Solve for AB


a: 3.6
b: 15
c: 4
d: 10

9514 1404 393

Answer:

  (81/43, -31/43) ≈ (1.884, -0.7209)

Step-by-step explanation:

The orthocenter is the intersection point of the altitudes of the triangle. Since this is not a right triangle, you need to find the equations of the altitude lines, then find where those intersect.

If we call the points A, B, C in the order given, the attached figure shows the altitude lines from B perpendicular to AC, and from C perpendicular to AB.

We can find the equation of the perpendicular line using the form ...

  ∆x·x +∆y·y = c

where ∆x and ∆y are the differences in coordinates between the points on the "side" and the value of constant 'c' is determined by evaluating the expression using x and y as the coordinates of the opposite vertex.

__

For line AC, we have ...

  (∆x, ∆y) = C - A = (2, -1) -(-3, 0.5) = (2+3, -1-0.5) = (5, -1.5)

Then the equation of the first altitude line is ...

  5x -1.5y = 6(3) -1.5(3) = 10.5

Multiplying by 2 puts this in standard form:

  10x -3y = 21

__

For line AB, we have ...

  (∆x, ∆y) = B - A = (3, 3) -(-3, 0.5) = (3+3, 3-0.5) = (6, 2.5)

Then the equation of the second altitude line is ...

  6x +2.5y = 6(2) +2.5(-1) = 9.5

Multiplying by 2 puts this in standard form:

  12x +5y = 19

__

Then the orthocenter is the solution to the system of equations ...

  10x -3y -21 = 0

  12x +5y -19 = 0

This set of equations can be solved a number of ways. One is the "cross-multiplication" method.

  1/(10·5 -12·(-3)) = x/(-3·(-19) -5·(-21)) = y/(-21(12) -(-19)(10))

  x = 162/86 = 81/43

  y = -62/86 = -31/43

The orthocenter is (81/43, -31/43) ≈ (1.884, -0.7209).

_____

Additional comment

The "cross multiply method" is based on cross products when the equations  are written in standard form:

  ax +by +c = 0

  dx +ey +g = 0

Usually, the coefficients are written in two rows of four, with the first column repeated at the end:

  a  b  c  a

  d  e  g  d

Then cross products are formed, where diagonal down is positive and diagonal up is subtracted from that:

  p1 = (ae -db), p2 = (bg -ec), p3 = (cd -ga)

These give the solution to the equations when put in the form ...

  1/p1 = x/p2 = y/p3   ⇒   x = p2/p1   and   y = p3/p1

If you look at videos of this "cross multiply method," they will put the 1/p1 at the end of the string of equalities, and they will use the coefficients in the order starting with b instead of a. I find the arrangement here easier to remember, so less likely to get confused.

Further comment

You can, of course, find the slopes of the lines, and their opposite reciprocals, then use a point-slope form or some other method for writing the equations of the altitude lines. The solution to the equations can proceed by substitution or elimination. No doubt these methods are somewhat familiar. The method used here tries to get to the answer much more quickly with a lot less writing. (Unfortunately, it takes a bit of writing to explain it all.)

Step-by-step explanation:

a) ST = 7m

b) SU = 8m

c) angle R = 46deg

d) angle Q = 75deg

e) angle S = 59deg

Answer: it represents “n” which is the number of bacteria

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

a. which is the best way to get the information to the police to be able to help you with the information you need to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport by your flight number at your airport to get the car in and you have been advised by our insurance broker to let you all

Answer:

g(x) = (x-3)^2 - 3

Step-by-step explanation:

to move up or down just add or subtract the constant equal to the units moved

so just to move it DOWN 3 would give us

g(x) = x^2 - 3

to move horizontally replace each x with (x ± c)

if you move it to the right, you need x - c

if you move it to the left , you need x + c

so , since we are moving 3 units to the right, we replace the x with x-3

g(x) = (x-3)^2 - 3

sorry if I get it wrong.

Answer:

C (Y = -5/8x - 10)

Step-by-step explanation:

first find the slope (y₂ - y₁) ÷ (x₂ - x₁)

(5 - (-20)) ÷ (-24 - 16)

-5/8 = slope (m)

now that we know the slope is -5/8 we can rule out A and B

now to find the y intercept just substitute a point in for x and y

5 = (-5/8)(-24) + b

multiply

5 = 15 + b

subtract 15 from both sides tp isolate b

-10 = b

Answer:

A.

Step-by-step explanation:

Answer:

Answer is C. (2)

for PLATO

Step-by-step explanation:

A'B' = 2 * AB

Therefore, the dilation factor is 2.

Answer:

I do not see the shapes copy and paste them here

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[tex]slope = \frac{3 - 9}{ - 10 - 15} \\ [/tex]

[tex]slope = \frac{ - 6}{ - 25} \\ [/tex]

[tex]slope = \frac{6}{25} \\ [/tex]

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Answer:

The slope is [tex]\frac{6}{25}[/tex] or [tex]0.24[/tex].

Step-by-step explanation:

This is the formula to calculate the slope from two given points: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] . Now, substitute (x1, y1) and (x2, y2) for (15,9) and (-10,3). [tex]slope=\frac{3-9}{-10-15}[/tex] . That equation becomes [tex]slope=\frac{-6}{-25}[/tex] . You have to change [tex]\frac{-6}{-25}[/tex] to [tex]\frac{6}{25}[/tex] . The slope is 6/25 or in decimal form, 0.24.

Answer:

3 3/4 teaspoons of cinnamon

Step-by-step explanation:

Proportions

Proportional relationships between two variables imply their ratios are constant.

