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.
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.
Read more about parallelogram and slopes at:
https://brainly.com/question/19654204
Find the distance between the points with the coordinates shown.
(-8,5) and (7,-3)
Answer:
17
Step-by-step explanation:
I give Brainliest to whom says this question is stupid. What is -2x-8
Answer:
No solution it IS STUPID.
Step-by-step explanation:
Answer:
that question is stupid.
Solve the following equation: 6x - 3x + 13 = 7 + 9x - 6
Answer:
x = 2
Step-by-step explanation:
Answer: 2
Step-by-step explanation:
Aisha changed 1.45 + 2.38 to 1.5 + 2.4 in order to estimate the sum. What estimation method did she use?
Answer:
Hi there!
She used rounding to estimate the sum!
5x-2=8+5y solve for y
Answer:
y = x - 2
Step-by-step explanation:
8 + 5y = 5x - 2
5y = 5x -2 - 8
5y = 5x - 10
5y/5 = (5x - 10)/5
y = x - 2
The equation 5x - 2 = 8 + 5y can be written as in terms of x as y = x - 2; the answer is y = x - 2.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The equation is:
5x - 2 = 8 + 5y
The above equation represents the linear equation in one variable.
To solve for y make the subject as y
5y = 5x - 2 - 8
5y = 5x - 10
y = (5x - 10)/5
y = x - 2
Thus, the equation 5x - 2 = 8 + 5y can be written as in terms of x as y = x - 2; the answer is y = x - 2.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
What are the coordinates of the point on the directed line segment from (-6, -10)
to (6, 8) that partitions the segment into a ratio of 2 to 1?
Answer:
(2,2)
Step-by-step explanation:
(4x+108) +(2x) =180
What is x? Help please
Answer:
x = 12
Step-by-step explanation:
For this problem, we can simply drop the parenthesis, combine like terms, and isolate x to find the value of x. Below is how to do this:
( 4x + 108 ) + ( 2x ) = 180
4x + 108 + 2x = 180
4x + 2x + 108 = 180
6x + 108 = 180
6x = 72
x = 12
Hence, the value of x is 12.
Cheers.
simplify the following expressions ( combine like-terms )
Answer:
x + 5
Step-by-step explanation:
Step 1: Write expression
x + 2 + 3
Step 2: Combine like terms (constants)
x + 5
A cab company charges $ 2 per cab ride, plus an additional $ 1 per mile driven. How long is a cab ride that costs $ 45 ?
Which of the following expression is equivalent to (3x^2y^3)^3?
A) 27x^5y^6
B) 27x^6y^9
C) 9x^6y^9
D) 3x^5y^6
The average hoverboard has a maximum speed of 8 miles per hour. How
many hours would it take Mr. Grigorian to get to school if he lives 18
miles away?
Someone please help me!!!
Answer:
thats easy you don't need help
Step-by-step explanation:
Solve for f please I need help
Answer:
See Below
Step-by-step explanation:
Isolate f
h = 4 + f
-4 -4
h - 4 = f
Or f = h-4
PLEASE HELP!!! 15 PTS FOR THIS!! (Please show work also) Convert y=3x-14 (slope intercept form) to standard form
Answer:
[tex]3x-y=14[/tex]
Step-by-step explanation:
To convert an equation into standard form, we want to get into the form [tex]ax + by = c[/tex].
If we have [tex]y=3x-14[/tex], our first step is to get the x term on the left side. We can do this by subtracting 3x from both sides.
[tex]-3x + y = -14[/tex]
I find it easier now to just divide both sides by -1, so that we have a more consistent equation.
[tex]3x - y = 14[/tex]
Hope this helped!
I NEED HELP ASAP. BEFORE 4:00
Answer:
The measure of x = 45 degrees
Answer:
x is equal to 50.
Explanation:
The three lines intersect creating a triangle. All angle measures for triangles in Euclidean geometry must have a sum of 180 degrees. Because of the Vertical angles theorem, which states if two angles are opposite they are congruent, this means the angle across from 40 degrees is also 40 degrees. Since we know that the second angle is 90 degrees based on the right angle sign. By adding 40 and 90 you get a sum of 130. Now you subtract 130 from 180. This gives you 50 degrees. Since the Vertical angle theorem states two opposite angles are congruent we know the x is equal to 50 degrees.
Use mental math to find a solution for 2 over eight= 3over x+2
The Answer: x= −12/7
Mel and Rob set the alarms on their phones to sound at 6:45am.
Both alarms sound together at 6:45am
Mel’s alarm then sounds every 9 minutes.
Rob’s alarm then sounds every 12 minutes.
At what time will both alarms next sound together?
Answer:
7:21 am
Step-by-step explanation:
9 18 27 36
12 .24 36
36 minutes later
How many inches are in 1 mile? (5280ft = 1mi; 12in = 1ft)
63660in
66330in
63360in
63066in
Sign out
6:10
1 mile * 5280 ft * 12 in = 63360 in
There are 63360 inches in one mile
Answer:
63360
Step-by-step explanation:
5280 × 12 = 63360
Mrs. Bryant is making 17
Christmas ornaments. It
takes 30 minutes to make
each ornament. If she
begins at 1430, at what
time will she finish?
