Let X and Y be random variables with joint density function f(x, y) = { 2e^-2x/x, 0 < y < x
0, otherwise.
Compute Cov(X, Y). Cov(X, Y) = _______
Answers
Let X and Y be random variables with joint density function f(x, y) = { 2e^-2x/x, 0 < y < x 0, otherwise. Compute Cov(X, Y). Cov(X, Y) = 5/8.
To compute the covariance of random variables X and Y (Cov(X, Y)), we need to find the expected values of X, Y, and their product XY. The formula for covariance is:
Cov(X, Y) = E(XY) - E(X)E(Y)
First, we'll find E(X) and E(Y):
E(X) = ∫∫ x * f(x, y) dy dx
E(Y) = ∫∫ y * f(x, y) dy dx
For E(X):
E(X) = ∫(0 to ∞) x ∫(0 to x) 2e^(-2x) dy dx
= ∫(0 to ∞) x (2e^(-2x) * y |_0^x) dx
= ∫(0 to ∞) 2xe^(-2x) dx
= -xe^(-2x) - (1/2)e^(-2x) |_0^∞
= 1/2
For E(Y):
E(Y) = ∫(0 to ∞) ∫(0 to x) 2ye^(-2x) dy dx
= ∫(0 to ∞) (e^(-2x) * y^2 |_0^x) dx
= ∫(0 to ∞) xe^(-2x) dx
= -(1/2)e^(-2x) * (x + 1) |_0^∞
= 1/4
Now, we'll find E(XY):
E(XY) = ∫∫ xy * f(x, y) dy dx
= ∫(0 to ∞) ∫(0 to x) 2x^2e^(-2x) dy dx
= ∫(0 to ∞) (2x^2e^(-2x) * y |_0^x) dx
= ∫(0 to ∞) 2x^3e^(-2x) dx
= (3/4)e^(-2x) * (x^2 + x + 1/2) |_0^∞
= 3/4
Finally, we can compute the covariance:
Cov(X, Y) = E(XY) - E(X)E(Y)
= (3/4) - (1/2)(1/4)
= 3/4 - 1/8
= 5/8
So, Cov(X, Y) = 5/8.
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Related Questions
Fill in each blank so that the resulting statement is true.
Consider the following long division problem.
3x-4)9x³ +6x² + 13x-5
Begin the division process by dividing
in the dividend.
Begin the division process by dividing
by
by, which obtains
***
which obtains
.Write this result above
.Write this result above in the dividend.
Answers
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
What are some examples of polynomials?
picture of a polynomial,Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.For instance, the polynomial 3x+2x-5.a description of polynomials.The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. The number 10 is not a polynomial by this definition.However, the polynomial is frequently represented by the number 10 (10,0,0,...).This is an illustration of a symbol that is "overloaded," which can occur in math on sometimes.Ideally, the context will always make the meaning evident. Because whole numbers are singular terms without a variable, they would not be considered polynomials by themselves. However, a whole number could be a part of a polynomial as that polynomial's constant term.The leading coefficient is the first term of a polynomial.4x5+2x2−14x+12.A polynomial is simply a sum of several monomials.A polynomial with only two terms can be referred to as a binomial, and a polynomial with three terms is referred to as a trinomial.(3x-4)9x³+6x²+13x-5
derivative of polynomial
axn-1
3x1-1
3x°
3×1
t=3
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A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers find the probability that the committee will consist of these people. (Assume that the selection will be random) a) all teachersB) 2 teachers and 2 parents c) all parents d) I teacher and 3 parents
Answers
This situation can be modeled with the binomial distribution if we consider each person as a teacher or not a teacher.
