on the set of real numbers by a*b = a + b - ab, where a, b£R.
(i) Determine whether or not * is distributive over ordinary addition (+) on R. on)
Answer:
isjsjdjejejrjebdkxn nsksksnenmdnxee nu pot snndnsnenenene
Given: C is the midpoint of NB; C is the midpoint of MA
Prove: ABC is congruent to NMC
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