5 Kari makes a kite in the form of a parallelogram, EDGF, as shown in the diagram. Its diagonals [DF] and [EG] intersect at point H. She plots the vertices on a coordinate system with the following coordinates:
D(3,6), G(1,3), H(4, y) and E(x, 6). Find the values of x and y.
![5 Kari Makes A Kite In The Form Of A Parallelogram, EDGF, As Shown In The Diagram. Its Diagonals [DF]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/swQQixrcLUxWzQXGlKVFqsNDt6ce90z5.png)
Answers
Answer:
The values of x and y are;
x = 7 and y = 4.5
Step-by-step explanation:
The question is a word problem, given that the shape of the kite Karl makes is a parallelogram
The coordinates of the vertices are;
D(3, 6), G(1, 3), H(4, y), and E(x, 6)
From the properties of a parallelogram we have;
The diagonals bisect each other
Therefore;
GH = EH = 1/2·GE
Therefore, we have;
The coordinates of the point H = The coordinate of the midpoint of the line EG
The coordinates of the midpoint of a line with end points, (x₁, y₁) and (x₂, y₂) is given as follows;
The coordinates of the midpoint of a line = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Therefore;
The coordinates of the midpoint of the line EG are ((1 + x)/2, (3 + 6)/2)
Given that the midpoint of EG is the point H and the coordinate of the point H is (4, y), we have;
(1 + x)/2 = 4, therefore;
2 × 4 = 1 + x
8 = 1 + x
x = 8 - 1 = 7
Similarly, we have from the coordinate of point H which is given as follows;
((1 + x)/2, (3 + 6)/2) = (4, y)
y = (3 + 6)/2 = 9/2 = 4.5
Therefore, x = 7, y = 4.5.
Parallel sides of a parallelogram have the same slope
The values of x and y are 6 and 3, respectively.
The coordinate points are given as:
[tex]\mathbf{D =(3,6)}[/tex]
[tex]\mathbf{G =(1,3)}[/tex]
[tex]\mathbf{H =(4,y)}[/tex]
[tex]\mathbf{E =(x,6)}[/tex]
Lines DG and HE are parallel.
This means that they have the same slope (m)
The slope is calculated as:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m_{DG} = \frac{3 - 6}{1 - 3}}[/tex]
[tex]\mathbf{m_{DG} = \frac{- 3}{- 2}}[/tex]
[tex]\mathbf{m_{DG} = \frac{3}{2}}[/tex]
Similarly
[tex]\mathbf{m_{HE} = \frac{6 - y}{x - 4}}[/tex]
The slopes are equal.
So, we have:
[tex]\mathbf{\frac{6 - y}{x - 4} = \frac 32}[/tex]
By comparison:
[tex]\mathbf{6 - y = 3}[/tex] and [tex]\mathbf{x - 4 = 2}[/tex]
Solve for y in [tex]\mathbf{6 - y = 3}[/tex]
[tex]\mathbf{y = 3}[/tex]
Solve for x in [tex]\mathbf{x - 4 = 2}[/tex]
[tex]\mathbf{x = 6}[/tex]
Hence, the values of x and y are 6 and 3, respectively.
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Related Questions
Solve for the indicated variable.
a -c=d-r. for a
a=
Answers
Answer:
a= d-r +c
Step-by-step explanation:
a-c = d-r
+c
a= d-r +c
Solving for a gives the result as a = d - r + c
What is a variable ?A variable is something which can vary from a given set of numerical values.We can also substitute some specific values to a variable.
A constant on the other hand is a fix value even if it is denoted by some letter it is a fixed numerical value that can not be changed.
According to the given question
a is the indicated variable.
Given a - c = d - r
a = d - r + c
moving any constant or variable from one side to another changes the sign of the constant or the variable.
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(30 points) find the measure of each lettered angle a= b= c= d= e= f= g= h= i=
Answers
Answer:
a=90 b=90 c=90 d=148 e=32 f=148 g= 122 h=58 l=122
Step-by-step explanation:
a is supp. to 90 degrees, therefore it is 90 (180-90)=90.
b and c are vertical angles, therefore they are the same as the angle directly across from them
d is supp. to 32 degrees, therefore it is 148 (180-32)=148
e and f are vertical angles, therefore they are the same as the angle directly across from them
g is supp. to 58 degrees, therefore it is 122 (180-58)=122
h and l are vertical angles, therefore they are the same as the angle directly across from them
HELP ME WITH THIS I NEED TO ANSWER IT ASAP
Answers
Answer:
e 125x
f 125 x 12 =150
Step-by-step explanation:
This graph shows the number of miles a freight train travels over a period of time.
Freight Train Travel Rate
What is the slope of the line?
Use the number pad to enter your answer in the box
Answers
I NEED HELP !!!!!!!!!
