Prove that the quadrilateral with vertices (2,5) (4,8) (7,6) and (5,3) is a rectangel
Answers
Answer: Line slopes:
m1= 3/2 defined by points (5,3) and (7,6)
m2= -2/3 defined by points (7,6) and (4,8)
m3 = 3/2 defined by points (4,8) and (2,5)
m4 = -2/3 defined by points (2,5) and (5,3)
All comply the orthogonal slopes rule (90º)
Step-by-step explanation:
As those 4 point define a polygon, to check is that polygon is a rectangle, you need to compare the slopes of the lines defined by the 4 points and check that accomplish the following rule:
m1 = -(1/m2). this shows that the slopes are intersected in 90º angle.
Final answer:
By calculating the dot products of the direction vectors for adjacent sides, all of which are zero, and checking the distances of opposite sides, which are equal, we prove that the given quadrilateral is a rectangle.
Explanation:
To prove that a quadrilateral with given vertices is a rectangle, we must show that the quadrilateral has four right angles and opposite sides are equal. A right angle exists between two sides if the dot product of their direction vectors is zero, as this indicates perpendicularity. Equal length of opposite sides can be shown by the distance formula. We are given the vertices of the quadrilateral: (2,5), (4,8), (7,6), and (5,3).
Calculate the direction vectors of adjacent sides:
AB: (4-2, 8-5) = (2,3)
BC: (7-4, 6-8) = (3,-2)
CD: (7-5, 6-3) = (2,3)
DA: (2-5, 5-3) = (-3,2)
Check the dot products of the direction vectors of adjacent sides to confirm right angles:
AB · BC = (2)(3) + (3)(-2) = 6 - 6 = 0
BC · CD = (3)(2) + (-2)(3) = 6 - 6 = 0
CD · DA = (2)(-3) + (3)(2) = -6 + 6 = 0
DA · AB = (-3)(2) + (2)(3) = -6 + 6 = 0
Use the distance formula to confirm equal lengths of opposite sides:
AB = √((4-2)² + (8-5)²) = √(13)
CD = √((7-5)² + (6-3)²) = √(13)
BC = √((7-4)² + (6-8)²) = √(13)
DA = √((2-5)² + (5-3)²) = √(13)
Since all adjacent sides are perpendicular and opposite sides are of equal length, the quadrilateral is a rectangle.
Related Questions
TEN CARDS NUMBERED 1-10 AR HEIRE MIXED TOGETHER AND THEN ONE CARD IS DRAWN WHAT IS PROBABILITY YOU WILL DRAW A CARD GREATER THAN 3
Answers
Answer:
To calculate probability you have to understand that P = favorable cases / possible cases. So, your probability is 7/10 (Consider all the cards, have the same probability when you pick one).
Step-by-step explanation:
Which are your favorables cases
card 4, card 5, card 6, card 7, card 8, card 9, card 10
Which are you possible cases
The 10 cards.
How many solutions does the equation have?
|g| − 8 = -3
NO SOLUTION, ONE SOLUTION, OR TWO SOLUTIONS
( PICK WHICH ONE THX)
Answers
Answer:
two solutions
Step-by-step explanation:
it could be 5 or -5
PLEASE HELP!!!!
-0.5 1/2 0.7 -4/4 from least to greatest
Answers
Step-by-step explanation:
Converting all the numbers to decimals,
1) -0.5
2) 1/2 = 0.5
3) 0.7
4) -4/4 = -1
We see that order of numbers from least to greatest is -1 < -0.5 < 0.5 < 0.7
Please mark Brainliest if this helps!
what is 2 1/2, 2.4, 2.35, 21/8 listed from greatest to least.
Answers
Answer: 21/8, 2 1/2, 2.4, 2.35
Step-by-step explanation:
21/8= 2.625
2 1/2= 2.5
2.4
2.35
look at the subtraction expression below. 3.0 — (—1.5) which number line models this expression?
Answers
Answer:
b
Step-by-step explanation:
Answer:
B.Did this help?If so, please click the five stars, and hit that pink heart!what is 0.9 repeating as a rational number?
Answers
Answer:
Step-by-step explanation:
https://brainly.com/question/13228520
Hope this helps!
48 miles per hour how many miles does it take to travel in 5 hours and 45 minutes
Answers
Answer: 276 miles in 5 hours and 45 minutes
5 x 48 = 240
240 + 36 = 276
Answer:
You would be able to travel 276 miles
Mark as brainiest
if its 11:45 in 2 1/2 hours what will it be
Answers
Answer:
Step-by-step explanation:
11:45 + 1 hour = 12:45
12:45 + 1 hour = 1:45
1:45 + 30 minutes = 2:15
Alaina colors 20% of the total shapes on her paper. She colors 10 shapes. Enter the number of shapes on Alaina's paper.
Answers
Answer:
50
Step-by-step explan
20% = 10
100% = 10 : 20 * 100
100% = 50
In one season,Kim ran 18 races. This was four fewer races than twice the number of races Kelly ran. How many races did kelly run?
Answers
Answer:
11 races
Step-by-step explanation:
The reason being that 18 is 4 less than twice the number Kelly ran. 18+4=2x when x equals the races Kelly ran. so, 18+4=22 so 22=2x. if you divide each side by 2, you get 11=x. so, kelly ran 11 races
Answer:
44
Step-by-step explanation:
18+4=22 time 2 =44
A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in field position after the 3 days.
Answers
To determine the football team's change in field position using a number line, one would sequentially move 5 units left for each loss of 5 yards over 3 plays, resulting in a total change of -15 yards.
To find the football team's change in field position after the 3 plays, you can use a number line to represent the yards on the field.
If we consider the team's starting point as zero on the number line, each loss of 5 yards will be represented as moving 5 units to the left (into the negative side) from that starting point. Here's how you would calculate it step by step:
Mark the starting point at zero on the number line.
Since the team lost 5 yards on the first play, move 5 units to the left and mark that new point, which represents -5 yards.
Repeat the process for the second play, moving another 5 units to the left from the -5 mark to reach -10 yards.
Finally, for the third play, move yet another 5 units to the left to end up at -15 yards.
Therefore, after 3 plays with each losing 5 yards, the team's field position has changed by -15 yards.
what do I do here cause I'm confused :/
Answers
Answer:you do 15 divided by 8
Step-by-step explanation:
find the zero of the linear function f(x)=-2x+5
Answers
Which equation could be used to create the data show in the table?
Answers
Answer:
Step-by-step explanation:
y = 4x + 1
We can see that for each value of x substituted into this equation will give us a value for y .
For example , if we take x to be 4 , and put the value in this equation we get 4(4) + 1 = y
We get y = 17
Which two operations are needed to write the expression that represents "eight more than the product of a number and two"?
multiplication and subtraction
division and subtraction
multiplication and addition
division and addition
Answers
For this case we must represent the following expression algebraically:
"eight more than the product of a number and two"
Let "x" be the variable that represents the unknown number
We have to:
the product of a number and two is represented as: [tex]2x[/tex]
Then, the full expression will be:
[tex]2x + 8[/tex]
Thus, we use multiplication and addition.
ANswer:
Option C
Answer: multiplication and addition
Step-by-step explanation:
In mathematics we use addition(+) operation to show "sum", subtraction (-) to show "difference" , multiplication (×) operation to show "product" and divide (÷) to show "quotient".
Given mathematical statement : eight more than the product of a number and two
Here, we use addition(+) operation to show "more than" and multiplication (×) operation to show "product" .
Hence, the two operations are needed to write the expression that represents are : multiplication and addition
During the past 13 days, Troy drove 546 miles. He drove the same number of miles each day. How many miles did Troy drive each day?
Answers
Answer:
42
Step-by-step explanation:
if you divide 546 with 13 it will give you 42 mostly because 546 is the total of miles that he drove so if you dive by how many days he has been driving you will get your answer.
Troy drove 546 miles over 13 days, resulting in an average of 42 miles driven each day after dividing the total miles by the number of days.
To find out how many miles Troy drove each day, we need to divide the total number of miles driven by the number of days. Troy drove a total of 546 miles over the course of 13 days.
Divide the total miles (546) by the number of days (13).
The calculation is:
546 miles / 13 days = 42 miles per day.
Therefore, Troy drove 42 miles each day.
Toby went to the arcade 2 times.He earned 5,150 points each time.What is the biggest prize toby can get ?
Answers
Find the nth term of this number sequence
18, 16, 14, 12,...
