3. [2 points.] use the original definition of the laplace transform to derive the laplace transform of the third derivative y 000(t). that is, compute the transform l {y 000(t)}
Answers
The Laplace transform of y'''(t) can be obtained by multiplying the Laplace transform variable s thrice and subtracting the initial conditions of y''(t), y'(t), and y(t) multiplied by the corresponding powers of s.
The Laplace transform of a function f(t) is defined as L{f(t)} = ∫[0, ∞] \(e^{(-st)}\) f(t) dt, where s is the complex transform variable. To derive the Laplace transform of y'''(t), we apply the definition and integrate by parts three times.
Let's assume that the Laplace transform of y(t) is Y(s). By applying the Laplace transform to y'''(t), we get:
L{y'''(t)} = ∫[0, ∞]\(e^{(-st)}\) y'''(t) dt
By integrating by parts three times, we can express this transform as follows:
L{y'''(t)} = [\(s^3\) Y(s) - \(s^2\) y(0) - sy'(0) - y''(0)]
Here, y(0), y'(0), and y''(0) represent the initial conditions of y(t), y'(t), and y''(t) respectively.
In summary, the Laplace transform of y'''(t) is given by [\(s^3\) Y(s) - \(s^2\) y(0) - sy'(0) - y''(0)], where Y(s) is the Laplace transform of y(t) and y(0), y'(0), and y''(0) are the initial conditions of y(t), y'(t), and y''(t) respectively.
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Related Questions
I NEED HELP WITH THIS
Answers
Answer:
(4x-9)^2.
Step-by-step explanation:
If you want to simplify 16x^2 - 72x + 81, you can use a cool trick called the square of a binomial rule. This rule says that if you have something like (a + b)^2, you can expand it as a^2 + 2ab + b^2. So, how do we apply this rule to our problem? Well, first we need to find a and b that make our expression look like (a + b)^2. We can do this by noticing that 16x^2 is the same as (4x)^2 and 81 is the same as 9^2. Then we can check that the middle term is -2 times the product of 4x and 9, which is -72x. So we can write our expression as (4x - 9)^2. That's it! We have simplified our expression using the square of a binomial rule.
What is the radius of polygon JKLMN ?
Answers
Answer:
Radius of the circle is 5 units.
Step-by-step explanation:
JKLMN is a regular polygon inscribed in a circle.
Since, its a regular polygon,
JN = NM = 5.88 units
"Perpendicular drawn from the center of the circle to any chord is the bisector of the chord"
Therefore, PQ will be the perpendicular bisector of chord NM.
QM = \(\frac{1}{2}(NM)\)
QM = \(\frac{1}{2}(5.88)\)
QM = 2.94 units
By applying Pythagoras theorem in ΔPQM,
PM² = PQ² + QM²
PM² = (4.05)² + (2.94)²
PM = \(\sqrt{16.4025+8.6436}\)
PM = \(\sqrt{25.0461}\)
PM = 5 units
Therefore, radius of the circle is 5 units.
2. pvalue
3.critical value
4.test value
5.make a desision
Noise Levels in Hospitals In a hospital study, it was found that the standard deviation of the sound levels from 30 areas designated as "casualty doors" was 6.4 dBA and the standard deviation of 28 areas designated as operating theaters was 4.1 dBA. At a 0.10, can you substantiate the claim that there is a difference in the standard deviations? Use a, for the standard deviation of the sound levels from areas designated as "casualty doors." Part 1 of 5 (a) State the hypotheses and identify the claim. H_0: sigma_1^ = sigma_2^ _____
H_1: sigma_1^ ≠ sigma_2^ _____
This hypothesis test is a___test.
Answers
The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.
The hypotheses for the test are:
H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.
To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.
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For every 3 dozen cookies, a bakery uses 8 cups of butter. How many dozen of cookies could you make with 20 cups of butter?
Answers
Answer:
7 1/2 dozen of cookies
Step-by-step explanation:
If for every 3 dozen cookies, a bakery uses 8 cups of butter then we can say;
3 dozens cookies = 8 cups of butter
x cups of cookies = 20 cups of butter
Cross multiply
8*x = 3 * 20
8x = 60
x = 60/8
x = 7 4/8
x = 7 1/2
Hence you will need 7 1/2 dozen of cookies
your friend claims that he can prove the parallelogram opposite sides theorem (thm. 7.3) using the sss congruence theorem (thm. 5.8) and the parallelogram opposite sides theorem (thm. 7.3). is your friend correct?
Answers
No, the assertion made by your buddy is false. It is impossible to utilize the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate itself. You must employ known facts and theorems rather than the theorem you are attempting to show in order to prove a theorem.
