Find the coordinates of the orthocenter of a triangle with the vertices (0,0), (8,2), (2,8) at each set of points on a coordinate plane?
Answers
Answer:
coordinates of the orthocenter = (16/5, 16/5)
Step-by-step explanation:
I have drawn a diagram showing this triangle with the vertices. I have also drawn altitude from B perpendicular to AC at point E.
I have also drawn altitude from from A perpendicular to BC at point D.
Now, we will find the slope of AC from the line slope equation; (y - y1) = m(x - x1)
m = (y - y1)/(x - x1)
Our coordinates are; A(0,0), B(8,2), C(2,8).
Thus;
Slope of AC; m = (8 - 0)/(2 - 0)
m = 4
Since BE is perpendicular to AC, slope of BE = -1/slope of AC = -1/4
Thus, equation of BE is;
(y - 2) = -¼(x - 8)
Multiply through by 4 to get;
4y - 8 = -x + 8
x + 4y = 16
Slope of BC is; m = (8 - 2)/(2 - 8) = 6/-6 = -1
AD is perpendicular to BC, thus slope of AD = -1/-1 = 1
Equation of AD is;
(y - 0) = 1(x - 0)
y = x
Putting x for y in equation of BE, we have;
x + 4x = 16
5x = 16
x = 16/5
Since y = x in equation AD, then y = 16/5
coordinates of the orthocenter = (16/5, 16/5)
Related Questions
In ARST, RS – TR and mZT = 15°. Find mZS.
Answers
Answer:
54
Step-by-step explanation:
Sadie's sweets is having a sale on all their baked goods they are regularly priced at $4 but they are marked down to $2.6 what percent off are they
Answers
Answer:
35% off
Step-by-step explanation:
= |4 - 2.6|/((4 + 2.6)/2) = 1.4/3.3 = 0.42424242424242 = 42.424242424242%
Percentage of decrease = |4 - 2.6|/4 = 1.4/4 = 0.35 = 35%
2.6 is a 35% decrease of 4.
Explanation: 30%= 0.30
4 times 0.30= 1.4
4-1.4= 2.6
Hello! I will give you fifteen points if you solve this correctly!
Answers
Answer:
mark each line about 1 in. apart
Plzzzzz give me Brainliest!!!!!
Please somebody help me with this
Answers
Answer:
the answer is C
Step-by-step explanation:
2x - 3y > -12
3x + 2y < or = 18
Please helppp! I’ll give Brainliest!!
Answers
Need help please help
Answers
Answer:
153.9 in²
Step-by-step explanation:
Using the formula: A = π r²
Where r = the radius and π is 3.14.
The radius is the diameter divided by 2.
14 divided by 2 is 7.
Plug in 7 into the formula:
A = π 7²
7² is 49.
49 times π is equal to 153.86.
Rounding this up to the nearest tenth, you'll get 153.9
A rock climber begins climbing at an altitude of 120 meters. She climbs at a rate of 50 meters per hour. Which equation can be used to find the altitude of the rock climber, y, after x hours?
Answers
Answer:
y=50x+120
Step-by-step explanation:
y is the ending altitude
x is the number of hours the climber has climbed
put 50 before x because that how fast the climber is climbing
then 120 is your y intercept
What is the slope of the line 6x + y = 24?
Answers
Answer:
-6
Step-by-step explanation:
You need to get it in Point-Slope form, or
y = mx + b
Isolate y by subtracting 6x
You are left with:
y = -6x + 24
M is the slope, so in this case, it is -6
Answer:
The slope is -6/1 but the slope-intercept form is y=-6x+24
Step-by-step explanation:
y=mx+b
6x+y=24
first you want to subtract 6x from each side.
y=-6x+24
m=-6x or -6/1
b= 24
can you please answer this for me :
A
B
C
D
Answers
Answer:
17/21
Step-by-step explanation:
Because i had that question and it was 17/21
Look for a Pattern: In a recent year. One United States dollar was equal to about 82 Japanese yen. How many Japanese Yen are equal to $100? $1,000? $10,000?
Answers
Answer:
[tex]\$100 = 8200\ Yen[/tex]
[tex]\$1000 = 82000\ Yen[/tex]
[tex]\$10000 = 820000\ Yen[/tex]
Step-by-step explanation:
Given
[tex]\$ 1 = 82\ Yen[/tex]
Solving (a): Equivalent of $100
Represent this with x.
