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]

Answers

Answer 1

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.

Answer 2

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.

Read more about parallelogram and slopes at:

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Related Questions

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

It issssssssssssssss 3/4 . X 3204

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


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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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 :)

Simplify Expression
16 - (1 - 5x) - 4x - 29

Answers

Answer:

-9x-14

Step-by-step explanation:

X=-14 hopefully this is helpful

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.

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

The answer is A because if u graph it it would be right

Find the sum of the first 15 terms of an ap whose 1st and last term are -4 and 46 respectively?

Answers

#1, ok
#2, no
first year --- 8 = 8*2^0
2nd year --- 16 = 8*2^1
3rd year --- 32 = 8*2^2
...
6th year ---- ??

#3 >>>

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

HELP ME WITH THIS I NEED TO ANSWER IT ASAP​

Answers

Answer:

e 125x

f 125 x 12 =150

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

radius=10 is the largest

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

0.45 repeating a whole number? Natural number? Real number?

Answers

Answer:

real number

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

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:

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

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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Which of the following is the Spanish expression for "me too"?
A. Yo también.
B. Hasta luego.
C. ¿Y tu?
Please help. :)

Answers

The answer is A.) Yo también

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.

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!

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.

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:

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]

Learn more about radicals here:

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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.

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

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

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 8c-4-2c+5= simplified

Answers

Answer:

6c+1

Step-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 me please ASAP!! :(

Answers

Answer:

m= -1/7  (slope)

b= -1 (y inter)

Step-by-step explanation:

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