Pls help
Answers
Answer:
20 - 2n
Step-by-step explanation:
The sequence is arithmetic since the difference between consecutive terms is constant, that is
d = 16 - 18 = 14 - 16 = 12 - 14 = - 2
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 18 and d = - 2, thus
[tex]a_{n}[/tex] = 18 - 2(n - 1) = 18 - 2n + 2 = 20 - 2n
[tex]a_{n}[/tex] = 20 - 2n
If we know that [tex]x_{1} = 18[/tex] and [tex]r = -2[/tex], then the n-th term of the number sequence is [tex]f(n) = 18 -2\cdot (n-1)[/tex].
This sequence is an example of an arithmetic sequence, since each consecutive pair of elements has one and only one difference, that is to say:
[tex]r = x_{i+1}-x_{i}[/tex], [tex]\forall\,i\in \mathbb{N}[/tex] (1)
The expression for any arithmetic sequence is described by the following formula:
[tex]f(n) = x_{1} + r\cdot (n-1)[/tex], [tex]n \ge 1[/tex] (2)
Where:
[tex]x_{1}[/tex] - First term of the sequence.[tex]r[/tex] - Arithmetical difference.[tex]i[/tex] - Identification for the element.If we know that [tex]x_{1} = 18[/tex] and [tex]r = -2[/tex], then the n-th term of the number sequence is [tex]f(n) = 18 -2\cdot (n-1)[/tex].
We kindly invite to check this question on number sequences: https://brainly.com/question/7043242
Gary said that a clockwise rotation of 90 followed by a translation 2 units to the right will make the angles coincide. What was Gary's mistake?
A. Gary did not make a mistake.
B. The translation is correct, but the rotation should have been 180.
C. The rotation is correct, but the translation should have been 2 units up.
D. The transformation should have been a reflection across the line x = 2.
Answers
Answer:
B. The translation is correct, but the rotation should have been 180°.
Step-by-step explanation:
A 90° - clockwise rotation would only turn the angle sideways.
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
The Correct Option is
Option B
The translation is correct, but the rotation should have been 180°.
Explanation
When Ray HI ,and GH, is rotated by an Angle of 180°, it will be ray HI and HG, in Opposite direction originating from same point H.
Now, when we shift this angle by 2 units ,the Angle will coincide with the Angle given in the Image.
in welcome to rise of the knights in which of these words from paragraph 3 has a neutral connotation
a. elaborate
b. engaging
c.multilevel
d.suspenseful
Answers
Answer: multilevel.
Multilevel has a neutral meaning in Welcome to Rise of the Knights.
A multilevel building is defined as one that has upwards of one level, such as various diagonal lines or surfaces at varying heights. Del Grosso lectured in what looked to be a traditional lecture hall, complete with long curving multileveled rows of permanent seats.Learn more:https://brainly.com/question/285672?referrer=searchResults
you read 16 pages in 20 minutes and your friends read 25 pages in 30 minutes who reads faster
Answers
Answer:
You read faster because in 20 minutes you read 16 pages but your friends had 30 minutes they had more time that's why they read more pages not because they read fast
You: 48pg/1hr 0.8pg/1min
Friend: 50pg/1hr 0.83pg/1min
3(9+a) = 54 I need answer
Answers
3(9+a)=54
3×9 + 3×a =54
27 + 3a = 54
3a - 27 = 54 -27 = 27
3a÷ 3 = 27÷ 3= 9
a = 9
Happy to help
Answer:
9
Step-by-step explanation:
i did 54 divided by 3 and got 18 so i know 9+9=18
18 times 3 =54
5/6 x= 15 solve for x
Answers
Answer:
X=18
Step-by-step explanation:
Multiply the 6 and the 15= 90
Then left with 5x so then divide 90 and 5= 18
Left with X= 18
The value of x in the given equation is x = 18.
Given is an equation 5x/6 = 15, we need to find the value of x,
To solve for x, you need to isolate x on one side of the equation.
Here's how you can do it step by step:
Start with the equation: 5/6 x = 15
To isolate x, you need to get rid of the fraction on the left side. Since the fraction has a denominator of 6, you can multiply both sides of the equation by 6 to eliminate it:
(6) × (5/6 x) = (6) × 15
The 6 on the left side cancels out the denominator 6, leaving:
5x = 90
Now, to find the value of x, you need to get x by itself on one side. Since 5x means 5 times x, you can undo this by dividing both sides by 5:
5x / 5 = 90 / 5
This simplifies to:
x = 18
So, the value of x is 18.