If your buddy is utilizing the SSS congruence theorem (Thm. 5.8) and the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate the theorem, they are not offering a proper proof since they are employing the theorem they are attempting to demonstrate as part of the proof itself. This results in a circular argument and is invalid as evidence
The parallelogram opposing sides theorem has to be proven using other well-known facts and theorems, like the definition of a parallelogram, the definition of congruent figures, and other relevant theorems and postulates from geometry.
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Please help me with my work
Answers
Answer:
1) -1/4
2) -1/2
3) 1/3
Step-by-step explanation:
perpendicular lines' slopes are opposite reciprocals so you flip it and change the positive or negative sign
parallel lines have the same slope
A certain type of digital camera comes in either a 3-megapixel version or a 4-megapixel version. A camera store has received a shipment of 15 of these cameras, of which 6 have 3-megapixel resolution. Suppose that 5 of these cameras are randomly selected to be stored behind the counter; the other 10 are placed in a storeroom. Let X be the number of 3-megapixel cameras among the 5 selected for behind the counter storage. a. Compute P(X = 2), P(X ≤ 2), and P(X ≥ 2). b. Calculate the mean value and standard deviation of X.
Answers
(a) To compute the probabilities:
P(X = 2): This represents the probability of selecting exactly 2 out of the 5 cameras to be 3-megapixel. We can calculate this using the binomial probability formula: P(X = 2) = C(5, 2) * (6/15)^2 * (9/15)^3, where C(5, 2) is the number of ways to choose 2 out of 5 cameras. Evaluate this expression to get the probability.
P(X ≤ 2): This represents the probability of selecting 0, 1, or 2 3-megapixel cameras out of the 5 selected. We can calculate this by summing the individual probabilities: P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2).
P(X ≥ 2): This represents the probability of selecting 2, 3, 4, or 5 3-megapixel cameras out of the 5 selected. We can calculate this by summing the individual probabilities: P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5).
(b) To calculate the mean value and standard deviation of X:
Mean (μ): The mean of a binomial distribution is given by μ = n * p, where n is the number of trials (5 in this case) and p is the probability of success (6/15).
Standard Deviation (σ): The standard deviation of a binomial distribution is given by σ = sqrt(n * p * (1 - p)).
Let's substitute the values to calculate the mean and standard deviation of X.
Given:
Number of trials (n) = 5
Probability of success (p) = 6/15
Mean (μ) = n * p
Mean (μ) = 5 * (6/15)
Mean (μ) = 2
Standard Deviation (σ) = sqrt(n * p * (1 - p))
Standard Deviation (σ) = sqrt(5 * (6/15) * (1 - 6/15))
Standard Deviation (σ) = sqrt(5 * (6/15) * (9/15))
Standard Deviation (σ) = sqrt(54/75)
Standard Deviation (σ) = sqrt(18/25)
Standard Deviation (σ) = sqrt(18)/sqrt(25)
Standard Deviation (σ) = 3/5
Therefore, the mean value of X is 2 and the standard deviation of X is 3/5.
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I have 2 twenty dollar bills, a five dollar, 3 one dollar coins, 2 twenty-five cents pieces and 3 ten cents coins in my pocket. How much money do i have in my pocket?
Answers
Answer:
128
Step-by-step explanation:
two twenty dollars which is 40,five dollars 5,three one dollars which is 3,two twenty five cents which is 25+25=50,three ten cents which is 3×10=30
40 +5+3+50+30
=128
Simplify the expression. Enter the answer in the box. 3 2/5 + (-7 1/5) = 3 + (-7) + 2/5 + (-1/5)
Answers
Solve for X: square root 4x-7 - square root 2x = 1
Answers
Root x = 2 is an extraneous solution for radical equation √(4 · x - 7) - √(2 · x) = 1, whose roots are 2 and 8, respectively.
How to determine the extraneous solution of a radical equation
In this problem we find the definition of a radical equation, whose roots must be found by combining algebra properties and power properties. A root is an extraneous solution if the result lead to an absurdity. (i.e. 1 = 0).
First, write the complete expression:
√(4 · x - 7) - √(2 · x) = 1
Second, apply algebraic substitution formula u = 2 · x to simplify the model:
√(2 · u - 7) - √u = 1
Third, use algebra properties to clear square roots:
√(2 · u - 7) = 1 + √u
Fourth, square both sides of the expression:
2 · u - 7 = (1 + √u)²
2 · u - 7 = 1 + 2 · √u + u
u - 7 = 1 + 2 · √u
u - 2 · √u - 8 = 0
Fifth, use algebraic substitution k = √u and solve the quadratic-like equation by factorization:
k² - 2 · k - 8 = 0
(k - 4) · (k + 2) = 0
k₁ = 4 or k₂ = - 2
Sixth, find the values of x by reversing algebraic substitutions:
√u₁ = 4 or √u₂ = - 2
u₁ = 4² or u₂ = (- 2)²
2 · x₁ = 4² or 2 · x₂ = (- 2)²
x₁ = 8 or x₂ = 2
Seventh, look for any extraneous solution:
x₁ = 8
√(4 · 8 - 7) - √(2 · 8) = 1
√25 - √16 = 1
5 - 4 = 1
1 = 1
x₂ = 2
√(4 · 2 - 7) - √(2 · 2) = 1
√1 - √4 = 1
1 - 2 = 1
- 1 = 1 (CRASH!)
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Suppose we know the homework scores in a particular (large) lecture class are Normally distributed with a mean of 82 and a standard deviation of 4.5. Based on this information, we can say that roughly 95% of students will be expected to have a homework score that falls between what two values?
Answers
Roughly 95% of students in the lecture class are expected to have a homework score that falls between 73.1 and 90.9. This interval represents the range within which the majority of students' scores are likely to lie.
In a normally distributed dataset, the empirical rule, also known as the 68-95-99.7 rule, states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. Given that the mean homework score is 82 and the standard deviation is 4.5, we can apply the empirical rule to determine the range of scores.
To find the range of scores within which 95% of students are expected to fall, we calculate two standard deviations above and below the mean. Two standard deviations below the mean is 82 - (2 * 4.5) = 73, and two standard deviations above the mean is 82 + (2 * 4.5) = 91. Therefore, we can say that roughly 95% of students are expected to have a homework score between 73 and 91.
It's important to note that the empirical rule provides an approximation and assumes a normal distribution. In reality, individual scores may deviate from this range, but the majority of scores are expected to fall within it.
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What is the area of the rectangle
Answers
Answer:
B) \(\frac{15}{4}\)
Step-by-step explanation:
Area of a rectangle formula:
A = bh
Given:
b = \(2\frac{1}{2}\)
h = \(1\frac{1}{2}\)
Work:
A = bh
A = \((2\frac{1}{2} )(1\frac{1}{2} )\)
A = \(\frac{15}{4}\)
Daily question:Help and I’ll make you brainliest and give you thanks show your work 11 points.
Answers
Answer:
y = 17x + 130$283 for 9 daysStep-by-step explanation:
The daily charge will be 17x for x days of rental. Added to the flat rate, the total becomes ...
y = 130 +17x
__
For 9 days, the cost is ..
y = 130 +17·9 = 130 +153 = 283 . . . . dollars charge for 9 days
The function rule for the input/output table is to multiply by 6. What number completes the table?
x y
-5 -30
0 0
7
67
49
48
42
Answers
The number that completes the table is:
x y
-5 -30
0 0
7 42
67 402
49 294
48 288
42 252
How to find the number that completes the table?A function is an expression that shows the relationship between the input and the output. A function is usually denoted by letters such as f, g, etc.
In this, case the input is x and the output is y. Since the function rule for the input/output table is to multiply by 6. We can say:
y = 6x
Thus, we can complete the table by multiplying the values of x by 6 to get the values of y. That is:
x y
-5 -30
0 0
7 42
67 402
49 294
48 288
42 252
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A poster has an area of 12 feet. Its perimeter is 16 feet. What are the dimensions of the poster?
Answers
Answer:
Length: 6, Width: 2
Step-by-step explanation:
6 times 2 is 12 and 6 + 6 + 2 + 2 = 16.
PLEASE HELP EASY SLOPE MATH its not 1.5
Answers
Answer: The answer is 4.5
Answer:
B. 4.5 miles per hour
Step-by-step explanation:
look at the graph and see where the line hits 1(time in hours) as you can see, the line hits in between 3 and 6, so the most reasonable answer would be 4.5. this doesn't work for all answers, but it seems to work for this one. I hope that helps you!