(Write in military time)
4x-6=x+9 i need help can someone show the work too please
Answer:
x = 5
Step-by-step explanation:
instructions in pic :)
4x - 6 = x + 9
4x - 6 - x - 9 = x + 9 - x - 9 [Subtract x + 9 from both sides]
3x - 15 = 0
3x - 15 + 15 = 0 + 15 [Add 15 to both sides]
3x = 15
3x/3 = 15/3 [Divide both sides by 3]
x = 5
Does anyone know the answer?
Answer:
1=163 degrees
2=×=10 degrees
3=×=3
Step-by-step explanation:
54x+1+9x-10=180 we are using this expression because alternate angles add up to 180 degrees
54x+9x+1-10=180
63x-9=180
63×=180+9
63×=189
63×÷63×=189÷63×
X=3
Angle in bold print is (54x+1)
54×3=162
162+1=163 degrees
No.2 Find x
7x+35+x+65 =180
7x+x+35×65=180
8x+100=180
8x=180-100
8x=80
8x÷8x=80÷8
X=10 degrees
No.3 Find x
54x+1+9x-10=180
54x+9x+1-10=180
63x-9=180
63x=180+9
63x=189
63x÷63x=189÷63
X=3
I hope I was of help
simplify the following expressions ( combine like-terms )
Answer:
2x+2y+z
Step-by-step explanation:
What is 4+5-52 times 4
Answer:
4+5-52*4=-199
Step-by-step explanation:
Translate the following verbal expression into an algebraic expression ... "The quotient of a number and four decreased by five"
Answer:
n/(4-5)
Step-by-step explanation:
A quotient of a number and... means that the number is being divided by whatever comes after. In this case the number that comes after is '4 decreased by 5', which is 4 - 5 as the -5 takes 5 away so it 'decreases it by 5'. Therefore is the expression is 'the quotient of a number and four decreased by five' then it is expressed in the following way (using n for number):
n/(4-5)
Hope this helped!
Solve the equation. -(7-4x)=9
Answer:
x=4
Step-by-step explanation:
-(7-4x)=9
-7+4x=9
4x=16
x=4
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-(7-4x)=9[/tex]
Let's divide both sides by -1. This cancels out the negative on the left:
[tex]7-4x=-9[/tex]
Subtract 7 from both sides. The left cancels:
[tex]-4x=-16[/tex]
Divide both sides by -4. All the negatives will cancel:
[tex]x=4[/tex]
And we're done!
1/cosec theta + cot theta -1/ sin theta=1/sin theta - 1/ cosec theta -cot
theta
Answer:
[tex]\theta =2n\pi, \;\frac{\pi}2+2n\pi \;\;\text{for all}\; n=0,1,2,...[/tex]
Step-by-step explanation:
[tex]\frac 1{\text{cosec} \theta}+\cot \theta-\frac 1{\sin \theta}=\frac 1{\sin \theta}-\frac 1{\text{cosec} \theta}-\cot \theta[/tex]
[tex]\Rightarrow \frac 2{\text{cosec} \theta}+2\cot \theta-\frac 2{\sin \theta}=0[/tex]
[tex]\Rightarrow \frac 1{\text{cosec} \theta}+\cot \theta-\frac 1{\sin \theta}=0[/tex]
[tex]\Rightarrow \sin \theta -\frac 1{\sin \theta}+\frac{\cos \theta}{\sin \theta}=0[/tex]
[tex]\Rightarrow \frac{\sin ^2\theta-1+\cos \theta}{\sin \theta}=0[/tex]
[tex]\Rightarrow \frac{-\cos ^2\theta+\cos \theta}{\sin \theta}=0\Rightarrow\frac{\cos \theta-\cos ^2\theta}{\sin \theta}=0[/tex]
[tex]\Rightarrow \cot \theta(1-\cos \theta)=0[/tex]
[tex]\text{If} \;\;1-\cos \theta=0\Rightarrow \cos \theta=1[/tex]
[tex]\Rightarrow \theta=2n\pi\;\; \text{for all}\; n=0,1,2,.....[/tex]
[tex]\text{If} \cot \theta=0\Rightarrow \frac{\cos \theta}{\sin \theta}=0\Rightarrow \cos \theta=0[/tex]
[tex]\Righarrow \theta =\frac{\pi}2+2n\pi\;\;\text{for all}\; n=0,1,2,...[/tex]
Hence, [tex]\theta =2n\pi, \;\frac{\pi}2+2n\pi \;\;\text{for all}\; n=0,1,2,...[/tex]
How do you find the distance of a line segment?
Answer:
Measure the distance from one endpoint to the other.
Answer:
a line segment is a portion of a straight line which is directly connected to two given points. the given points has coordinate x and y
distance = √(x2-x1)²+(y2-y1)²
example : find distance between two points (2,6) and (3,4) ( find the length of a segment)
d = √(3-2)²+(4-6)
d=√1²+2²
d=√5
Divide.
-4 4/5 divided by 4
Answer:
-1 1/5
Step-by-step explanation:
!!!50 points!!
What are two other names for <2?
Answer:
C.
Step-by-step explanation:
Because R is the vertex and you always name a angle with its vertex in the middle, R would have to be in the middle. So the only possible answer is C.