Learn more about Equations click;
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What is the equation o
f a line with a slope of –2 that passes through the point (6, 8)?
Answers
Answer:
y - 8 = -2(x - 6)
y - 8 = -2x + 12
y = -2x + 20
write a phrase to represent each algebraic expression
2x-9
2(x-9)
Answers
Answer:
See below.
Step-by-step explanation:
2x - 9: Nine less than 2 times a number.
2(x - 9) Two times some number less than nine.
A poll reported that 66% of adults were satisfied with the job the major airlines were doing. Suppose 20 adults are selected at random and the number who are satisfied is recorded.
The probability that exactly 12 are satisfied with the airlines is
Answers
The problem involves calculating a binomial probability for 12 out of 20 adults being satisfied with airlines, given a satisfaction rate of 66%. This uses the formula for Binomial Probability: P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)).
Explanation:The question involves using Binomial Probability in statistics. Here, the experiment is repeated 20 times (20 adults are selected), each trial is independent (one adult's answer doesn't affect another's), there are two possible outcomes (satisfied or unsatisfied), and the probability of success (being satisfied) is constant (66%).
To calculate the probability of exactly 12 adults being satisfied, we use the formula for Binomial Probability:
P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
Where:
C(n, k) is the number of combinations of n items taken k at a time.p is the probability of success (66% or 0.66 in this case).n is the number of trials (20 adults).k is the number of successes we're interested in (12 adults being satisfied).By subbing in these values, we can calculate the desired outcome.
Learn more about Binomial Probability here:https://brainly.com/question/39666605
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What’s The Answer?
I don’t seem to understand... can you guys help ??
Answers
Answer:
-7y
Step-by-step explanation:
It's just -7y because you have to put like terms together, so 3x+(-3x) = 0
PLEASEEE HELP THANK YOU!!
Answers
Answer:
6i[tex]\sqrt{21}[/tex]
Step-by-step explanation:
Note that [tex]\sqrt{-1}[/tex] = i
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radical, that is
[tex]\sqrt{-84}[/tex]
= [tex]\sqrt{4(21)(-1)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{21}[/tex] × [tex]\sqrt{-1}[/tex]
= 2 × [tex]\sqrt{21}[/tex] × i
= 2i[tex]\sqrt{21}[/tex]
Hence
3[tex]\sqrt{-84}[/tex]
= 3 × 2i[tex]\sqrt{21}[/tex]
= 6i[tex]\sqrt{21}[/tex]
A. X^4-2x^2+5x+6
B. X^3-2x^2-5x+6
C. X^3-2x^2+5x+6
D. -X^4-2x^2+5x+6
Answers
Answer:
B
Step-by-step explanation:
x^3-2x^2-5x+6
Answer:
its b
Step-by-step explanation:
Match each ratio with it’s simplest form.
Answers
Second is 3:1
Third is 2:3
Forth is 1:3
Fifth is 9:7
Last is 6:7
Step-by-step explanation:
We need to write the following ratios with its simplest form.
1. [tex]\dfrac{21}{28}[/tex]
Factors of 21 = 3, 7
Factors of 28 = 2, 7, 2
[tex]\dfrac{21}{28}=\dfrac{3}{4}[/tex]
2. [tex]\dfrac{96}{32}[/tex]
Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 32 = 1, 2, 4, 8, 16, 32
[tex]\dfrac{96}{32}=\dfrac{3}{1}[/tex]
3. [tex]\dfrac{22}{33}[/tex]
Factors of 22 = 1, 2, 11, 22
Factors of 33 = 1, 3, 11, 33
[tex]\dfrac{22}{33}=\dfrac{2}{3}[/tex]
4. [tex]\dfrac{12}{36}[/tex]
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
[tex]\dfrac{12}{36}=\dfrac{1}{3}[/tex]
5. [tex]\dfrac{72}{56}[/tex]
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
[tex]\dfrac{72}{56}=\dfrac{9}{7}[/tex]
6. [tex]\dfrac{54}{63}[/tex]
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
Factors of 63 = 1, 3, 7, 9, 21, 63
[tex]\dfrac{54}{63}=\dfrac{6}{7}[/tex]
Hence, this is the required solution.