Three of the vertices of quadrilateral MARY are M (-3,1), A(3,3), and R(5,7). Find the
coordinates of Y, such that, quadrilateral MARY is a parallelogram.
Use coordinate geometry to prove that MARY is a parallelogram.
Answers
9514 1404 393
Answer:
Y = (-1, 5)
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, so have the same midpoint. That is ...
(M +R)/2 = (A +Y)/2
Y = M + R - A . . . . . . multiply by 2 and subtract A
Y = (-3, 1) +(5, 7) -(3, 3) = (-3 +5 -3, 1 +7, -3) . . . . . substitute point coordinates
Y = (-1, 5)
Coordinate geometry was used to find Y that makes MARY a parallelogram. The fact that there is a solution is proof enough that MARY is a parallelogram.
_____
Your teacher may expect the "proof" to be either or both of ...
showing opposite sides have the same slopeshowing opposite line segments have the same lengthGiven the method used above, both of these are unnecessary. However, in the interest of completeness, we will demonstrate.
Slope and Length of MA
slope = (3 -1)/(3 -(-3)) = 2/6 = 1/3
length = √(2²+6²) = √40
Slope and Length of AR
slope = (7 -3)/(5 -3) = 4/2 = 2
length = √(4² +2²) = √20
Slope and Length of RY
slope = (5 -7)/(-1 -5) = -2/-6 = 1/3 . . . . same as opposite side MA
length = √((-2)²+(-6)²) = √40 . . . . . . . same as opposite side MA
Slope and Length of YM
slope = (1 -5)/(-3 -(-1)) = -4/-2 = 2 . . . . same as opposite side AR
length = √((-4)² +(-2)²) = √20 . . . . . . same as opposite side AR
Opposite sides have the same slopes, so the figure is a parallelogram.
Opposite sides have the same lengths, so the figure is a parallelogram.
Related Questions
A rainwater was 2/3 full of water. After 60 liters of water were used from the barrel, it was 5/12 full. How much water does the barrel hold when full?
Answers
Answer: 240 liters
=======================================================
Work Shown:
x = capacity of barrel in liters
This value of x is some positive real number. It represents the most amount of water the barrel can hold.
The problem states that the barrel is 2/3 full to start with. This means, we start off with (2/3)x liters of water. Then we subtract off 60 of them to get to 5/12 full, meaning we have (5/12)x liters left.
We can form this equation
(2/3)x - 60 = (5/12)x
Multiply both sides by 12 to clear out the fractions
(2/3)x - 60 = (5/12)x
12*( (2/3)x - 60 ) = 12*(5/12)x
12*(2/3)x - 12*60 = 12*(5/12)x
8x - 720 = 5x
From here we solve for x
8x - 5x = 720
3x = 720
x = 720/3
x = 240
The barrel's full capacity is 240 liters
--------------------------
Check:
2/3 of 240 = (2/3)*240 = 160
The barrel starts off with 160 liters of water inside.
We then use 60 of them to be left with 160-60 = 100 liters
Note how 100/240 = (5*20)/(12*20) = 5/12, showing that 100 liters out of 240 total reduces to the fraction 5/12. In other words, when we say "5/12 full" we mean 100 liters full. This helps confirm we have the right answer.
Help!! Find the indicated angle measure. Show your work.
Answers
Answer:
m∠NPM = 101
Step-by-step explanation:
Since LM is a straight line, Angle LPM and Angle NPM have to equal 180 degrees (they are supplementary), so we make the equation:
180-79=measure of angle NPM
m∠NPM = 101
Answer:
<NPM = 101°
Step-by-step explanation:
<NPM = 180° - <LPN ( because LPM is a straight line and it should measure 180°)
<NPM = 180° - 79°
<NPM = 101°
Elise says, "If you subtract 18 from my number and multiply the difference by - 3, the result is
- 33." What is Elise's number?
Answers
Elise's number is 29.
If you think of multiplying a value by -3 to get -33, it would obviously be 11.
So in this case, you would want to add 18 to 11 to get Elise's number, which is 29. Subtracting 18 from 29 would get you back to the value of 11, which you can then multiply it by -3 again to get -33.
angle A and angle B are vertical angles. If m_A = (7x – 6) and m B = (8x – 27), then find the measure of angle b
Answers
Answer:
A = B; 7x - 6° = 8x -27°; x = 21°. So B = 8·21° - 27° = 141°
Step-by-step explanation:
hiii please help i’ll give brainliest if
you give a correct answer and maybe explain thankss
Answers
Answer:
4:3
16:12
Step-by-step explanation:
Both of those numbers can be multiplied or divided to equal 8:6
I need help like NOW!