So, we have:
[tex]\$100 = x[/tex] and
[tex]\$ 1 = 82\ Yen[/tex]
Cross Multiply:
[tex]x * \$1 = 82\ Yen * \$100[/tex]
[tex]x * 1 = 82\ Yen * 100[/tex]
[tex]x = 8,200\ Yen[/tex]
Hence:
[tex]\$100 = 8200\ Yen[/tex]
Solving (b): Equivalent of $1000
In (a)
[tex]\$100 = 8200\ Yen[/tex]
Multiply both sides by 10
[tex]10 *\$100 = 8200\ Yen * 10[/tex]
[tex]\$1000 = 82000\ Yen[/tex]
Solving (c): Equivalent of $1000
In (a)
[tex]\$100 = 8200\ Yen[/tex]
Multiply both sides by 100
[tex]100 *\$100 = 8200\ Yen * 100[/tex]
[tex]\$10000 = 820000\ Yen[/tex]
is the relationship between the side length of a square and the area of a square proportional?
Answers
Answer:
Students make in-out tables to assist them in noticing patterns and generalizing the mathematical relationships. Expect students to discover that area increases proportionally to the square of how much the side length increases.)
Plllllllllllllllllllllllzzzzzzzzzzzz help me out I’m confused 25 points
Answers
Answer:
-4+(-2)=-6
Step-by-step explanation:
So the arrow goes from -4 to -6 so the end answer is -6 and -4-2 is -6
148 ft above ground level
Answers
Answer: What??????
Step-by-step explanation:
What is the first step to solve this equation?
2x + 3 = 13
Answers
Move all terms not containing
x
to the right side of the equation.
Tap for more steps...
2
x
=
16
Divide each term by
2
and simplify.
Tap for fewer steps...
Divide each term in
2
x
=
16
by
2
.
2
x
2
=
16
2
Cancel the common factor of
2
.
Tap for more steps...
x
=
16
2
Divide
16
by
2
.
x
=
8
Answer:
move the constant to the right 2x=13-3 subtract 2x =10 divided both sides by 2 x=5
Round your answer to the nearest tenth.
Answers
Answer:
The value of MB = 8.4
Step-by-step explanation:
We know that the point of intersection of the Medians of a triangle is called the centroid of a triangle.
Thus,
For the given triangle ΔJKL,
The point M is the centroid of the triangle.We also know that the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.
Also, each Median is split into two parts such that the longer part is 2 times the length of the smaller part.
In our case,
The median KB is split into two parts such that the longer part KM is 2 times the length of the smaller part MB.
i.e.
KM = 2 MB
Given KM = 16.8
so substitute KM = 16.8 in the equation KM = 2 MB
16.8 = 2 MB
MB = 16.8/2
MB = 8.4
Therefore, the value of MB = 8.4
or false if that was worried and simplify to say it was a slave through his own curiosity and I was worried because of the fact I have had been working in my last three months but the following x are the
Write an expression for the sequence of operations described below.
add 3 and the sum of 9 and v
Do not simplify any part
the expression.
Submit
Answers
Answer:
We conclude that:
''add 3 and the sum of 9 and v'' is algebraically represented by the expression as:
3 + 9 + vStep-by-step explanation:
Given the statement
''add 3 and the sum of 9 and v''
Let us break down the statement
Let the number be: vThe sum of 9 and v: 9+vso
Adding 3 and the sum of 9 and v will be: 3 + 9 + v
Therefore, we conclude that:
''add 3 and the sum of 9 and v'' is algebraically represented by the expression as:
3 + 9 + vEasy area problem
Need fast
Answers
Answer:
48 ft²
Step-by-step explanation:
The area of the green shaded part will be :
Area of the entire rectangle green shape assumed complete minus the area of the removed parts{ small rectangle + triangle }
Area of the entire rectangle green shape assumed complete
Area= length * width
A= l*w
A= 5ft * 12 ft = 60 ft²
Area of small rectangle removed part
2 * 3 = 6 ft²
Area of the triangle removed
A= 1/2 * b * h
A= 1/2 * 3 * 4
A= 6 ft²
Area of the outdoor carpet needed for the hole
60-{6+6}
60 -12 = 48 ft²
Can someone help (8 grade math)
Answers
Answer:
B) 110.92 u²
Step-by-step explanation:
to find the surface area, find the area of each side and add them together.
here are all 6 sides:
4.5 * 6.8
4.5 * 6.8
4.5 * 2.2
4.5 * 2.2
2.2 * 6.8
2.2 * 6.8
4.5 * 6.8 = 30.6
4.5 * 6.8 = 30.6
4.5 * 2.2 = 9.9
4.5 * 2.2 = 9.9
2.2 * 6.8 = 14.96
2.2 * 6.8 = 14.96
30.6 + 30.6 + 9.9 + 9.9 + 14.96 + 14.96
110.92
Anissa owns a brick house in the country worth $85,000, and the contents of the house are valued at $15,000. Use the table below to calculate her annual property insurance premium.
