1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ksivusya [100]
2 years ago
6

PLEASE HELP I WILL GIVE A LOT OF POINTS!

Mathematics
1 answer:
vazorg [7]2 years ago
3 0

9514 1404 393

Answer:

  (2.27, 0.96)

Step-by-step explanation:

The orthocenter is the point of intersection of altitudes of the triangle. The equation for an altitude is the equation of a line through a vertex that is perpendicular to the opposite side.

For example, the line perpendicular to side AC can be found as ...

  (∆x, ∆y) = C-A = (3, -1) -(-4, 2) = (7, -3)

  ∆x(x -h) +∆y(y -k) = 0 . . . . perpendicular through point (h, k)

For side AC, we want the point to be B(4, 5), so the equation is ...

  7(x -4) -3(y -5) = 0

  7x -3y -13 = 0

Similarly, the altitude to side AB can be written as ...

  (∆x, ∆y) = B -A = (4, 5) -(-4, 2) = (8, 3)

  8(x -3) +3(y +1) = 0

  8x +3y -21 = 0

__

By the "cross multiplication method", the solution to these equations is ...

  x = (-3(-21) -(3(-13))/(7(3) -8(-3)) = (63+39)/(21+24) = 102/45 = 2 4/15 ≈ 2.27

  y = (-13(8) -(-21)(7))/45 = 43/45 ≈ 0.96

The orthocenter is near (2.27, 0.96).

__

A graphing application confirms this result.

_____

<em>Additional information about the cross multiplication method</em>

For the general form equations ...

  • ax +by +c = 0
  • dx +ey +g = 0

The "cross multiplication method" has you write the array ...

  \begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}

and form the "cross products" in groups of four coefficients:

  D = ae -db, X = bg -ec, Y = cd -ga

Then the solution to the set of equations is ...

  1/D = x/X = y/Y   ⇒   x = X/D, y = Y/D

__

<em>Additional note</em>

Videos of this method show you writing the array as bcab/egde and using the final equation x/X=y/Y=1/D. The above gets the same result in a more straightforward manner.

You might be interested in
help I need answer to both of the photos down below I’ll mark brainlest for both answers and give 20 points pls help
S_A_V [24]
I believe the first question is 4 feet / 1 second and the second answer is 16 oz / 1 lb
8 0
2 years ago
Jose drove from newyork to Florida. Resting for 1 hour for every 5 hours he drove. if he drove for 35 hours. how many hours did
g100num [7]
7 hours because 35 / 5 is 7
7 0
2 years ago
Read 2 more answers
Which expression is equivilent to 3x/x+1 divided by x+1?​
Sveta_85 [38]

Step-by-step explanation:

\frac{3x}{x + 1}  \div (x + 1) \\  \\  =  \frac{3x}{x + 1}  \times   \frac{1}{(x + 1) }  \\  \\  =  \frac{3x}{ {(x + 1)}^{2} }

6 0
3 years ago
Help me with this please
Iteru [2.4K]

Answer: is it -3,11

Step-by-step explanation:

7 0
3 years ago
PLS HELP ME QUICK BRAINLIEST +15 POINTS!!!!!
Ipatiy [6.2K]

Answer:

3/4

Step-by-step explanation:

The mean of a data set is synonymous with the average. To find the mean, add up all the values in the data set and then divide by the number of elements.

From the table, there is 12 values. Thus, add up all the 12 values and then divide by 12:

\bar x=\frac{(-3)+4+8+(-1)+(-4)+(-2)+0+2+5+2+(-3)+1}{12}

Simplify:

\bar x=\frac{9}{12}

Reduce:

\bar x=3/4

Therefore, the mean of the data set is 3/4.

For the data set, this means that the average person guesses the temperature too high by about 3/4°F.

(Note: the symbol of x with a bar over it denotes the mean of a set)

7 0
3 years ago
Other questions:
  • hat is the law of large numbers? As the sample size decreases, the relative frequency of outcomes gets closer to the theoretical
    11·1 answer
  • You can get a quart bottle of cola for $1.50 or a liter bottle for $1.57. Which is the better buy in terms of price per volume?
    5·1 answer
  • What is the volume of the prism with a base of 6 height of 5 and lenght of 10
    15·1 answer
  • How do u solve y-5&gt;-15
    5·2 answers
  • Jade ha Jade has $451.89 in her checking account. After 3 checks, each for the same amount, are deducted from her account, she h
    10·1 answer
  • 20 points.<br> Please answer and explain if possible.<br> Multiply.<br> -2y^2 * xy^4
    9·2 answers
  • Can someone help me with these 4 questions please :) .
    13·1 answer
  • WHOEVER IS FIRST GETS BRAINLIEST
    10·2 answers
  • Plz help. Will give brainliest
    13·2 answers
  • A function is represented by the graph. Complete the statement by selecting from the drop-down menu. The y-intercept of the func
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!