Answers
Answer:
b
d
e
Step-by-step explanation:
the standar form is
[tex]ax^{2} +bx+c=0[/tex]
so it's
[tex]0.5x^{2} -3.2x+5.8=0\\\\-x^2-3x+20=0\\\\\frac{1}{2}x^2+4x-3=0\\\\[/tex]
only that
if it is 5:30 pm what time would it be a half and hour later
Answers
Answer:
6 pm if you're saying in half a hour. 7 if you're saying an hour and a half
Step-by-step explanation:
Which of the following is the Spanish expression for "me too"?
A. Yo también.
B. Hasta luego.
C. ¿Y tu?
Please help. :)
Answers
The other choices mean
B. And you?
C. See you later or bye
Answer:
A. Yo tambien.
Step-by-step explanation:
There is no explanation. I'm not sure why this was in the math section.
A coordinate plane with a line passing through the points (0, negative 4) and (2, 2).
What is the equation of the graphed line written in standard form?
–3x + y = –4
y = 3x – 4
y + 3x = 4
3x – y = 4
Answers
Answer:
The answer is D
Step-by-step explanation:
The only logical explanation
Equation of the graphed line passing through the points (0, - 4) and (2, 2) is equals to [tex]y = 3x - 4[/tex].
What is coordinate plane?" Coordinate plane is defined as the two dimensional plane formed by number line named x-axis and y-axis."
Formula used
Standard equation of the line
[tex]\frac{y-y_{1} }{x-x_{1} } =\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
According to the question,
Points passing through coordinate plane,
[tex](x_{1} ,y_{1} ) = (0,-4)\\\\(x_{2} ,y_{2} ) = (2,2)[/tex]
Substitute the coordinates in the formula to get the equation of line ,
[tex]\frac{y-(-4) }{x-0 } =\frac{2-(-4) }{2-0}[/tex]
⇒ [tex]\frac{y+4 }{x } =\frac{6 }{2}[/tex]
⇒[tex]y + 4= 3x[/tex]
⇒[tex]y=3x-4[/tex]
Hence, the equation of the line is [tex]y=3x-4[/tex].
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Given: f(x)=4x-9 and g(x)= 2x-3. What is the value of (f+g)(0)=?
A.-9
B.-10
C.-11
D.-12
Answers
Answer:
D. -12
Step-by-step explanation:
if f=4x-9, and g=2x-3, and the value is (f+g), then we have to add the equations. This is equal to 6x-12. And then, in '(f+g)(0)', it is asking what is the y-value at x=0. Plug in 0 into the equation, and the y-value equals -12.
0.45 repeating a whole number? Natural number? Real number?
Answers
Answer:
real number
Step-by-step explanation:
Find the sum of the first 15 terms of an ap whose 1st and last term are -4 and 46 respectively?
Answers
#2, no
first year --- 8 = 8*2^0
2nd year --- 16 = 8*2^1
3rd year --- 32 = 8*2^2
...
6th year ---- ??
#3 >>>
I have a terrible problem. I cannot figure it out. What is the blank? 6= _ - (-8)
Answers
Answer:
x=-2
Step-by-step explanation:
[tex]6=x-(-8)\\\\6=x+8\\\\6-8=x+8-8\\\\-2=x[/tex]
Answer:
- 2
Step-by-step explanation:
Step 1:
x - ( - 8) = 6
Step 2:
x + 8 = 6
Step 3:
x = 6 - 8
Answer:
x = - 2
Hope This Helps :)
15x + 3 + 2x + 9r - (8 - r)
Answers
Answer:
17x + 10r -5
Step-by-step explanation:
15x +3 + 2x + 9r- (8-r)
17x +3 +9r -8 +r
17x+ 10r+ -5
helppp pleaseeeeeeeee
Answers
Answer:
The probability would be 30/52
Step-by-step explanation:
if there is 52 cards in a deck, there is 26 red card, plus 4 queens equals 30
the product of -3 and the square of a number decreased by 8.
Answers
Answer:
[tex]n^{2}(-3) -8[/tex]
Step-by-step explanation:
So the "product of" means the answer to a multiplication problem. That means -3 is being multiplied by a number which is squared. I used the variable "n" for number but you could use any letter you want.
This is what we have so far,
[tex]n^{2} \\[/tex] x -3 or [tex]n^{2}[/tex](-3)
The term decreased means to reduce or subtract. Which means we are left with....
[tex]n^{2}(-3) -8[/tex]
Hope that helps and have a great day!
What’s this polynomial in standard form
Answers
Answer:
-[tex]3t^{3}[/tex][tex]-6t^{2}[/tex]+4t
Step-by-step explanation:
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ { - 3t}^{3} - 6 {t}^{2} + 4t}}}}}[/tex]
Step-by-step explanation:
Given terms : + 4t , -6t² , -3t³
Arrange the terms from biggest exponent to lowest exponent:
[tex] \dashrightarrow{ \boxed{ \sf{ - 3 {t}^{3} - 6 {t}^{2} + 4t}}}[/tex]
Hope I helped!
Best regards! :D
P
-4x - 3y= -26
-5x+2y= -21
Find the solution to the system of equations shown above by graphing.