The probability that a person is a teacher is computed as follows:
\(p=\frac{\text{ number of teachers}}{total\text{ number of people}}=\frac{5}{20+5}=0.2\)The binomial distribution formula is:
\(P(x)=_nC_x\cdot p^x\cdot q^{n-x}\)where:
P: binomial probability
x: number of times for a specific outcome within n trials
nCx: combinations
p: probability of success on a single trial (in this case, success means the person is a teacher)
q: probability of failure on a single trial (computed as 1 - p)
n: number of trials
a) Substituting with x = 4, n = 4, p = 0.2, q = 0.8 (= 1 - 0.2), we get:
\(\begin{gathered} P(4)=_4C_4\cdot0.2^4\cdot0.8^{4-4} \\ P(4)=1\cdot0.2^4\cdot1 \\ P(4)=0.0016 \end{gathered}\)b) Substituting with x = 2, n = 4, p = 0.2, q = 0.8 (= 1 - 0.2), we get:
\(\begin{gathered} P(2)=_4C_2\cdot0.2^2\cdot0.8^{4-2} \\ P(2)=6\cdot0.2^2\cdot0.8^2 \\ P(2)=0.1536 \end{gathered}\)c) Substituting with x = 0, n = 4, p = 0.2, q = 0.8 (= 1 - 0.2), we get:
\(\begin{gathered} P(0)=_4C_0\cdot0.2^0\cdot0.8^{4-0} \\ P(0)=1\cdot1\cdot0.8^4 \\ P(0)=0.4096 \end{gathered}\)d) Substituting with x = 1, n = 4, p = 0.2, q = 0.8 (= 1 - 0.2), we get:
\(\begin{gathered} P(1)=_4C_1\cdot0.2^1\cdot0.8^{4-1} \\ P(1)=4\cdot0.2^{}\cdot0.8^3 \\ P(1)=0.4096 \end{gathered}\)Solve this quick please thank you.
Answers
Answer:
\(y=-\dfrac{8}{x}\)
Step-by-step explanation:
Inverse proportions can be represented by an equation in the form:
\(\boxed{y=\dfrac{k}{x}}\)
where:
y and x are the two quantities in the proportion.k is the constant of proportionality.To write an expression for the graphed function, first input the given point (-2, 4) into the inverse proportion equation and solve for k:
\(\implies y=\dfrac{k}{x}\)
\(\implies 4=\dfrac{k}{-2}\)
\(\implies 4 \cdot (-2)=\dfrac{k}{-2}\cdot (-2)\)
\(\implies -8=k\)
\(\implies k=-8\)
Therefore, the expression for the graphed function is:
\(\boxed{y=-\dfrac{8}{x}}\)
3+11(x+y)-4(x+y)^{2}
Answers
Answer:
3+11x+11y-4x^2-8xy-4y^2
Step-by-step explanation:
Using the distributive property, we get 3+11x+11y-4x^2-8xy-4y^2
NEED HELP PLZZZ
Write an equation that represents the transformations formed by the following items
(a) horizontally shifting the graph 4 units to the left of f(x) = sqrt(x) and then vertically compression by a factor of 1/3
(b) vertically stretching the graph by a factor of 4 of f(x) = sqrt(x) and then vertically shifting the graph 3 units up
(c) horizontally stretching the graph of f(x) = sqrt(x) by a factor of 2 and then vertically shifting the graph units down
Answers
Using translation concepts, it is found that the equations that represents the transformations formed by the following items are given by:
a) \(g(x) = \frac{1}{3}\sqrt{x + 4}\)b) \(g(x) = 4\sqrt{3} + 3\)c) \(g(x) = \sqrt{\frac{x}{2}} - 3\)What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.Item a:
The function is:
\(f(x) = \sqrt{x}\)
Horizontal shift of 4 units to the left, hence:
\(g(x) = f(x + 4) = \sqrt{x + 4}\)
Vertical compression by a factor of \(\frac{1}{3}\), hence a multiplication by \(\frac{1}{3}\), that is:
\(g(x) = \frac{1}{3}\sqrt{x + 4}\)
Item b:
Vertical stretch by a factor of 4, that is, a multiplication by 4, so:
\(4f(x) = 4\sqrt{3}\)
Vertical shift of 3 units up, hence addition of 3, that is:
\(g(x) = 4\sqrt{3} + 3\)
Item c:
Horizontal stretch by a factor of 2, that is:
\(g(x) = f(\frac{1}{2}x) = \sqrt{\frac{x}{2}}\)
Vertical shift of 3 units down, hence subtraction by 3, that is:
\(g(x) = \sqrt{\frac{x}{2}} - 3\)
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MO
R
S
Activity 1
Given: <QPR <SPW
р
Prove: QRws
W
Statement
Reason
1. <QPR <SPW
2. m <QPR = m <SPW
3. m<QPR = m QR and m<SPW = m WS
4. m QR = m Ws
5. QR LWS
Answers
Answer:
Is dis a question...??????
find the torque τ about p due to f⃗ . your answer should correctly express both the magnitude and sign of τ . express your answer in terms of rm and f or in terms of r , θ , and f .
Answers
Torque is the cross product of the distance from the pivot point to the force, denoted by r, and the force applied, denoted by F. τ= r×F, where r is the moment arm, and F is the force. The direction of torque is either clockwise or counterclockwise depending on whether the force causes rotation that is clockwise.
Also, it is denoted by a positive sign for a counterclockwise torque and a negative sign for a clockwise torque.Let's assume that the vector F, acting on a rigid body about pivot point P, creates a moment, i.e., torque. The torque about P is determined by the product of the force magnitude, F, and the perpendicular distance, rm, from point P to the line of action of F.
That is, τ=rm ×F. If F and rm are known, we may substitute them into the equation to obtain the torque in the direction of rotation.τ = rm × Fsin(θ) where θ is the angle between the two vectors F and rm.Therefore, the torque about P due to F is expressed in terms of rm and F or in terms of r, θ, and F as τ=rm ×Fsin(θ) or τ = rFsin(θ), respectively.
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one number is less than a second number. the first is more than times the second. find the numbers.
Answers
We can't find the exact values of x and y without more information. However, we know that y must be a negative number and x must be more than three times that negative number plus a positive constant. To solve this problem, we can use algebraic equations. Let's call the first number "x" and the second number "y".
From the problem, we know that:
- x is less than y
- x is more than 3 times y
We can write these statements as:
- x < y
- x > 3y
Now we need to solve for both x and y. One way to do this is to use substitution. We can rearrange the second equation to solve for x in terms of y:
x = 3y + c
where "c" is some constant. We don't know what "c" is yet, but we can use the first equation to help us find out.
If x is less than y, we can substitute "x" with the expression we just found:
3y + c < y
Now we can solve for y:
2y < -c
y < -c/2
So we know that y is negative and less than -c/2.
Next, we can use the second equation to solve for "c":
x > 3y
3y + c > 3y
c > 0
So "c" must be positive.
Putting it all together, we know that:
- y is negative and less than -c/2
- c is positive
Therefore, we can't find the exact values of x and y without more information. However, we know that y must be a negative number and x must be more than three times that negative number plus a positive constant.
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Please answer!it is grade 6 math
Answers
AB+BE+EF+GF+HG+AH = 14 #EQU 1
BC+CD+DE+EF+GF+BG = 22 #EQU 2
AB+BC+CD+DE+EF+GF+HG+AH = 24 #EQU 3
IMPLEMENTING EQU 2 IN EQU 3
AB+22-EF+ HG+AH = 24 # EQU 5
FROM EQU 1
AB+HG+AH = 14-(BE+EF+GF) #EQU 4
IMPLEMENTING EQU 4 IN EQU 5
22+14 - (BE+EF+GF+EF) = 24
36 - 24 = BE+EF+GF+BG(EF=BG)
12 = PATH TAKEN ON THURSDAY
-5x’2+9x-3=0
Descriminant:
Number of real solution:
Answers
Answer:
2 x ^2 − 2 x + 4 = 0
x ^2 − 2 x + 4 = 0
2 x ^2 − x = 0
Step-by-step explanation:
nikolas is suspected of a crime and is asked to take a polygraph test. although he is innocent, what are the chances that he will be falsely accused?
Answers
The chances that Nikolas will be falsely accused in a polygraph test are dependent on the accuracy of the test and the criteria used to determine guilt or innocence.
Polygraph tests, also known as lie detector tests, are controversial and have varying degrees of accuracy. The accuracy of a polygraph test depends on many factors, including the expertise of the administrator, the type of test administered, and the physiological response of the individual being tested.
Furthermore, the criteria used to determine guilt or innocence based on the results of a polygraph test can vary. In some cases, a single inconclusive result may be enough to exonerate an individual, while in other cases, a single positive result may be enough to accuse an individual.
It is not possible to provide a specific numerical probability for the chances of Nikolas being falsely accused in a polygraph test.
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Please solve this both questions
Answers
Answer:
None of the batches will be the same shade of pink.
Step-by-step explanation:
You can only make the same shade of pink if you have an equivalent ratio, and none of the numbers are equivalent in either questions.
You are given the following points:A = (12, 10, -17),B = (-18, 0, -6),C = (-9, -3, 15).