Annual Premium per $100 of coverage Brick Steel Mixed Wood Building Contents Building Contents Building Contents Building Contents rating City 0.39 0.43 0.5 0.54 0.55 0.65 0.66 0.76 Suburb 10.45 0.52 0.56 0.63 0.72 0.74 0.83 0.85 Rural 0.69 0.71 0.8 0.89 0.91 1 1.02
O A. $918.65
O B. $950.00
O C. $613.50
O D. $150.00
Answers
Answer:
Step-by-step explanation:
$6903 so thos is the answer
Answer:
answer is $613.50
Step-by-step explanation:
y=x+5
x-5y=-9
Can someone please help ASAP
Answers
Y = 1
1 = -4 + 5
-4 - 5(1) = -9
Increase £2400 by 9%
Answers
x^2 + 6x +15=0 solve the equation using the quadratic formula
Answers
4y + 10 = 5x 2.5x + 2y = -10
Answers
Answer:
are they seperate equations?
Step-by-step explanation:
Which equation has a graph that is parallel to the graph of 2x - y=-1?
Answers
6-9 questions that’s all
Answers
7. 16.8
8. 92 degrees
9. 53 degrees
Challenge!
A. 13
B. 24
C. 6
D. 34
Answers
Answer:
A. 13.
Step-by-step explanation:
x + 9 = 2(3x - 38)
X + 9 = 6X - 76
85 = 5x
x = 85/5
x = 17
So RS = 3(17) - 38
= 51 - 38
= 13
Your baseball team has won 6 game and lost 4 game.If the the team dosen;t lose anymore games how many games must the team win to have a win:the ration is 2:1 ? Explain your answer
Answers
Answer: 2 more games
Step-by-step explanation:
From the question, we are informed that a baseball team has won 6 game and lost 4 game.
We are further told that the team dosent lose anymore games and want to know the number of games they must win to have a ratio of 2:1.
Since they have lost 4 games and need a ratio of 2:1. This means we have to multiply the game lost by 2. This will be: = 4 × 2 = 8 games.
Since they've won 6 games already, they'll need to win = 8 - 6 = 2 games more.
The Singapore Flyer is a giant observation
wheel with a seating capacity of 784
passengers. The number of passengers that
each capsule can carry is equal to the total
number of capsules on the Singapore Flyer.
Find the total number of
capsules on the Singapore Flyer.
Answers
Answer:
28
Step-by-step explanation:
Let x be the number of capsules on the Singapore Flyer.
Each capsule can carry x passengers.
Therefore x^2 = 784.
x = 28
The total number of capsules on the Singapore Flyer is 28.
To find total number of capsules on the Singapore Flyer.
What is volume?Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.
Given that:
Let x be the number of capsules on the Singapore Flyer.
Total capacity : 784 passengers.
Each capsule can carry x passengers.
Therefore x^2 = 784.
x = 28
So, the total number of capsules on the Singapore Flyer is 28.
Learn more about volume here:
https://brainly.com/question/20700768
#SPJ2
What is the measure of an exterior angle of a regular 13-gon?
Answers
Step-by-step explanation:
Size of Exterior angle = 360°/n, where n is the number of sides of the regular polygon.
Hence we have 360°/13 = 27.7° (1d.p.)
The measure of an exterior angle of a regular 13-gon is 27.69°.
What is a regular 13-gon?A regular 13-gon is a polygon that has 13 equal sides, 13 equal interior angles, and 13 vertices.
The given polygon is a regular 13-gon.
Therefore, all the exterior angles of this polygon are equal.
We know, each exterior angle of a regular polygon with 'n' sides is
= (360 / n)°
Here, n = 13.
Therefore, the value of each exterior angle
= (360 / 13)°
= 27.69°
Learn more about a polygon here:
https://brainly.com/question/13879119
#SPJ2
please help i dont know this question
Answers
[tex]x {}^{2} + 8x + 15 = 0[/tex]
[tex]x^2 -5x-3 x +15=0[/tex]
[tex]x(x-5)-3(x-5)=0[/tex]
[tex](x-5)(x-3)=0[/tex]
[tex]x=5,3[/tex]
Hope its Helpful!Answer: x = -3, -5
Step-by-step explanation:
Solve by Factoring
x^2 + 8x + 15 = 0
Factor x2 + 8x + 15 using the AC method.
Consider the form x2 + bx + c. Find a pair of i ntegers whose product is c and whose sum is b. In this case, whose product is 15 and whose sum is 8.
3, 5
Write the factored form using these integers.
(x + 3) (x + 5) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x + 3 = 0
x + 5 = 0
Set x + 3 equal to 0 and solve for x.
Set x + 3 equal to 0.
x + 3 = 0
Subtract 3 from both sides of the equation.
x = −3
Set x + 5 equal to 0 and solve for x.
Set x + 5 equal to 0.
x + 5 = 0
Subtract 5 from both sides of the equation.
x = −5
The final solution is all the values that make (x + 3) (x + 5) = 0 true.
x = −3, −5