let abcd be an arbitrary quadrilateral. show that the midpoints of the four sides are the vertices of a parallelogram.
Answers
The midpoints of the four sides of an arbitrary quadrilateral ABCD form a parallelogram.
A more detailed explanation of the answer.
To show that the midpoints of the four sides of an arbitrary quadrilateral ABCD form a parallelogram, follow these steps:
1. Label the midpoints of the four sides: Let M be the midpoint of side AB, N be the midpoint of side BC, P be the midpoint of side CD, and Q be the midpoint of side DA.
2. Draw segments connecting the midpoints: Connect the midpoints M, N, P, and Q with line segments MN, NP, PQ, and QM.
3. Use the midpoint theorem: The midpoint theorem states that if you connect two midpoints of a triangle, the resulting segment is parallel to the third side and half its length. Apply the midpoint theorem to triangles ABD and BCD separately:
- In triangle ABD, QM is parallel to BD, and QM = 1/2 BD (by the midpoint theorem).
- In triangle BCD, NP is parallel to BD, and NP = 1/2 BD (by the midpoint theorem).
4. Prove MN || PQ and QM || NP: Since QM and NP are both parallel to BD and have the same length (1/2 BD), they are parallel and equal in length. Therefore, QM || NP. Similarly, by applying the midpoint theorem to triangles ABC and ADC, you can prove that MN || PQ.
5. Conclude that MNPQ is a parallelogram: Since opposite sides of MNPQ (MN and PQ, QM and NP) are parallel and equal in length, MNPQ is a parallelogram.
Thus, the midpoints of the four sides of an arbitrary quadrilateral ABCD form a parallelogram.
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Related Questions
What is the Inverse of x^2 - 9, x >= -9, The Main thing I need Help with is the x >= -9
Answers
The inverse functiοn οf\(f(x) = x^2 - 9, x \ge -9\) is:
\(f^{(-1)(x)} = \±\sqrt{(x + 9)}, y \ge -3\)
What is the inverse οf the functiοn?a functiοn's reverse functiοn A functiοn called f reverses the actiοn οf f. If and οnly if f is bijective, the inverse οf f is true.
Tο find the inverse οf the functiοn \(f(x) = x^2 - 9, x \ge -9\), we need tο fοllοw these steps:
Replace f(x) with y: \(f(x) = x^2 - 9, x \ge -9\)
Swap the pοsitiοns οf x and y: \(x = y^2 - 9, y \ge -9\)
Sοlve fοr y:\(x + 9 = y^2, y = \±\sqrt{(x + 9)\)
Since the οriginal functiοn is defined οnly fοr x ≥ -9, we must restrict the dοmain οf the inverse tο y ≥ -3.
Therefore, the inverse function of \(f(x) = x^2 - 9, x \ge -9 is\):
\(f^(-1)(x) = \±\sqrt{(x + 9)}, y \ge -3\)
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Can someone please help on this I’ll give you brainliest
Answers
Answer:
SS of the graph is attached and for Standard form its y= -0.5x^2 - 1x + 7.5
Step-by-step explanation:
ANSWER QUICK PLSSS
A diver is 15 feet below the surface of the water 10 seconds after he entered the water and 90
feet below the surface after 40 seconds. What is the rate of change? *
(1 Point)
1.5 feet per second
4.5 feet per second
3.5 feet per second
2.5 feet per second
Answers
Answer:
2.5 feet per second.
Step-by-Explanation:
So we have
(10,15) (40,90)
Plug them in the slope-formula
y2-y1/x2-x1
90-15/40-10
75/30
2.5 feet per sec.
Solve for 2:
4x + 188
6x + 216°
Answers
Steps:
See attachment.
Description:
The first step is to simplify the equation step by step and to simplify an equation you can first multiplying the factors and use the exponent rules to remove the parentheses. After that you need to combine it a terms. Then you will get your answer.
For more steps and graph see the attachment.
Answer: =1890x+216
Hope this helps.
Answer:-14
Step-by-step explanation: -14
a paddle wheel on a boat is 4 feet in diameter. the fins along the outer edge travel at a speed of 1.3 feet per second. how long does it take the paddle wheel to complete 100 full revolutions ? round to the nearest second.
_ minutes and _ seconds.
Answers
Answer: To find out how long it takes the paddle wheel to complete 100 full revolutions, we need to calculate the circumference of the paddle wheel and divide that by the speed at which the fins along the outer edge are traveling.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle.