Answers
Answer:
5t
Step-by-step explanation:
kinda self explanatory
dividing it, adding it, and subtracting it wouldnt make sense for the equation youre trying to solve.
Answer:
5t
Step-by-step explanation:
The data for three different relay race runners is represented below. Use the representations of each runner to determine which runner starts running closest to the starting line.
Answers
Answer:
It's C or the third option.
Step-by-step explanation: Edge 2021
Answer:
C.
Explaination:
just did on edge 2021
PLEASE HELP WILL GIVE BRAILEST TO CORRECT ANSWER!!!!
Marcus states that the polynomial expression 3x3 – 4x2y + y3 + 2 is in standard form. Ariel states that it should be y3 – 4x2y + 3x3 +2. Explain which student is correct and why.
Answers
Answer:
opps type miss
Step-by-step explanation:
miss type
PLS HALP-
Liam placed 24 patio pavers as shown below.
A rectangular array of four pavers wide by six pavers long. The length of the total rectangle is sixty-three and two-tenths inches.
What is the length of a single patio paver?
A. 18.2 in.
B. 15.8 in.
C. 10.53 in.
D. 2.63 in.
Answers
Answer:
the correct answer is B
Step-by-step explanation:
i got this correct on my test UWU
please helppp i’m on a time limit
Answers
Answer:
It is 3 because it is both in red and blue and that is the only section that shows it’s in both
Answer:3
The area of the triangle is 119 square feet. Find the base and the height.
(x + 3) ft.
(x + 6) ft.
Answers
Answer:
14 and 17
Step-by-step explanation:
(X+3)(x+6)0.5=119
x^2+9x+18=238
x=11
11+3=14
11+6=17
Find ,giving your answer correct to 3 significant fig where necessary a. 60%of 850
Answers
Answer:
60%of 850
60×850÷100
=510
PLEASE HELP HURRY LOOK AT IMAGE!!!!
Answers
NEED HELP FAST PLEASE.
Please answer all these.
AND BECAUSE YOUR GONNA ANSWER ALL OF THEN IMA GIVE YOU 50 POINT
Answers
Answer:
60
Step-by-step explanation:
Has anyone done this before ?
Answers
no i haven't
sorryyyyyyy
the temperature is 50 degrees Fahrenheit the temperature will decrease 4 degrees each hour let H be the number of hours when will it be 32 degrees
write a inequality
Answers
Answer:
LGFJDbvoRUWSVBIeLas
Step-by-step explanation:
Select the correct answer.
Simplify the following expression.
1
OA
OB. 5(-3)
О с.
53
OD.
Answers
Answer:
B) 5(-3) either way its telling you to multiply 5 by -3
The simplifying form of the expression 5⁻³ is,
⇒ 1 / 5³
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression for simplifying is,
⇒ 5 ⁻³
Now,
By rule of exponent;
⇒ a⁻ⁿ = 1 / aⁿ
Hence, We can formulate simplifying form of the expression 5⁻³ is,
⇒ 5 ⁻³
⇒ 1 / 5³
Thus, The simplifying form of the expression 5⁻³ is,
⇒ 1 / 5³
Learn more about the mathematical expression visit:
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BRAINLIEST IF CORRECT
A state offers two lottery games, Winone and PlayBall. Both games cost $2 per ticket.
• In Winone, the player picks a single letter from A to J and a single digit from 0 to 9. If both the letter and the digit match the letter and the
digit picked on that day, the player wins $150.
• In PlayBall, the player picks a single letter from A to T and a single digit from 0 to 9. If both the letter and the digit match the letter and the
digit picked on that day, the player wins $280.
If the prize for WinOne were increased to $200 for matching both the letter and the digit, what would the expected value be?
ОА.
-$0.80
OB. $0.65
C. $0
OD. $0.80
Answers
digit picked on that day, the player wins $280, changed to 250.
Game cost = 1 dollar
There are 20 alphabets and 9 digits
No of ways to select at random =
No of ways to win = 1
So probability to win =
Since he has to pay 1 dollar whether he wins or not
PDF of X amount net won or net value would be
X -1 249 Total
p 1
xp -
Expected value = 0.38889
A sales person at a Jewwlry store earns 5% commission each week. last week ,Heidi sold $640 worth of jewelry. Home much did she make in commission? How much did the jewellery store make from her sale?