khanya builders are paid R480 for 8 hours of work,whiles rex builders are paid R660 for 12 hours of work.which company is paid the higher rate
Answers
Answer:
khanya pays higher
Step-by-step explanation:
You have to find the $/hr ratios:
khanya's is 480/8->$60/hr
rex's is 660/12->%55/hr
Khanya pays the higher rate
Determine whether AB and CD are parallel, perpendicular, or neither. Graph each line to verify your answer. A(4, 2), B(-3, 1), C(6, 0), D(-10, 8)
Answers
The lines AB and CD are neither parallel nor perpendicular,
Determining the relationship between lines AB and CDFrom the question, we have the following parameters that can be used in our computation:
A(4, 2), B(-3, 1), C(6, 0), D(-10, 8)
The relationship between lines AB and CD can be determined using the slope formula
The slope of a line is calculated using
Slope = Change in y/Change in x
using the above as a guide, we have the following:
Slope AB = (1 - 2)/(-3 - 4)
Slope AB = 1/7
Slope CD = (8 - 0)/(-10 - 6)
Slope CD = -1/2
The above slopes are neither equal nor opposite reciprocals
This means that the lines AB and CD are neither parallel nor perpendicular,
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Samuel's family took a road trip to Mount Rushmore. Samuel fell asleep after they had traveled 990 miles. If the total length of the trip was 1000 miles, what percentage of the total trip had they traveled when Samuel fell asleep?
Answers
The percentage of the total trip that they traveled when Samuel fell asleep is 99%.
What percentage of the total trip had they traveled when Samuel fell asleep?Given that Samuel's family took a road trip to Mount Rushmore. Samuel fell asleep after they had traveled 990 miles and the total length of the trip was 1000 miles,
The percentage of the total trip that they traveled when Samuel fell asleep will be:
= Trip feel asleep / Total trip × 100
= 990/1000 × 100
= 99%
The percentage is 99%.
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Which statement describes the relationship, if any, that exists between triangle KLM and triangle NPQ? Triangle L K M. Side K L is 16, L M is 22, K M is 12. Triangle P N Q. Side P N is 8, N Q is 6, P Q is 11. Angles L and P are congruent, Q and M are congruent, K and N are congruent.
Answers
Answer:
Its B I think
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Answer and explanation please
Answers
because the cube root of 27 is 3 and 15/3 is 5
Help me with this!!!
Answers
Answer:
it is second one
it is a RAY
All students in Ridgewood Junior High School either got their lunch in the school cafeteria or brought it from home on Tuesday. 4% of students brought their lunch. 34 students brought their lunch. How many students in total are in Ridgewood Junior High School?
Answers
Answer: There are 850 students total
Step-by-step explanation: First step is to analyze, 34 brought lunch which makes up 4% so to find total we will divide because dividing percentages gives you bigger numbers.
We will do 34/4%= 850
Therefore there are 850 students attending Ridgewood Junior High School
in 2000, india's population reached 1 billion, and it's projected to be 1.45 billion in 2025. use the function f(x)
Answers
a) The value of p₀=1
b) The population in the year 2020 is 1.3 billion.
c) The function f(x)=1.5 billion reaches India's population in the year 2030.
What is meant by a function?A function is a relationship between two or more inputs, each of which corresponds to exactly one output. A domain and a codomain or range are assigned to each function.
a) Given, The population of India after x years is f(x)=p₀(1.01355)ˣ⁻²⁰⁰⁰
Also in 2000, the population reached 1 billion.
That is when x=2000, f(x)=1
f(2000)=1
p₀(1.01355)ˣ⁻²⁰⁰⁰⁻²⁰⁰⁰=1
p₀×1=1
p₀=1
Hence p₀=1
b) Here the objective is we have to find the population in the year 2020
Then the value of f(x) when x=2020
Hence,
f(2020)=p₀(1.01355)ˣ⁻²⁰²⁰⁻²⁰²⁰
f(2020)=1(1.01355)²⁰
f(2020)=1.3
Therefore, the population in the year 2020 is 1.3 billion.
c) f(x)=1.5
p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5
1×p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5
p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5
ln(p₀(1.01355)ˣ⁻²⁰⁰⁰)=ln(1.5)
(x-2000)ln(1.01355)=ln(1.5)
x-2000=ln(1.5)/ln(1.01355)
x=(ln(1.5)/ln(1.01355))+2000
x=30.12+2000
x=2030.12
Hence in the year 2030, the population might reaches to 1.5 billion.
Therefore, f(x)=1.5 billion
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The complete question is:
In 2000 , India's population reached 1 billion, and its projected to be \( 1.45 \) billion in 2025 . Use the function \( f(x
Show transcribed data
In 2000 , India's population reached 1 billion, and it's projected to be
1.45
billion in 2025 . Use the function
f(x)=P0(1.01355)
x−2000
find the help find the following a) What is p₀
? billion b) Predict India's population in 2020 to the nearest tenth of a billion. billion c) Use the function to determine the year when India's population might reach
1.5
billion. (Round to the nearest year) Question 21 Out of pocket spending for healthcare in the United States increased between 2000 and 2008 . The function
f(x)=2572e
0.0359x
models the average annual expenditures per household, dollars, In this model,
x
represents the year,
x=0"
A 2 - gallon bottle of bleach costs $ 7.68 . What is the price per cup ? $
Answers
Answer:
$0.24
Step-by-step explanation:
7.68/32=0.24
There are 32 cups per 2 gallons. The total cost for 2 gallons is 7.68
The swamp middle school basketball team purchased new equipment and uniforms. The total cost of the equipment was $245 and each uniform cost $21. If the total cost of their purchase was $518, how many uniforms did they buy? Create an equation for this situation.
