Find the coordinates of the orthocenter of a triangle with the vertices (5,3), (8,6), (0,14) at each set of points on a coordinate plane?

Answers

Answer 1

Answer:

coordinates of the orthocenter = (8, 6)

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(5,3), B(8,6), C(0,14)

Thus;

Slope of AC; m = (14 - 3)/(0 - 5)

m = -11/5

Since BE is perpendicular to AC, slope of BE = -1/slope of AC = -1/(-11/5) = 5/11

Thus, equation of BE is;

(y - 6) = (5/11)(x - 8)

Multiply through by 11 to get;

11y - 66 = 5x - 40

11y - 5x = 66 - 40

11y - 5x = 26

Slope of BC is; m = (14 - 6)/(0 - 8) = 8/-6 = -1

AD is perpendicular to BC, thus slope of AD = -1/-1 = 1

Equation of AD is;

(y - 3) = 1(x - 5)

y - 3 = x - 5

y = x - 5 + 3

y = x - 2

Putting x - 2 for y in equation of BE, we have;

11(x - 2) - 5x = 26

11x - 22 - 5x = 26

6x - 22 = 26

6x = 26 + 22

6x = 48

x = 48/6

x = 8

Put 8 for x in equation AD, then y = 8 - 2 = 6

coordinates of the orthocenter = (8, 6)

Find The Coordinates Of The Orthocenter Of A Triangle With The Vertices (5,3), (8,6), (0,14) At Each

Related Questions

NEED HELP WITH THIS MATH QUESTION, WILL GIVE BRAINLIST!!!! HELP ASAP

Answers

Answer:

b

Step-by-step explanation:

Answer:

32.4

Step-by-step explanation:

The equation for area of a triangle is a=1/2bh. So all triangles on outside have area of a=1/2x4.5x3.5. Then you multiply what you get times 3 bc there are three triangles. Then you add that number to the area of the inside triangle. Which you find by doing a=4.5x3.9x1/2

Can I please get some help really quick??

I need help on both please TwT

Answers

Answer:

1) fourth table

2) last option

Can you help me!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

yes

Step-by-step explanation:

by giving us a question and letting us answer it

The answer is B my guy

What is the value of x in cm

Answers

Answer:

13.5

Step-by-step explanation:

look at the bottom and line it up to the top

Answer
13.5
Explanation

45 is 26% of what number? Round to the nearest hundredth if necessary.

A. 11.7

B. 173.08

C. 1.73

D. 0.58

Answers

D I think .................

What is the exact value of cos theta?

Answers

Answer:

C

Step-by-step explanation:

Use the discriminant to determine the number and type of solutions for the equation 2x^2−4x+7=0

(A). The equation has 2 real solutions because the discriminant is positive.
(B). The equation has 1 real solution and 1 imaginary solution because the discriminant is negative.
(C). The equation has 2 imaginary solutions because the discriminant is negative.
(D). The equation has 1 real solution because the discriminant is 0.

Answers

Answer:

it is c

Step-by-step explanation:

Suppose that Omar's marginal utility for cups of coffee is constant at 1.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for the first doughnut he eats, 9 for the second doughnut he eats, 8 for the third he eats, and so on (that is declining 1 unit for each additional doughnut consumed). Suppose that coffee costs $1.00 per cup and doughnuts $1.00 each, and Omar has a budget that he can spend only on doughnuts and coffee. How large would his budget need to be before he would spend a dollar on coffee?

Answers

Answer:

$6.5

Step-by-step explanation:

The marginal utility per dollar of a commodity is obtained by:

Marginal utility of coffee = 5.5

Price of coffee = $1

The marginal utility of doughnut declines by 1 per additional unit of donut consumed :

10 / 1, 9 /1..... 1/1

Therefore , before a dollar can be spent on coffee, then the marginal. Utility of coffee should be greater than doughnut.

5.5 doughnuts will be purchased, at this time marginal utility of doughnut will be 5.5/1, the 6th doughnut will have a marginal utility of 5 which is less than that of coffee.

