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
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
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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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:
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
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
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 >>>
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:
(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
Simplify Expression
16 - (1 - 5x) - 4x - 29
Answers
Answer:
-9x-14
Step-by-step explanation:
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
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
Help me please ASAP!! :(
Answers
Answer:
m= -1/7 (slope)
b= -1 (y inter)
Step-by-step explanation:
0.45 repeating a whole number? Natural number? Real number?
Answers
Answer:
real number
Step-by-step explanation:
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 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]
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
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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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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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
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.
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
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 :)
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
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
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
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.
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.
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:
HELP ME WITH THIS I NEED TO ANSWER IT ASAP
Answers
Answer:
e 125x
f 125 x 12 =150
Step-by-step explanation: