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
F(x) = x2. What is g(x)?
Anarel [89]

Answer:

i think is is c but I not sure.

Step-by-step explanation:

6 0
2 years ago
The movement of the progress bar may be uneven because questions can be worth more or less (including zera
kakasveta [241]

Answer:

600

Step-by-step explanation:

Because the tens digit is less than 5, round down to 600

5 0
2 years ago
Read 2 more answers
Help me please as soon as possible
SIZIF [17.4K]
If each case weighs 24 pounds, then 1p=24 pounds. so if we're trying to find a function of weight, p=24c.

Example: When you have 2 cases, you plug in a 2 for c

p=24c
p=24(2)
p=48

So if you have two cases, it will total 48 pounds,

So that is why the equation is p=24c. Hope this helps!


6 0
3 years ago
For the diagram at right, write and solve an equation to find x
Tomtit [17]

Answer:

x = 24

Step-by-step explanation:

The formula for determining the sum of interior angles is:

(n-2) * 180

4 * 180 = 720

Therefore to determine an equation for x, we must add up all the interior angle equations and set them equal to 720.

(2x+3) +(3x+12) + (7x+14) + (9x+2) + (4x+8) + (3x+9) = 720\\28x + 48 = 720\\28x = 672\\x = 24

The equation and answer above shows how to find x, which equals 24.

3 0
2 years ago
Helpppppppppppp please give me the answer
Romashka [77]

10/12 in simplest form is 5/6.

Equivalent ratios would be 15/18, 20/24, and 25/30.


The rest is easy, give it a try.

6 0
3 years ago
Other questions:
  • Solve this problem what is the answer x=4.7+8.3
    5·1 answer
  • max is four years younger than his sister brenda. the total of their age is 16. write and solve an equation to find their ages.
    8·2 answers
  • An 8-pack of juice boxes costs $5. How much do 32 juice boxes cost?
    6·2 answers
  • 4.36x + 54.31 = -19.81 <br><br> x=?<br><br> Show work please !
    12·1 answer
  • PLEASE HELLLPPP!!!! WILL GET BRAINIEST!!
    15·1 answer
  • Write the number in standard form.
    7·1 answer
  • 8ft - 11inches to decimal inches. ​
    5·1 answer
  • Jenae buys some scarves that are $14 each and 2 wallets that each cost $12. Jenae's total is $94. Write an equation that could b
    6·1 answer
  • Find the value of f(5) for the function.<br> f(x) = -5(x + 4)<br> f(5)=(sImplify your answer.)
    15·1 answer
  • The quotient of a number and 6 minus 3 is 1
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!