Which point is closest to the yz-plane? B
What is the distance from the yz-plane to this point? 0
Which point is farthest from the xy-plane? A
What is the distance from the xy-plane to this point? 17
Answers
So the point farthest from the xy-plane is A = (12,10,-17). The distance of point A from xy-plane is 17 units.
The equation of the yz-plane is x=0.
So the yz-plane is the plane which passes through the points (0,1,0), (0,0,1) and (0,0,0).
For a point P(x,y,z), the distance between P and
the plane Ax + By + Cz + D = 0 is
|Ax+By+Cz+D| / sqrt(A²+B²+C²).
Thus, the distance from a point to the yz-plane is |x|.
Using this formula for the given points:
A = (12,10,-17) : |x| = |12| = 12B
= (-18,0,-6) : |x| = |-18| = 18C
= (-9,-3,15) : |x| = |-9| = 9
So the point closest to the yz-plane is C = (-9,-3,15).
The distance of point C from yz-plane is 9 units.
So the answer is: 9.
The equation of the xy-plane is z=0.
So the xy-plane is the plane which passes through the points (0,0,1) and (0,0,0).
The distance from a point to the xy-plane is |z|.
Using this formula for the given points:
A = (12,10,-17) : |z| = |-17| = 17B
= (-18,0,-6) : |z| = |-6| = 6C
= (-9,-3,15) : |z| = |15|
= 15
So the point farthest from the xy-plane is A = (12,10,-17).
The distance of point A from xy-plane is 17 units.
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pls help me classify this asap?!?!
Answers
Since all the angles of the first triangle are different, it is a scalene triangle, Similarly, since all the sides of the second triangle is also different, it is a scalene triangle.
Classification of trianglesTriangles is a 3-D shape with 3 sides and angles. The types of triangle that we have include;
ScaleneIsoscelesEquilateralObtuseRight triangleSince all the angles of the first triangle are different, it is a scalene triangle, Similarly, since all the sides of the second triangle is also different, it is a scalene triangle.
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Use the graph of the lines to determine if the two lines
are parallel.
units and right
Line MN was translated down
units to create line M'N'.
The slope of MN
The slope of M'N'
Answers
Answer:
(in order): 4, 8, -2, -2
Step-by-step explanation:
The slope of MN = -1.
The slope of M.N. = -1.
What is a slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given information:
The two lines MN and M'N' are parallel.
Transformation rule:
Line MN was translated down to 4 units and right to 6 units to create line M'N'.
And line MN passes through two points (-2, 0) and (-6, 8).
Therefore, the slope of line MN,
= (8- 0)/(-6-2)
= -1
Since lines MN and M'N' are parallel, they have the same slope.
Therefore, the slope of M'N' is also -1.
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The combined perimeter of the rectangle and triangle is 63 inches. The model shows the dimensions of the rectangle. What is the perimeter in inches of the triangle?
Answers
*See diagram in the attachment
Answer:
27 inches
Step-by-step explanation:
Combined perimeter = perimeter of rectangle + perimeter of triangle = 63 inches
Perimeter of rectangle = 2(L + W)
L = 11 in.
W = 7 in.
Perimeter of rectangle = 2(11 + 7) = 36 in.
Let perimeter of the triangle be represented by x
Therefore:
36 + x = 63
Subtract 36 from each side
x = 63 - 36
x = 27
Perimeter of triangle = 27 inches
read the picture plsssssssssssss
Answers
If the expression be 23 x² + 3x + 8 then the constant exists 8.
What is meant by expression?The addition, subtraction, multiplication, and division arithmetic operators are used to write a group of numbers together to form a numerical statement in mathematics. The expression of a number can take on various forms, including verbal form and numerical form.
A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
During the course of a program's execution, a constant's value cannot change. As a result, the value is constant, as implied by its name. During the course of a program's execution, a variable's value can change. As a result, the value might change, as implied by its name.
Let the expression be 23 x² + 3x + 8
then the constant exists 8.
Therefore, the correct answer is option C. 8.
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Which inequality describes all the solutions to 4 X - 8 ≥ 20
Answers
Answer:
Inequality Form:
X ≥ 7
Interval Notation:
[ 7 , ∞ )
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
X ≥ 7
Interval Notation:
[ 7 , ∞ )
i think its this
point-slope equation for perpendicular lines y=-2x-7 that passes through (-2,-3)
Answers
Answer: below! ^^
Step-by-step explanation:
Hii, do you need an answer to your question? Let me help you out! (;
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Part 1 ⚜Perpendicular lines have slopes that are opposite inverses of each other.