It means that one variable is always a constant value times the other.

We are told that 1 1/2 (1.5) teaspoons of cinnamon are good to make 2 dozen oatmeal cookies. Two dozen is equivalent to 24, thus the ratio between oatmeal cookies and teaspoons of cinnamon is 24 / 1.5 = 16.

It means for each teaspoon of cinnamon you can make 16 oatmeal cookies.

If we wanted to make 60 oatmeal cookies, we need 60/16 = 3.75 teaspoons of cinnamon.

The number 3.75 is equivalent to

3+0.75 = 3 + 3/4, or 3 3/4 teaspoons of cinnamon

Answer:

r = 4

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define equation

-5 + 22 = r - 4 + 3r + 5

Step 2: Solve for r

Step 3: Check

Plug in r to verify it's a solution.

Answer:

y + (-3) = -8

Step-by-step explanation:

i just know

pls mark branliest

Answer:

Grade ano po

Step-by-step explanation:

Para maidentify ko po

Any number that is 13 to Infinity

Any number greater then 12

Assume;

Given number = a

So,

Four times a number;

4 × a

4a

Greater then 48

So,

4a > 48

By solving inequality

a > 12

So,

Any number greater then 12 is the possible value

Learn more:

https://brainly.com/question/1301963?referrer=searchResults

Answer:

5.33%

Step-by-step explanation:

(28,400,000÷30,000,000 ) × 100%

= 94.67%

the reduced amount = 100 - 94.67

= 5.33%

Answer:

5.333333333333334%

Step-by-step explanation:

5.333333333333334% of 30,000,000 = 1,600,000

Tip: Don't get scared by numbers, percentage don't change by how many zeros, i found this just by figuring out by: 1.6 is what percentage of 30?

You could find it on a "Percentage calculator"

Hope this helps!

Ace Carlos

Answer:

it is b !!

Step-by-step explanation:

a^2 + b^2 = c^2 :)

Answer:

Number of stock A = 200

Number of stock B = 300

Step-by-step explanation:

Let :

Number of stock A shares = a

Number of stock B shares = b

Worth of stock A = 50 * a = 50a

Worth of stock B = 60 * b = 60b

50a + 60b = 28000 - - - (1)

Triple the value of stock B:

3 * 60 = 180

Value of stock A goes up by 50%

(100 + 50)% * 50 = 1.5 * 50 = 75

75a + 180b = 69000 - - - (2)

50a + 60b = 28000

75a + 180b = 69000

Multiply equation 1 by 3 and subtract

150a + 180b = 84000

75a + 180b = 69000

75a = 15000

a = 15000/75

a = 200

75(200) + 180b = 69000

15000 + 180b = 69000

180b = 69000 - 15000

180b = 54000

b = 300

Answer:

54 degrees

Step-by-step explanation:

Since we know that the angles are supplementary, we can set them to be equal to 180 degrees when combined.

(7x+14) + (5x-26)=180

Drop the parentheses.

7x+14+5x-26=180

Combine like terms.

12x-12=180

Add 12 to both sides.

12x=192

Divide both sides by 12.

x=16

Since the question asks for the measure of angle B, we need to plug x back into that expression to find its measure.

5(16)-26

80-26

54

Angle B has a measure of 54 degrees.

HTH :)

Answer:

quadratics and absolute value

Step-by-step explanation:

they both go up but Quadratic is U and absolute value is V

Answer:

6.7

Step-by-step explanation:

Answer: She has not hit the boundary 4/5 of the time.

Step-by-step explanation: 6/30 is 1/5. Subtract 1 - 1/5.

Answer:

-37z

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Identify the ones place and check the number to the right.

5.5252

Since we round up if the number to the right is greater than or equal to 5, and the number is a 5, we round up.

Therefore,

5.5252 ≈ 6

Hope this helps.

Answer:

(3x+5)(x+3)

Step-by-step explanation:

3x^2+14x+15

SIMPLIFY INTO COMMON FACTOR

3x^2+9x+5x+15

FACTOR OUT DISTRIBUTION

3x(x+3)+5(x+3)

(3x+5)(x+3)

Answer:

55

Step-by-step explanation:

Please let me know if you need an explanation.

Answer:

1/2

Step-by-step explanation:

4 and 8 are both divisible by four so divide four by four and divide and by four and you get 1/2

Answer:

4,-4

Step-by-step explanation:

[tex]\sqrt16=4\\\sqrt16=-4.\\[/tex]

Both are possible. Hope this helps and if you can, hit the crown ;D

Answer:

He will receive $1, 400 for interest

&

A total amount of $6, 400

Step-by-step explanation:

To find the interest, we must apply the following formula:

I = P × R × T

I represents interest

R represents rate

T represents time

P represents principle

Steps:

1. Change the rate, which is 2%, into a decimal.

2. Multiply the principle, which is 5,000, by the rate, which is 0.02.

3. Multiply the product of the principle and rate, which is 100, by the time, which is 14 years.

So he will receive $1, 400 interest.

To find the total amount he recieved, we must:

Add the principle, which is 5,000, and the current interest, which is 1, 400.

5,000 + 1,400= 6,400

He will receive a total of $6, 400

I hope this helps! I'm sorry if it's wrong.

Answer:

longest

Step-by-step explanation:

was Answer Expert Verified on a different question :)

Answer:

Longest

Step-by-step explanation:

Edgen 2021

Answer:

slope is -3/2

Step-by-step explanation:

Use the slope formula

y2-y1/x2-x1=m (rise over run)

(7,5) (5,8)

x1 y1 x2 y2

8-5/5-7=m

-(3/2)=m