Answers
Answer:
224
Step-by-step explanation:
5 percent of 640=32
32 times by 7=224
what is the solution for this
Answers
Answer:
(-2,4)
Step-by-step explanation:
Since this is a system of equations, just look where the two lines intersect.
In this case, the intersecting pair is: (-2, 4)
In a system of two linear equations, the lines represented by each equation have the same slope. Which could be the total number of solutions to the system of equation
Answers
Answer:
Please see explanation
Step-by-step explanation:
A system of linear equations in two variables represents two lines on graph.
When both the lines have same slope, there can be two cases
Same slope with different y-interceptsWhen two lines have same slope and different y-intercepts, that means that both lines are parallel and parallel lines have no solution.
Same slope with same y-interceptsWhen the slope of both lines is same and the y-intercept is also same, this means that both the equations refer to the same line. This means that the system has infinite number of solutions.
What is the value of x in the diagram below?
49
14
2
Answers
The value of x in the diagram is 7 (D) because 2 * 7 = 14 and 7 * 7 = 49.
The value of x in the given diagram will be 7.
What are similar triangles?Similar triangle are those which have two pairs of interior corresponding angles are equal.
We have,
Two triangles as shown in the given figure,
Now,
Both the given triangles have 90° corresponding angles and also the opposite angle of 90° of both triangles is equal.
So,
Using triangle similarity rule,
i.e.
Sides are in equal proportion,
i.e.
[tex]\frac{49}{x} =\frac{14}{2}[/tex]
⇒
14x = 49 × 2
14x = 98
[tex]x=\frac{98}{14}[/tex]
x = 7
Hence, we can say that the value of x in the given diagram will be 7.
To know more about similar triangle click here
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1.) Ivan made a scale drawing of his cell phone using the scale factor 1 mm = 2 in. How long is the drawing of his phone if the actual phones is 8 inches? Arecine for rice pudding calls for un
Answers
Using proportions, it is found that the length of his drawing is of 4 mm.
Proportions:This question is solved by proportions, using a rule of three.The scale means that each mm drawn corresponds to 2 inches of actual length. What is the length of the drawing if the actual length is of 8 inches?The rule of three is:
1 mm - 2 in
x mm - 8 in
Applying cross multiplication:
[tex]2x = 8[/tex]
[tex]x = \frac{8}{2}[/tex]
[tex]x = 4[/tex]
The length of his drawing is of 4 mm.
To learn more about proportions, you can take a look at https://brainly.com/question/24372153
When you flip a biased coin the probability of getting a tail is 0.41.
Find the probability of getting a head.
Answers
I'll give Brainliest to whoever can help! I need help ASAP..!!
Answers
Answer:
1. b d
2. is c or d
3. a or c
4. b or c
5. c
Step-by-step explanation:
2)B
3) I can’t really see the numbers on the number line
is 6z-2z+4=4+2z+6z equivalent
Answers
Answer:
Step-by-step explanation:
0
Answer:
Yes
Step-by-step explanation:
Lol
What’s the sum of -3a+2 and 5a-3
Answers
Answer:
2a-1
Step-by-step explanation:
Answer:
2a-1
Step-by-step explanation:
you take the -3a and add the 5a, and that gives you 2a. 2-3 is -1.
Algebra 1 Q. Checkpoint: Function concepts HWA The organizers of the Clark County Fair keep track of daily revenue from ticket sales. The function f(x) gives the revenue from ticket sales on day x of the fair. The revenue is measured thousands of dollars. What does f(4) > f(1) tell you? The revenue from ticket sales on day 4 was greater than $1,000. The fair had greater revenue from ticket sales on day 4 than on day 1. On day 1, the revenue from ticket sales was less than $4,000. $4,000 in ticket revenue is greater than $1,000 in ticket revenue. Submit.
Answers
1000*1.40=482892 algebra 6x+73=8228
Answer:
The fair had greater revenue from ticket sales on day 4 than on day 1.
Step-by-step explanation:
Find 2a for a = 3 1/4. 23 1/4 6 1/4 6 1/2 5 1/2
Answers
Answer:
6 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
you are adding 3 1/4 to 3 1/4 which is 6 2/4 or 6 1/2
or you can multiply 13/4 by 2 to get 26/4 or 13/2 which, again, is 6 1/2
Which of the following are adjacent angles?
Answers
Answer:
c
Step-by-step explana i think its right