The slope (m) of the line that is perpendicular to y=-2x-7 is \(\sf -\cfrac{1}{2}\).
Part 2 ⚜⚜ Point slope formula\(\boldsymbol{y-y1=m(x-x1)}\)
⚜Stick in the known values\(\boldsymbol{y-(-3)=-\cfrac{1}{2}(x-(-2)}\)
⚜ Simplify\(\boldsymbol{y+3=-\cfrac{1}{2}(x+2)}\)
Voila! There's our answer, cheers! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Hope I helped! Best wishes!
Reach far. Aim high. Dream big.
\(\underbrace\)
I am on the roof of a 1200ft building, and I am looking at an even taller skyscraper. I have an inclinometer. WhenI look up at the top of the skyscraper, my inclinometer reads that I am looking up at an angle of elevation of35 degrees above the horizontal. When I look down at the base of the skyscraper, my inclinometer reads that Iam looking down at an angle of depression of 60 degrees below the horizontal. I also know that the building andskyscraper are 600 ft apart. Find the height of the skyscraper in exact and approximate form.
Answers
Let's try to draw a rough diagram of the problem:
From here, we can dissect a triangle as shown below:
From this diagram, we are going to find H, the height of the skyscraper.
We already know that part of the side length "H" is 1200 feet. We need to find the other part of "H". Let's label it h1.
Finding h1:
\(\begin{gathered} \tan 35=\frac{h1}{600} \\ h1=600\tan 35 \\ h1=420.12 \end{gathered}\)Thus,
\(\begin{gathered} H=h1+1200 \\ H=420.12+1200 \\ H=1620.12 \end{gathered}\)The height of the skyscraper is 1620.12 feet
Solve the following system using ALGEBRA methods and list the solutions:
5y ² + 24x-77 =0
14x² + 5y² +150x+119=0
Answers
Answer:
(x, y) ≈ (-2.17, ±sqrt(95)) or (x, y) ≈ (-1.03, ±sqrt(21))
Step-by-step explanation:
To solve this system of equations, we can use the method of substitution. We can start by isolating one of the variables in one of the equations and substituting it into the other equation. Let's solve for x in the first equation:
5y² + 24x - 77 = 0
24x = 77 - 5y²
x = (77 - 5y²)/24
Now we can substitute this expression for x into the second equation:
14x² + 5y² + 150x + 119 = 0
14((77-5y²)/24)² + 5y² + 150((77-5y²)/24) + 119 = 0
Simplifying this expression gives:
49y^4 - 5390y² - 108090y - 404271 = 0
We can solve for y using the quadratic formula:
y² = (5390 ± sqrt(5390² - 4(49)(-404271)))/(2(49))
y² = (5390 ± sqrt(16946804))/98
y² = (5390 ± 4118)/98
y² = 95 or y² = 21
Substituting each value of y into the expression we found for x earlier gives:
x = (77 - 5(±sqrt(95))²)/24 ≈ -2.17 or x = (77 - 5(±sqrt(21))²)/24 ≈ -1.03
Therefore, the solution to the system of equations is:
(x, y) ≈ (-2.17, ±sqrt(95)) or (x, y) ≈ (-1.03, ±sqrt(21))
two basketball teams play until one team wins two games. team a has probability 0.6 of winning each game while team b has probability of 0.4 of winning each game. if team a wins the first game what is the probability team b wins the series?
Answers
Answer:
0.16
Step-by-step explanation:
You want the probability that team b will win 2 games in a row, given that the probability of team a winning is 0.6, and the probability of team b winning is 0.4.
OutcomesAfter one win for team A, the series can have the possible outcomes ...
A – team a wins with probability 0.6
BA – team a wins with probability (0.4)(0.6) = 0.24
BB – team b wins with probability (0.4)(0.4) = 0.16
The probability of team b winning the series is 0.16.
__
Additional comment
The probability team a wins the series after winning the first game is 0.6 +0.24 = 0.84 (= 1 -0.16). At the beginning of the series, the probability b wins is 0.352, dropping dramatically after a wins the first game.
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The probability that Team B wins the series after Team A wins the first game is 0.4 or 40%.
What is probability?
Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.