The radius of the paddle wheel is 2 feet (the diameter of 4 feet divided by 2), so the circumference is:
C = 2π * 2 = 8π feet
To find out how long it takes the paddle wheel to complete 100 full revolutions, we divide the number of feet traveled in one revolution (the circumference of 8π feet) by the speed at which the fins are traveling (1.3 feet per second):
100 * 8π feet / 1.3 feet per second = 615.38 seconds
Rounded to the nearest second, it takes approximately 615 seconds for the paddle wheel to complete 100 full revolutions.
the product of z and the complex number 5-6i is a real number. find two possible nonzero values of z.
Answers
To find the values of z that make the product with the complex number 5-6i a real number, we need to consider the imaginary part of the product.
The product of z and 5-6i can be written as:
z * (5 - 6i)
Expanding this expression, we get:
5z - 6zi
For the product to be a real number, the imaginary part (-6zi) must be equal to zero. This means that the coefficient of the imaginary unit i, which is -6z, must be zero.
Setting -6z = 0, we find:
z = 0
So, one possible nonzero value of z is 0.
However, since we are looking for nonzero values of z, we need to find another value that satisfies the condition.
Let's consider the equation for the imaginary part:
-6z = 0
Dividing both sides of the equation by -6, we have:
z = 0/(-6)
z = 0
Again, we find z = 0, which is not a nonzero value.
Therefore, there are no other nonzero values of z that make the product with the complex number 5-6i a real number. The only value that satisfies the condition is z = 0.
Calculate the mean, median, and mode for the set 7, 9, 8, 8, 10, 9, 8, 7, 8, 6, 9, 5, 6, 8, 9, 7, 7, 8, 10, 8 please answer asap
Answers
Step-by-step explanation:
Mean (Average):7.89474. Median (Middle):8. Mode (Most Common):8
Answer:
Mean= 7+9+8+8+10+9+8+7+8+6+9+5+6+8+9+7+7+8+10+8/20= 7.85
Mode= 8(the most repeated number)
Median= 7+8/2=7.5 (the two numbers in the middle divided 2)
To go to the dog beach, it costs $3 plus $2 per dog l. Which equation shows this situation, where x represents the number of dogs?
Answers
Answer:
the equation would look like x = 2x + 3
Step-by-step explanation:
Answer:
y=2x=3
Step-by-step explanation:
Cause then you'd only get one answer to study.
Now back to the
a collection of facts,
Numbers, measurements and things like that.
conclusion
estimate
data
Answers
A collection of information, such as numbers, measurements, or observations, is commonly referred to as data.
Data can be collected from a wide variety of sources, such as surveys, experiments, or observations, and can be analyzed to reveal patterns, trends, and relationships.
Data can be represented in many different ways, including tables, graphs, charts, or statistical summaries, and can be used to make informed decisions in a wide range of fields, including business, science, healthcare, and social sciences.
However, it is important to ensure that the data is accurate, reliable, and unbiased, and that appropriate statistical methods are used to analyze and interpret it.
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Full Question: What is a collection of information such as number measurement or observation called?
thianamccornell1 no one else
Answers
Answer:
Oh I see, that’s weird
Step-by-step explanation:
Maybe you have to wait a while or wait for somebody else to answer because that’s what happens to me sometimes
T/F If the equilibrium wage in the market for unskilled labor is $8.00 per hour, and the government sets a minimum wage at $7.50 per hour, unskilled workers will receive a pay cut of about 50 cents per hour.
Answers
The minimum wage set by the government at $7.50 per hour does not result in a pay cut for unskilled workers, as it is below the equilibrium wage of $8.00 per hour.
The wage rate remains unchanged, and the labor market remains in balance.
The statement is false.
False.
The equilibrium wage in the market for unskilled labor is $8.00 per hour, which means that the market naturally sets the wage rate at this level, based on the forces of supply and demand.
The government then sets a minimum wage at $7.50 per hour.
Since the minimum wage is below the equilibrium wage, it does not directly impact the wage rate for unskilled workers.
The equilibrium wage represents the point at which the supply of labor (the number of workers willing to work at a given wage) equals the demand for labor (the number of workers that employers are willing to hire at a given wage).
In this case, both workers and employers are satisfied with the $8.00 per hour wage, and the labor market is balanced.
The government sets a minimum wage below the equilibrium wage, it essentially sets a wage floor that is not binding. Employers are still willing to pay the equilibrium wage of $8.00 per hour, and workers are still willing to accept this wage.
The wage for unskilled workers remains at $8.00 per hour, and there is no pay cut of 50 cents per hour.
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Which lists all the multiples of 6 that are less than 20?
6, 9, 12, 15, 18
6, 12
6, 12, 18
6, 12, 18, 24
Answers
..................
