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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Answers
9/5 F = N - 67
Add 67 to both sides
9/5 F + 67 = N
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Divide both sides by 9/5
9/5 F = N - 67
Add 67 to both sides
9/5 F + 67 = N
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A container ship is overtaking an oil tanker on the way out of Harwich Harbor, and the first mate notices that if he starts walking from the front of the container ship when the two ships start overlapping, he reaches the back as the two ship separate. He walks at 3 km/hour.
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[tex]\frac{7x}{8}-\frac{1}{40}[/tex]
Step-by-step explanation:
[tex](\frac{3x}{4}-\frac{5}{8})+(\frac{x}{8}+\frac{3}{5})[/tex]
By combining the like terms,
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Is the following sometimes, always, or never true? If two lines intersect to form congruent adjacent angles, then the lines are perpendicular.
Answers
Answer:
sometime
Step-by-step explanation:
A company wants to develop audio speakers using an inexpensive type of plastic that has a very high quality of sound output. Which customers would most likely give a high evaluation of this product?
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Answer:
the answer is A
Step-by-step explanation:
those who want to save money and will only use product for a few years
Answer:
those who want to save money an will use the product for only a few years
Step-by-step explanation:
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Answer:
f(x) = x² + 5 / x - 5
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Answers
Answer:
D = [tex]5\sqrt{5}[/tex]
Step-by-step explanation:
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d= \sqrt{(-7-(-2))^2+(-7-3)^2} \\d= \sqrt{(-5)^2+(-10)^2} \\d= \sqrt{25+100} \\d= \sqrt{125} \\d= 5\sqrt{5}[/tex]
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Answer:
= 6
Step-by-step explanation:
7 x 1 - 4 x 1/4
7 - 4 x 1/4
7 - 1
= 6
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Answers
Answer:
principal (p) = 2400
Amount (A) =2646
time (t) = 2 years
Interest = A-p
=2646-2400=246
T = I * 100/(P*T)
= 246*100/(2400 *2) = 5.125%
Step-by-step explanation:
The rate of interest will be 5.125% for the given data.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given that the sum of rs 2400 compounded to rs 2646 in 2 years. The compound interest will be calculated as,
principal (p) = 2400
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time (t) = 2 years
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Hence, the interest rate will be %5.125.
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Answer:
33.32 m squared
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34 divided by 20 equal 1.7
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Hey there!☺
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[tex]Explanation:[/tex]
[tex]3y+2[/tex]
Since there are no like terms and it can't be factored the answer is:
[tex]3y+2[/tex]
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Answers
Answer:
The car is 13 years old
Step-by-step explanation:
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x + 3 = (x / 1/2 + 7 / 1/2)------- >
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
6x - 7 = 6(x + 4)
Step-by-step explanation:
The value of the number (n) is -7.
What is an Algebraic Expressions?When we apply the mathematical operations on constants and variables then we get the mathematical statements, these are known as algebraic expressions.The mathematical operators include, division, addition, multiplication and subtraction.Let a number we want to find be n.
Hence, according to the given condition, the equation will be:
⇒ 6n - 7 = -49
⇒ 6n = -42
Dividing both sides by 6, we get:
⇒ n = -7
Therefore, the number that satisfy the algebraic expression is n = -7.
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Answer:
120 ways
Step-by-step explanation:
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Answer:
Step-by-step explanation:
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Answer:
x = 1
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Answer:
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we know that
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Answers
Answer:8:3
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Answers
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Step-by-step explanation:
To solve for y, you need to use algebraic properties to isolate y.
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Answers
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2x² +x + 3
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3x²-2x+4x-x²+3-x
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Answers
Step-by-step explanation:
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Answers
Answer:
120 seconds/2 minutes
Step-by-step explanation:
divide the distance (270 m) by the rate (2.25 m/s) and you have 270/2.25 = 120 seconds, or 2 minutes.
It will take Ari 120 seconds to jog 270 meters.
To find the time it will take Ari to jog 270 meters at an average rate of 2.25 meters per second, we can use the formula:
Time = Distance / Rate
where:
Distance = 270 meters
Rate = 2.25 meters per second
Time = 270 meters / 2.25 meters per second
Time = 120 seconds
Therefore, it will take Ari 120 seconds to jog 270 meters.
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