Answers
Answer:
13 uniformsStep-by-step explanation:
Step one:
given data
total cost of equipments= $245
cost of each uniform=$21
Total purchase = $518
Step two:
The amount spent on uniform is total purchase minus the total cost of equipment
=518-245
=$273
Hence the total cost of the uniform is $273
if one will cost $21, then the number of uniforms they bought is
=273/21
=13 uniforms
Answer:
25 uniforms
Step-by-step explanation:
518/21= 24.6 round to 25
a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion is called
Answers
The sample is a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion .
A sample is a collection of people, things, or things used in research that is taken for analysis from a larger population. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.
We must utilize inferential statistics to discover a population's characteristics by directly observing only a subset (or sample of the population) in order to derive conclusions about populations from samples.
Since it is frequently impractical and hardly ever possible, we acquire a sample of the population.
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For each of the following functions, write the formula for the function's inverse. a. f(x) = 0.7%^x where y = f(x). f-'(y) = b. f(x) = 4.5(2.7)^x where y = f(x).
f-'(y) =
Answers
The formula for the function's inverse is
(a) f⁻¹(y) = Iny/In(0.7)
(b) f⁻¹(y) = [Iny - In(4.5)]/In(2.7)
(a) The function is;
f(x) = 0.7ˣ where y = f(x).
So y = 0.7ˣ
Taking In on both side,
Iny = x In(0.7)
Divide by In(0.7) on both side, we get
x = Iny/In(0.7)
f⁻¹(y) = Iny/In(0.7)
(b) The function is;
f(x) = 4.5(2.7)ˣ where y = f(x).
So y = 4.5(2.7)ˣ
Divide by 4.5 on both side, we get
y/4.5 = (2.7)ˣ
Taking In on both side,
In(y/4.5) = In(2.7)ˣ
Iny - In(4.5) = xIn(2.7)
Divide by In(2.7) on both side, we get
x = [Iny - In(4.5)]/In(2.7)
f⁻¹(y) = [Iny - In(4.5)]/In(2.7)
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The complete question is:
For each of the following functions, write the formula for the function's inverse.
a. f(x) = 0.7ˣ where y = f(x).
f⁻¹(y) =
b. f(x) = 4.5(2.7)ˣ where y = f(x).
f⁻¹(y) =
Complete the steps in the proof that show quadrilateral with vertices , , , and is a kite. Using the distance formula, , , = , and =. Therefore, is a kite because.
Answers
By using distance formula and using the property of quadrilateral and kite we can prove it is a kite.
What is distance formula?The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points being used to find the distance between them.
What are the properties of kite?It has two pairs of equal-length sides, which are called diagonals.
The diagonals of a kite intersect at right angles.
A kite has two opposite pairs of congruent (equal) angles.
The diagonals of a kite bisect (cut into two equal parts) each other.
The sum of the interior angles of a kite is 360 degrees.
A kite is a type of convex quadrilateral, meaning that all of its interior angles are less than 180 degrees and its sides do not intersect.
To prove that a quadrilateral with vertices A, B, C, and D is a kite, you can follow these steps:
Use the distance formula to calculate the lengths of the sides of the quadrilateral. The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points being used to find the distance between them.
Determine which pairs of sides are diagonals of the kite. A kite has two pairs of sides that are diagonals, which means they intersect at right angles.
Use the distance formula to calculate the lengths of the diagonals.
Check that the lengths of the diagonals are equal. In order for a quadrilateral to be a kite, the lengths of the diagonals must be equal.
If the lengths of the diagonals are equal, then the quadrilateral is a kite. If the lengths of the diagonals are not equal, then the quadrilateral is not a kite.
So, using this process, you can prove that a quadrilateral with vertices A, B, C, and D is a kite if you can show that the lengths of the diagonals are equal.
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Explain why a + b = d.
B
A
C
swer
Answers
Answer:
Explanation below
Step-by-step explanation:
Angles in a Triangle
There are two basic relations of angles we need to recall:
Supplementary angles add up to 180°Internal angles of a triangle add up to 180°Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:
c = 180 - ( a + b )
Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus
c = 180 - d
From the two relations above, it follows that:
a + b = d