Answer:
C
Step-by-step explanation
An easy way to figure is to see if all of the numbers in that group can be divided by 6.
In this first one, 9 and 15 are not divisible by 6.
In the second one 6, 12 are multiples ok 6 but there is one more.
In the last one 24 is over the 20 limit.
So, C is correct.
Omega House Family restaurant is midway between Forsyth Tech Community College
and the Dash baseball stadium. The coordinates of Forsyth Tech are (7, −5) and the
coordinates of the Dash baseball stadium are (−4, 3). What are the coordinates of the
Omega House?
Answers
The coordinates of Omega house is (3/2, 1)
Data;
Forsyth Tech = (7,-5)Stadium = (-4, 3)Midpoint of a LineTo find the coordinates of Omega house, we can use the formula of midpoint of a line since Omega house falls between Forsyth Tech and Stadium
\(x,y = (\frac{x_1+ x_2}{2} , \frac{y_1+y_2}{2})\)
We can substitute the values and solve for both x and y coordinates.
\(x = \frac{x_1+x_2}{2} \\x = \frac{7 + (-4)}{2} = \frac{3}{2}\)
The value of the y-coordinate is
\(y = \frac{-5+ 3}{2} = 1\)
The coordinates of Omega house is (3/2, 1)
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In a class of 29 students, 19 are female and 14 have an A in the class. There are 8 students who are male and do not have an A in the class. What is t
Answers
If In a class of 29 students, 19 are female and 14 have an A in the class then 2 male students have an A in the class.
We can calculate the number of students who are male and have an A in the class by subtracting the given values from the total number of students.
Total students = 29
Female students = 19
Male students = Total students - Female students = 29 - 19 = 10
Students with an A = 14
Male students without an A = 8
To calculate the number of male students with an A, we subtract the number of male students without an A from the total number of male students.
Male students with an A = Male students - Male students without an A = 10 - 8 = 2
Therefore, there are 2 male students who have an A in the class.
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A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this population prefers the color red. If 14 buyers are randomly selected, what is the probability that exactly 2 buyers would prefer red
Answers
Answer:
The probability that exactly 2 buyers would prefer red car is 0.0317.
Step-by-step explanation:
Let the random variable X represent the number of buyers would prefer red car.
The probability of the random variable X is, p = 0.40.
A random sample of n = 14 buyers are selected.
The event of a buyer preferring a red car is independent of the other buyers.
The random variable X thus follows a Binomial distribution with parameters n = 14 and p = 0.40.
The probability mass function of X is:
\(P(X=x)={14\choose x}(0.40)^{x}(1-0.40)^{14-x};\ x=0,1,2,3...\)
Compute the probability that exactly 2 buyers would prefer red car as follows:
\(P(X=2)={14\choose 2}(0.40)^{2}(1-0.40)^{14-2}\)
\(=91\times 0.16\times 0.0021768\\=0.031694208\\\approx 0.0317\)
Thus, the probability that exactly 2 buyers would prefer red car is 0.0317.
What is the area of the triangle?
Answers
Answer:
20
Step-by-step explanation:
Given f(x) = x3+7xy-3y+y2 the saddle point
is (?,?), and the local minimum is (?, ?). Round your answer to 4
decimal places.
Answers
Therefore, the saddle point is approximately (-0.2852, 0.9953), and the local minimum is approximately (0.9649, 2.0047).
To find the saddle point and local minimum of the function\(f(x) = x^3 + 7xy - 3y + y^2\), we need to calculate the partial derivatives with respect to x and y, and then find the critical points by setting these derivatives equal to zero.
The partial derivative with respect to x (f_x) is:
\(f_x = 3x^2 + 7y\)
The partial derivative with respect to y (f_y) is:
f_y = 7x - 3 + 2y
Setting f_x = 0 and f_y = 0, we can solve for the critical points:
From \(f_x = 3x^2 + 7y = 0:\)
\(3x^2 = -7y\\x^2 = -7/3 * y\)
From f_y = 7x - 3 + 2y = 0:
7x = 3 - 2y
x = (3 - 2y)/7
Substituting this value of x into\(x^2 = -7/3 * y\), we have:
\((3 - 2y)^2 / 49 = -7/3 * y\)
Expanding and simplifying the equation, we get:
\(9 - 12y + 4y^2 = -49y/3\)
Multiplying both sides by 3, we have:
\(27 - 36y + 12y^2 = -49y\)
Rearranging terms, we obtain:
\(12y^2 - 13y + 27 = 0\)
Solving this quadratic equation, we find two possible values for y: y ≈ 0.9953 and y ≈ 2.0047.