To determine the probability that Team B wins the series after Team A wins the first game, we need to consider the different possible outcomes of the remaining games.
Since the series continues until one team wins two games, there are three possible scenarios:
Team A wins the next game (Team A wins the series)
Team B wins the next game, followed by Team A winning the third game (Series tied at 1-1)
Team B wins both the next and third games (Team B wins the series)
We'll calculate the probabilities of these scenarios and then determine the probability of Team B winning the series.
Scenario 1: Team A wins the next game (Team A wins the series):
The probability of Team A winning the next game is 0.6.
Scenario 2: Team B wins the next game, followed by Team A winning the third game (Series tied at 1-1):
The probability of Team B winning the next game is 0.4.
The probability of Team A winning the third game is 0.6.
To calculate the probability of this scenario, we multiply the individual probabilities:
Probability = 0.4 * 0.6 = 0.24
Scenario 3: Team B wins both the next and third games (Team B wins the series):
The probability of Team B winning the next game is 0.4.
The probability of Team B winning the third game is 0.4.
To calculate the probability of this scenario, we multiply the individual probabilities:
Probability = 0.4 * 0.4 = 0.16
To find the probability of Team B winning the series, we add the probabilities of Scenario 2 and Scenario 3 since both outcomes result in Team B winning the series:
Probability = 0.24 + 0.16 = 0.4
Therefore, the probability that Team B wins the series after Team A wins the first game is 0.4 or 40%.
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if a polynomial function is in factored form, what would be a good first step in order to determine the degree of the function?
Answers
To determine the degree of a polynomial function given in factored form, a good first step is to count the highest power of the variable in the factored expression.
In factored form, a polynomial function is expressed as the product of linear factors or irreducible quadratic factors.
Each factor represents a root or zero of the function.
The degree of a polynomial is determined by the highest power of the variable in the expression.
To find the degree of the function, examine each factor in the factored form.
For linear factors, the degree is 1 since the highest power of the variable is 1.
For irreducible quadratic factors, the degree is 2 since the highest power of the variable is 2.
By observing the highest power in the factored expression, you can determine the degree of the polynomial function.
If the highest power is 1, the polynomial has a degree of 1 (linear function). If the highest power is 2, the polynomial has a degree of 2 (quadratic function). And so on.
It's important to note that the degree of a polynomial corresponds to the highest power of the variable in the expression and not the number of factors.
The number of factors indicates the number of roots or zeros of the polynomial, but it doesn't determine the degree.
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# 12) Quadrilateral ABCD has the coordinates: A (-5, 2) B (-2, 6) C (3,5) D (0, 1)
a) Sketch the quadrilateral on graph paper
b) Write an equation in y = mx + b form for each of the sides
c) Determine which type of quadrilateral it is using the equations and your sketch to explain
Answers
The quadrilateral given is Parallelogram.
What are Quadrilaterals?Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
(a) The quadrilateral is sketched as shown in the graph below.
(b) We have to write the equation of four lines AB, BC, CD and AD in the form y = mx + b. m is slope and b is intercept along Y axis.
Coordinates of vertices are A(-5, 2), B(-2, 6), C(3, 5) and D(0,1).
Equation of line AB :
Slope = (6 - 2) / (-2 - -5) = 4/3
Equation in point slope form is
(y - 2) = 4/3(x - -5)
y - 2 = 4/3 x + 20/3
y = 4/3 x + 26/3
Equation of line BC :
Slope = (5 - 6) / (3 - -2) = -1/5
Equation in point slope form is,
(y - 6) = -1/5 (x - -2)
y - 6 = -1/5 x - 2/5
y = -1/5 x + 28/5
Equation of line CD :
Slope = (1 - 5) / (0 - 3) = -4/-3 = 4/3
Equation in point slope form is,
y - 5 = 4/3 (x - 3)
y - 5 = 4/3 x - 4
y = 4/3x + 1
Equation of line AD :
Slope = (1 - 2) / (0 - -5) = -1/5
Equation in point slope form is,
y - 1 = -1/5 (x - 0)
y - 1 = -1/5 x
y = -1/5 x + 1
(c) Opposite sides are having the same slope.
From the sketch, opposite sides are equal.
So quadrilateral is either parallelogram or rectangle.
But if the figure is rectangle, adjacent sides are perpendicular and therefore the product of their slope is -1.
But it is not the case here.