Cost of 5.5 donuts = $5.5

Cost of coffee = $1

Total = $(5.5 + 1) = $6.5

help please! area of rectangles and squares.

Answers

Answer:

2x squared + 25

Step-by-step explanation:

Step-by-step explanation:

area of rectangle

height×base

(2x-5)(2x-2)=

=4x^2-4x-10x+10

=4x^2-14x+10

(we get quadratic equation)

a=4 b=-14 c=10

firat find discriminant with formula:

D=b^2-4ac(-14)^2-(4×4×10)=196-160=36

now find x1 and x2 with formula:

X=(-b±√D)/2a

x1=(14+√36)/8=20/8=2.5

x2=(14-√36)/8=8/8=1

lets put values :

if we put x2 value as a base, which is 1 in given height and base, we will get 2(1)-2=0. measure of amy side can't be 0.

and if we put x2 in height, it will give us zero.

so no matter which one we put as value. we will get 0cm^2. so i think it cant be detected. im sorry if im wrong

A compound is made up of various elements totaling 90 ounces. If the total amount of uranium in the compound weighs 18 ounces, what percent of the compound is made up of uranium? If necessary, round your answer to the nearest hundredth.

Answers

Answer:

20%

Step-by-step explanation:

The percent of the compound that is made of uranium is calculated as:

(Number of ounces of uranium /Number of ounces of the compound)

× 100

Total amount of uranium in the compound weighs = 18 ounces

A compound is made up of various elements totaling = 90 ounces.

Hence:

= 18/90 × 100

= 1800/90

= 20%

Therefore, the percent of the compound that is made up of uranium is 20%

Write the equation of the line with the given information.

Slope: -2
y-intercept: 5

Answers

Answer:

your mom

Step-by-step explanation:

I really need help on this thank you. if I don’t turn this on time I will fail math class just like how I have failed my life:(

Answers

A. Total after tax is $26.70

B. 26.70 x 1.19 = $31.773

C. 84% of 75 is 63

what is the slope intercept form x+y=-15

Answers

Answer:

y=-x-15

Step-by-step explanation:

used mathaway calculator!! probably would be useful if youre doing more question like shown. :) mark brainlest pls

To find the slope intercept form, you need to isolate y.

We need to get x on the other side of the equation.

You can do this by subtracting x from each side of the equation.

x+y-x = y

-15-x = -15-x

You get...

y = -15-x

Now you need to get the x before the -15.

So just switch them.

y = -x-15

And your done.

i’ll give brainliest!

Brad made a graph showing how many students were absent from school every day last week.

2. how many students were absent on day3? explain how you know.

3.on which day were the greatest number of students absent? how many students were absent that day?

Answers

ANSWER:

2.) There are 5 students absent on day 3 because the dot is in the line of 5 in day 3.

3.) The 2 day is the greatest number of students absent beacause on that 2 day, 10 students were absent

I obviously know this is the answer

2x – 5 = 7 to 2x = 12 What property of equality was used?

Answers

Property of Addition and division.

Human skin has a thickness of about 5 * 10-3 meter. A
grain of sand has a thickness of about 1x 10-3 meter.
About how many grains of sand would it take to match the thickness
of human skin?
Grains of Sand
Human Skin
(1 x 10-3)
(5 x 10-3)
DONE

Answers

Answer:

1.Human skin is thicker than the grain of sand.

2.It will take 5 grains of sand to match the thickness of a humans skin

Step-by-step explanation:

Please tell me how to solve for x and y for these

Answers

Answer:

multiply 60×5 and get your answer for x then divide x by 5 and get why

You multiply the numbers and then divide and you’ll get your answer

Solve the inequality 3x-1 < 2x+5​

Answers

Answer:

x<6

Step-by-step explanation:

Solve for x

by simplifying both sides of the inequality, then isolating the variable.

Inequality Form:

x<6

(Will give Brainliest to serious answer) A glass dropper delivers liquid so that 25 drops equal 1.00 milliliters. How many drops would be required to get 0.68 liters?