A. X= 5, y= 2
B. X= 5, y=3
C. X= 2, y = 5
D. x= 6, y= 2
PLEASE EXPLAIN!!!
Answers
In a year, there are 12 months. Seven months have 31 days. How many have 28 days? *
Answers
Answer:
ALLL OF THEM 12
Step-by-step explanation:
Answer:
4 months are 28 days
Step-by-step explanation:
Identify ALL of the constants & coefficients of the following equation:
18 - 5W + 7w-4 = 28
Answers
Answer:
constants are 18, -4 and 28
coefficients are -5, 7
Step-by-step explanation:
constants are numbers not attached to variables
coefficients are numbers attached to variables
Help!!!!!! Put the circle with the greatest area on top. circumference = 30 diameter = 3 radius = 10
Answers
then the circumference=30
and the smallest circle is radius=3
Answer:
10 , 30 , 3
Step-by-step explanation:
Your radius: 10 is the greatest
The circumference is 30 that came from 10 x 3( diameter x radius)
and the diameter is 3 which is the smallest
an elevator traveled up to the 9th floor and then down to the third floor. how many floors did the elevator travel down
Answers
Answer:
in went down 6 floors.
Step-by-step explanation:
9-6=3 so that's how I found the answer.
What is the 4th term in the sequence?
a(n) = -1/16(2)n−1
Answers
Answer:
To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 = 8. Example.
Step-by-step explanation:
Hope this helps
What is 8c-4-2c+5= simplified
Answers
Answer:
6c+1Step-by-step explanation:
[tex]8c-4-2c+5\\\\\mathrm{Group\:like\:terms}\\=8c-2c-4+5\\\\\mathrm{Add\:similar\:elements:}\:8c-2c=6c\\=6c-4+5\\\\\mathrm{Add/Subtract\:the\:numbers:}\:-4+5=1\\=6c+1[/tex]
express 6^1/4 b^3/4 c^1/4 using a radical
Answers
Answer:
B
Step-by-step explanation:
[tex]6^{\frac{1}{4} } b^{\frac{3}{4} }c^{\frac{1}{4} }\\\\=(6^1b^3c^1)^{\frac{1}{4} }\\\\=(6b^3c)^\frac{1}{4} \\\\=\sqrt[4]{6b^3c}[/tex]
so answer is B
[tex]6^{\frac{1}{4} }b^{\frac{3}{4} }c^{\frac{1}{4} }[/tex] expressed as a radical is d. [tex]\sqrt[4]{(6b^{3}c )}[/tex]
To answer the question, we need to know what radicals are.
What are radicals?Radicals are roots of numbers. They are written in the form [tex]\sqrt[n]{x}[/tex] where n is the nth root of x.
Now given that we want to express [tex]6^{\frac{1}{4} }b^{\frac{3}{4} }c^{\frac{1}{4} }[/tex] as a radical, we having using the laws of indices
[tex]6^{\frac{1}{4} }b^{\frac{3}{4} }c^{\frac{1}{4} } = (6b^{3}c )^{\frac{1}{4} } \\6^{\frac{1}{4} }b^{\frac{3}{4} }c^{\frac{1}{4} }= \sqrt[4]{(6b^{3}c )}[/tex]
Thus, we have expressed it as a radical.
So, [tex]6^{\frac{1}{4} }b^{\frac{3}{4} }c^{\frac{1}{4} }[/tex] expressed as a radical is d. [tex]\sqrt[4]{(6b^{3}c )}[/tex]
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john is trying new things on his adventure vacation and is excited about riding a zip line for the first time the zip line is 12 feet high and run distance of 200 feet what is the slope of zip line
Answers
Answer:
12/200
Step by Step:
What is the common ratio (r) of the geometric sequence 1, 5, 25, 125?
Answers
Answer:
The common ratio is 5
Step-by-step explanation:
We know this because the first term times 5 equals the second term and the second term times five equals the third term and so forth.
Sarah and her 4 friends share some cookies. If each person gets 3 cookies, how many cookies were shared? Write a mathematical equation that represents this situation.
Answers
Equation:
3 x 5 = 15
15 cookies is the answer.
Sarah and her 4 friends are 5 people in total.
They are each getting 3 cookies.
You are adding three cookies for each friend. That is the same as multiplying 5 times.
Answer:
Step-by-step explanation:
c/5. = 3
5c = 3
c/4. = 3
4c = 3
Simplify Expression
16 - (1 - 5x) - 4x - 29
Answers
Answer:
-9x-14
Step-by-step explanation:
Help me please ASAP!! :(
Answers
Answer:
m= -1/7 (slope)
b= -1 (y inter)
Step-by-step explanation:
Solve for y.
8+4y= -8
Answers
Answer:
-4
Step-by-step explanation:
8+4y= -8
4y= -8 -8
4y= -16
divide both sides by the coeffient of the variable. in this case divide both sides by 4
y=-4
Answer:
y = -4
Step-by-step explanation:
8+4y= -8
4y = -8 -8
4y = -16
y = (-16) ÷ 4
y = -4