So it is parallelogram.
Hence the given figure is a parallelogram.
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Identify the relation that is a function.Day of the week to the dateProfessional golfers to their rankingsShoe size to a person's nameIncome to color of their car
Answers
Hello!
First of all, let's remember when a relation is also a function:
• To be a function, it must follow two rules:
,• All elements in the domain has a range.
,• Each element in the domain has only one range.
can anyone solve 84=4(1 - 4g) step by step?
Answers
Answer:
g= -5
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
84-(4*(1-4*g))=0
84 - 4 • (1 - 4g) = 0
3.1 Pull out like factors :
16g + 80 = 16 • (g + 5)
16 • (g + 5) = 0
4.1 Solve : 16 = 0
This equation has no solution.
A a non-zero constant never equals zero.
4.2 Solve : g+5 = 0
Subtract 5 from both sides of the equation :
g = -5
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Answer:
g = -5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define equation
84 = 4(1 - 4g)
Step 2: Solve for g
Distribute 4: 84 = 4 - 16gIsolate g term: 80 = -16gIsolate g: -5 = gRewrite: g = -5Step 3: Check
Plug in g into the original equation to verify it's a solution.
Substitute in g: 84 = 4(1 - 4(-5))Multiply: 84 = 4(1 + 20)Add: 84 = 4(21)Multiply: 84 = 84Here we see that 84 does indeed equal 84.
∴ g = -5 is a solution of the equation.
3/8=r+2/3 what is r=?
Answers
Answer:
\(\frac{-7}{24}\)=r
Step-by-step explanation:
3÷8=r+2÷3
\(\frac{3}{8}\)=r+\(\frac{2}{3}\)
\(\frac{3}{8}\)-\(\frac{2}{3}\)=r
(make the denominators same)(LCM of 8 and 3=24)
\(\frac{3}{8}\)(\(\frac{3}{3}\))+\(\frac{2}{3}\)(\(\frac{8}{8}\))=r
\(\frac{9}{24}\)-\(\frac{16}{24}\)=r
\(\frac{9-16}{24}\)=r
\(\frac{-7}{24}\)=r
What is mean, median and mode?
4 6 7 7 9 11 13 14 15
A. Mean = 9.56 Median = 11 Mode = 7
B. Mean = 9 Median = 86 Mode = 7
C. Mean = 9.56 Median = 9 Mode = 7
D. Mean = 10.75 Median = 9 Mode = 7
Answers
Answer: A. Mean = 9.56, Median = 11, Mode = 7
Step-by-step explanation:
The mean, median and the mode for the given data is 9.56, 9, and 7 respectively.
How to find the mean, median, and mode of the data?Given data below:
4, 6, 7, 7, 9, 11, 13, 14, 15.In order to find the mean, it can be calculated by dividing a sum of all the data points with the number of data points in the data set.
The formula is:
\(\bar{M}=\dfrac{\sum M}{N}\)
\(\bar{M}=\dfrac{4+6+7+7+9+11+13+14+15}{9}\)
\(\bar{M}=\dfrac{86}{9}\)
\(\bar{M}=9.56\)
Next, we will find the median.
In order to find the median, we got to place the numbers in value order and find the middle.
So,
\(\text{Median}=9\)
Lastly, we will find the mode.
To find the mode, order the numbers lowest to highest and see which number appears the most often.
So,
\(\text{Mode}=7\)
Thus, the mean, median and the mode for the given data is 9.56, 9, and 7 respectively.
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I need help Pleaseeeee WILL GIVE BRAINLIEST
Answers
Answer:
C.540 square cm
Step-by-step explanation:
The object is 6 times as big as the scale drawing. The area of the scaled object , to find the area of the object.. you have to multiply the area of the scaled object by the scale factor squared
15×6^2=15×36=540
The area of the object ia 540 square centimeters
Answer: c. 540
Step-by-step explanation:
Help me please
Solve the system algebraically using substitution.
Answers
Answer:
y = 5/3
x = 8/3
Steps:
y = x - 1
2x + y = 7
Substitute y = x-1
(2x + x - 1 = 7)
Simplify: 3x - 1 = 7
Isolate x: 3x - 1 = 7: x=8/3
Plug the valuse of x into the other equation (y = x- 1): y = 8/3 - 1
8/3 - 1 = 5/3
y = 5/3
y = 5/3, x = 8/3