Answers

Answer:

17000 drops in the bottle

what is 55 x 25 equaled to

Answers

Answer:

1375

Step-by-step explanation:

The product 55 x 25 equaled to 1375

What is Multiplication?

Multiplication is a method of finding the product of two or more numbers

55 x 25 is equal to 1,375.

To calculate this product, we can multiply the units digit (5) of the two numbers and write it as the units digit of the result.

Then, we multiply the tens digit (5) of 55 by 25 and add any carry-over from the previous step (0) to get the tens digit of the result.

   55

x 25

----

 1375

Hence, the product 55 x 25 equaled to 1375

To learn more on Multiplication click:

https://brainly.com/question/5992872

#SPJ5

The ratio of the perimeter of the rectangle ABCD to the perimeter of rectangle EFGH is 4:7. The value of x is

Answers

Answer:

x = ~8.76

Step-by-step explanation:

Since we know that the scale factor is 4:7, we can figure that 5 will be 4/7 the size of x.

4/7 = 0.571

5 / 0.571 = ~8.76

2 + yx; use x = 6, and y = 5

Answers

Answer:

answer: 32

Step-by-step explanation:

2+5*6

=32

can someone help pleaseee its due soon

Answers

Answer:is a rectangle

Step-by-step explanation:

Answer:

rectangle

Step-by-step explanation:

A video game is now being sold at 22% off for a price of $31.20. What was the original price of the video game?

Answers

Answer:

$38.06

Explanation:

Multiply $31.20 by 0.22 (22%)
Which equals 6.864
Add that to $31.20 and you get 38.064
Then you round it and get $38.06

A pupil has 343 small cubes,each of a side 1 cm .He placed these cubes together to make a larger cube.
what is the length of a side of the larger cube?

Answers

Answer:

85.75 I think. not 100%

Step-by-step explanation:

HELP ASAP Solve for x. Show or explain your work.

Answers

Answer:

[tex]x=4.5[/tex]

Step-by-step explanation:

From AAA, both triangles in this figure are similar. Therefore, we can set up the following proportion:

[tex]\frac{x}{9}=\frac{x+3}{15}[/tex] or [tex]\frac{x}{9}=\frac{3}{6}[/tex].

Cross-multiplying, we get:

[tex]6x=9(3),\\6x=27,\\x=\frac{27}{6}=\fbox{$4.5$}[/tex].

PLS help me
if you get it right i will give brainliest

Answers

Given:

In a right angle triangle,

Perpendicular =  8 units

Base = x units

Hypotenuse = 17 units

To find:

The exact value of x.

Solution:

The given triangles is a right angle triangle. So, side lengths form a Pythagorean triplet.

[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]

[tex](17)^2=(x)^2+(8)^2[/tex]

[tex]289=x^2+64[/tex]

[tex]289-64=x^2[/tex]

[tex]225=x^2[/tex]

Taking square root on both sides.

[tex]\pm \sqrt{225}=x[/tex]

[tex]\pm 15=x[/tex]

Side cannot be negative. So, [tex]x=15[/tex].

Therefore, the required value is [tex]x=15[/tex] and yes, the side lengths form a Pythagorean triplet, i.e., (8,15,17).

A hot air balloon is traveling at a altitude of 2400 feet. It begins to descend at a rate of 75 per minute. What is an expression that represents the rate of descent for the hot air balloon

Answers

Answer:

y=-75x+2400

Step-by-step explanation:

y is the height

-75 is the rate of change so you put that before your x

2400 is your starting value/y intercept

not very good explanation but hope this helps

determine the length of AB​

Answers

Answer:

the answer is 2.

Step-by-step explanation:

How do I know this? well, those red arrows on the line show that those 2 sides (ED) and (AB) are congruent which means they are equal. therefore if they are equal and we know ED is 2, then we know AB is also 2. Hope this helped :)

Solve 4k−16
the solution is __



2. graph the solution.

Answers

Root:(4,0 )
Domain:k€ℝ
Range:y€ℝ
Vertical intercept : (0,-16)
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