Substituting these values back into x = (3 - 2y)/7, we can determine the corresponding x-values.
For y ≈ 0.9953, x ≈ -0.2852.
For y ≈ 2.0047, x ≈ 0.9649.
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Add and simplify your answer. Show your work 1 / 8 + 1 / 8
Answers
Answer:
1/4.
Step-by-step explanation:
1/8 plus 1/8 is 2/8. This is because if we add the numerators it is 2, and therefore it is 2/8. This simplifies to 1/4 if you divide the numerator and denominator by 2. Hope this helps!
Answer: 1/4
Step-by-step explanation: 1/8 + 1/8= 2/8 and if you simplify that it would be 1/4 sorry if this doesn't help
Evaluate the distance between the following pair of integers -7 and 41
Answers
Answer:
\( 41 - ( - 7) = 41 + 7 = 48\)
What digit is in the ten thousand place 7,612,045
Answers
Answer:
the digit in the ten thousandths place is 1
Step-by-step explanation:
Answer:
1 is the digit that is in the ten thousandth place
Step-by-step explanation:
can i get brainlisest
1) Each student has 2 shoes. How many shoes are there for 8 students?
Answers
Answer:
16 shoes
Step-by-step explanation: If every student has 2 shoes and you want to know how many shoes for 8 students. Then you do 8 times 2 which is 16 shoes for 8 students. Hope this helps
Solving Two Step Equations
State the properties you used to solve.
3(x + 4) - 5 = 2x + 4
Answers
Answer:
Step-by-step explanation:
3(x + 4) - 5 = 2x + 4
solve for x
x = -3
what is the product of the square root of 16 and the square of 9?
Answers
Answer:
324
Step-by-step explanation:
√16=49^2=814×81=324Answer:
324
Step-by-step explanation:
√16*9²
4*81
324
Plz mark as brainliest
ASSIGNMENT: WS 4 - Factoring using DOTS and PST
What are the dimensions of a rectangle whose area is represented by the expression 4932 – 16?
49x - 16
LENGTH:?
WIDTH:?
Answers
What are the dimensions of a rectangle whose area is represented by the expression 4932 – 16?
49x² - 16
LENGTH: 3
WIDTH: 11
Hope this helps ~
Find the value of x using the diagram below. Will give Brainly.
Answers
Answer:
120
Step-by-step explanation:
can you help me please
Answers
Dennis has a credit card with an APR of 10. 14% and a billing cycle of 30 days. The following table shows his transactions with that credit card in the month of November. Date Amount ($) Transaction 11/1 517. 87 Beginning balance 11/9 31. 63 Purchase 11/23 64. 10 Purchase 11/26 65. 75 Payment If the finance charge for November is $3. 82, which method of calculating the finance charge does Dennis’s credit card company use? a. Adjusted balance method b. Previous balance method c. Daily balance method d. There is not enough information to determine which method was used Please select the best answer from the choices provided A B C D.
Answers
The method employed by the credit card company is the adjusted balance method, the correct option is A.
What is the adjusted balance method?The adjusted balance method is a financial accounting method that bases finance charges on the amounts owed at the end of the current billing cycle after credits and payments post to the account.
Though the payment is not given but from the beginning balance and the purchases, Dennis owes a certain amount of money.
The finance charge is based on the amount owed by Dennis.
Thus, the method employed by the credit card company is the adjusted balance method.
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What is the problem and to what extent is it a problem? What information leads you to your conclusion?
These are excessive and poor starving people in Ireland. Due to the lack of work women and their children are having to resort to being baggers in the streets, Swift describe seeing mothers and their children begging in the streets
Answers
The problem in Ireland is the widespread poverty and hunger affecting women and children, forcing them to beg on the streets due to the lack of employment opportunities.
This is a significant problem that highlights the dire economic conditions and social inequality in the country. Jonathan Swift's description of seeing mothers and children begging in the streets provides evidence of the severity of the situation.
The fact that women and children have to resort to begging for survival indicates that the existing social safety net is inadequate, and urgent action is needed to address this issue.
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A triangle has angle measurements of 44 degrees,87 degrees, and 49 degrees. What kind of triangle is it? acute,right, and obtuse.
Answers
*PLEASE ANSWER I DONT GET IT*
What is a deduction?
a.) An allowance you can use for tax purposes.
b.) Money that you have to pay for Medicare.
c.) Part of your salary.
Answers
Answer:
A
Step-by-step explanation:
im pretty sure im right
Answer:
c.) Part of your salary.
Step-by-step explanation: