What Is The Distance Between Point G (4,2) And The Line Through The Points E(1,-2) And F(7, -2)? Help (2024)

Mathematics College

Answers

Answer 1

Answer:

4 units

Step-by-step explanation:

Given

[tex]G = (4,2)[/tex]

[tex]E = (1,-2); F = (7,-2)[/tex]

Required

Determine the distance

We need to calculate the equation of EF

But first, we calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (1,-2)[/tex]

[tex](x_2,y_2) = (7,-2)[/tex]

So:

[tex]m = \frac{-2 - (-2)}{7 - 1}[/tex]

[tex]m = \frac{0}{6}[/tex]

[tex]m = 0[/tex]

The equation is then calculated as:

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex]m = 0[/tex] and [tex](x_1,y_1) = (1,-2)[/tex]

[tex]y - (-2) = 0(x - 1)[/tex]

[tex]y +2 = 0[/tex]

So, we are to calculate the distance between point [tex]G = (4,2)[/tex] and line [tex]y +2 = 0[/tex]

The distance is calculated using:

[tex]d = \frac{|Ax_1 + By_1 + c|}{\sqrt{A^2 + B^2}}[/tex]

In [tex]G = (4,2)[/tex], we have:

[tex](x_1,y_1) = (4,2)[/tex]

A general equation has [tex]Ax + By + c = 0[/tex] as its format

By comparison

[tex]A = 0[/tex]

[tex]B = 1[/tex]

[tex]c = 2[/tex]

[tex]d = \frac{|Ax_1 + By_1 + c|}{\sqrt{A^2 + B^2}}[/tex] becomes

[tex]d = \frac{|0 * 4 + 1 * 2 + 2|}{\sqrt{0^2 + 1^2}}[/tex]

[tex]d = \frac{|0 + 2 + 2|}{\sqrt{0 + 1}}[/tex]

[tex]d = \frac{|4|}{\sqrt{1}}[/tex]

[tex]d = \frac{4}{1}[/tex]

[tex]d = 4[/tex]

Hence, the distance is 4 units

Related Questions

Help, I’ll give brainliest if you tell me what like terms and terms are.

Answers

Answer:

Step-by-step explanation:

7x + 6 + 5

six and five both are regular numbers but the 7x is not like term

7x + 11

Find the value of x in the triangle shown below.
15
X
19

Answers

Answer:

B. x = 12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

We have a right triangle. Therefore, we can use PT to solve for the missing side.

Step 2: Identify Variables

Leg a = 9

Leg b = x

Hypotenuse c = 15

Step 3: Solve for x

Substitute: 9² + x² = 15²Isolate x term: x² = 15² - 9²Exponents: x² = 225 - 81Subtract: x² = 144Isolate x: x = 12

Answer:

Value of X = 12

Given - A right angle triangle

To find - Value of X

Solution -

using Pythagoras Theorem

(Altitude)^2 + (base)^2 = (Hypotenuse) ^2

(x)^2 + (9)^2 = (15)^2

x^2 + 81 = 225

x^2 = 225 - 81

x^2 = 144

x= root 144

x = 12

id : 237 514 2470
pass : frmCV5​

Answers

Answer:

which subject ....

Which of the following is equivalent to 3(y – 1 + 2y)?

Answers

Answer:

Simplify the expression.

3(y-1+2y)

3y - 3 + 6y

9y - 3

In how many ways can 4 people sit down in 6 seats in a row

Answers

Answer:

360

Step-by-step explanation:

1st person can be seated in 6 ways, 2nd person in 5 ways, 3rd person in 4 ways and 4th person in 3 ways.

Required number of ways =(6×5×4×3)=360.

Hope this helps!!! Have a great day!! :D

Use substitution to solve the system.
X = 2y +6
2x + 5y = 3

Identify the line of reflection,
O X-axis
OY- axis

Answers

Y- Axis

Bc it is being reflected from the Y- Axis

2.
What is the approximate perimeter of the triangle
Shown below

A. 15.7 units
B. 18.7 units
C. 19.2 units
D. 19.8 units

Answers

Answer:

This is B I think if I'm wrong I'm sorry for wasting your time

Answer: It's C 19.2 Units

Got it Right on my test

Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy.

Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Empathy Score 37 48 42 52 56 61 62 46 45 47 55 70 24 72 31 102
Brain Activity -0.12 0.389 0.018 0.363 0.012 0.406 0.106 0.52 0.15 0.744 0.246 0.568 0.216 0.721 0.369 0.79

Given that the equation for the regression line is ŷ = 0.00753x - 0.06759, what is the residual for subject 15?

Answers

Answer:

the residual is 0.2032

Step-by-step explanation:

The regression line has been given as:

Y^ = 0.00753X-0.06759

The paired observation for X is (31, 0.369)

The value of X is the empathy score under subject 15 = 31

The value of the brain activity under subject 15 is 0.369

So we have y^ = 0.00753(31) - 0.06759

= 0.1658

Then the residual = y - y^

= 0.369 - 0.1658

= 0.2032

Therefore the residual is 0.2032

Please check the attachment for the table, it will aid you in understanding the solution

if 6L + 5B = 52 and 12L + 13B = 119 how much is L worth?

Answers

Answer:

4.5 I already did it on the other problem

Step-by-step explanation:

anyone know this and can help?!

Answers

Answer:

65.4°

Step-by-step explanation:

According to question

The equation is

Cos(x)=5/12

x=acos(5/12)

x=65.4°

Determine if the given lines are parallel, perpendicular, or neither.

-2x-3y=9

4x+6y=24

Answers

Answer:

The lines are parallel.

Step-by-step explanation:

Given the lines

[tex]-2x-3y=9[/tex]

[tex]4x+6y=24[/tex]

Writing the equations in the slope-intercept form

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept

[tex]-2x-3y=9[/tex]

[tex]y=-\frac{2}{3}x-3[/tex]

Thus, the slope = m₁ = -2/3

also

[tex]4x+6y=24[/tex]

[tex]y=-\frac{2}{3}x+4[/tex]

Thus, the slope = m₂ = -2/3

We know that parallel lines have equal slopes

As

m₁ = m₂

Thus, the lines are parallel.

NEED HELP ON 17 AND 18!!!

Answers

For question 17 it’s the last one

#17: C+D=0

This is because -4+4 is 0. And 0 is equal to 0...

Find the median of each set of data.
12, 8, 6, 4, 10, 1
6, 3, 5, 11, 2, 9, 5,0
30, 16, 49, 25

Answers

1) 7
2) 5
3) 27.5

hope this helped I put the answers in the order that you wrote them on here(:

Please helppppppppp!!!!!!!!

Answers

Answer:

1. f(12), 2. F(m)=2500, 3. F(v)>_3000, 4. 0.9f(30)

Step-by-step explanation:

Emma has a rectangular garden. She wants to make the width and length of the garden 3 times as large as it is now!
How many times larger will the area of the enlarged garden be compared to the area of the original garden?
A. 3
B. 6
C. 9
O
OD. 12

Answers

Area of enlarged garden is 9 times the area of the original garden.

What is Area?

" Area is the space occupied by an object which is two dimensional in shape."

Formula used to find Area

Area of a rectangle = Length × Width

Let 'l' be the length of the garden.

And 'b' be the width of the garden.

According to the question,

New length = 3l

New Width = 3b

Area of original garden = l × b

Area of enlarged garden = 3l × 3b

= 9 ( l × b )

= 9 × ( Area of original garden)

Hence Area of enlarged garden is 9 times the area of the original garden.

Learn more about Area of rectangular garden here

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Billy has 80 dollars to go shopping. He sees a video game for 60 dollars. What percent of his money
would he be spending?
Help ASAP

Answers

Answer:75%

Step-by-step explanation:

Answer:

100/$80 = 1.25

1.25 x $60 = 75%

Billy would have spent 75% of his money

Step-by-step explanation:

100/$80 = 1.25

1.25 x $60 = 75%

Billy would have spent 75% of his money

3
A farmer has a rectangular field.
The field is 300 m long and 200 m wide.
(a) Calculate the perimeter of the field.

The farmer is buying fence panels.
He needs a total length of 200 m of fence panels.
Each fence panel is 2.5 m in length.
(b) Work out how many fence panels the farmer will need to buy.
(2)​

Answers

Answer:

(a) 1km

(b)80 fence panels

Step-by-step explanation:

(a) perimeter = 300+300= 600

200+200= + 400

=1000m

1km = 1000m

(b).

1panel = 2.5 m 1× 200÷2.5 = 80

=200m

Find the length of AC

Answers

Answer:

we can use tan to solve this

tan=opposite/adjacent

tan(a)=BC/AC

tan(34)=29/AC

ACtan(34)=29

AC=29/tan(34)

by using a calculator we see that AC=42.9942678856 or 43 rounded

Step-by-step explanation:

A line passes through the points (-4,-8) and (6,10). Write an equation that represents a line parallel to this line.

Answers

Answer:

The answer is Jksbns because it is relevant to communism and kim jong un

Which quantity is proportional to 20/5?

Answers

Answer:

100/25, 60/15, and 4/1

Step-by-step explanation:

Answer:

It's 10/2, 100/25 and 60/15

Step-by-step explanation:

Can u make an equation?

Answers

Answer:

3x + -3 = 3

Step-by-step explanation:

3x + -3 = 3

x = 1

Answer:

B

Step-by-step explanation:

3x-3=3

3x=6

x=2

What is the answer to this math problem?

Answers

Answer:

F is -5, 4

G is 0, 1

H is 0, 4

I hope this is right and if it is not then I'm sorry.

I need a lil help y’all lol .

Answers

Answer: 9 gallons

Step-by-step explanation:

the rule is every 2 minutes 3 gallons of water go away

so if you do after 12 minutes, the answer would be 9

hope I explained it well

If a customer has $50 to spend for how many hours can they rent the bicycle if it's $12 an hour

Answers

Answer:

4 1/6 hours

Step-by-step explanation:

This is true because you have to divide $50 by 12 to get the answer because 50 is how much they have to spend and it will take 12 dollars to rent the bike for 1 hour, meaning that they have to divided 50 by 12

This was the only major battle fought in New England during the War. Twelve hundred Patriots surrounded Boston, hoping to force the British to leave the city. When they succeeded, it became apparent that the untrained Patriot soldiers could possibly win the Warcchhhh

Answers

Step-by-step explanation:

Bunker Hill was the name of the battle!

please answer this 3/4 of x=16 find x​

Answers

Answer:

12

Step-by-step explanation:

Simplify. 19x - 24x

What is the answer

Answers

Answer:

x=0

Step-by-step explanation:

Simplifying

19x + -24x = 0

Combine like terms: 19x + -24x = -5x

-5x = 0

Solving

-5x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '-5'.

x = 0

Simplifying

x = 0

Answers:−5

solution:19−24

Complete the function digits(n) that returns how many digits the number has. For example: 25 has 2 digits and 144 has 3 digits

Answers

Answer:

Step-by-step explanation:

We can get this done by using the code

def digits(n):

count = 0

if n == 0:

return 1

while (n > 0):

count += 1

n= n//10

return count

Also, another way of putting it is by saying

def digits(n):

return len(str(n))

------------------------------------------

print(digits(25)) # Should print 2

print(digits(144)) # Should print 3

print(digits(1000)) # Should print 4

print(digits(0)) # Should print 1

Doing this way, we've told the system to count the number of figures that exist in the number. If it's 1000 to 9999, then it records it as 4 digits. If it's 100 - 999, then it records it as 3 digits. If it's 10 - 99, it records as 2 digits. If it's 0 - 9, then it has to record it as a single digit.

Thanks

Following are the digits function that calculte the digits:

Program Explanation:

In this question, we define two in which one use predefine methods and one is used for calculate value by logics, which can be defined as follows: Defining a method "digits" that takes "n" variable inside the parameter.Inside the method "x"variable that converts parameter value into string and counts its length value and use return keyword that return the length of x.Outside the method, a variable n is define that inputs value, and call the method and print its return value.

Program:

def digits(n):#defining a method digits that takes n variable in the parameter

x=len(str(n))#defining a variable x that converts parameter value into string and counts its length value

return x#using return keyword that return the length of x

n=int(input("Ennter number: "))#defining a variable n that inputs value

print(n, "has", digits(n) ,"digits") #using print method that calls the digits method and print its value

OR

def digits(n):#defining a method digits that takes n variable in the parameter

x = 0#defining an integer variable x

if n == 0:#defining an if block that checks n value equal to 0

return 1#return value 1

while (n > 0):#defining a while loop that check n value grater than 0

x += 1#incrementing the value of x

n =n//10#calculating the digits

return x#return digits value

n=int(input("Ennter number: "))#defining a variable n that inputs value

print(n, "has", digits(n) ,"digits") #using print method that calls the digits method and print its value

Output:

Please find the attached file.

Learn more:

brainly.com/question/21289326

4 cards are chosen at random from a deck of 52 cards without replacement. what's the probability of choosing a ten, a nine, an eight, and a seven in order?

Answers

Answer:

12%

Step-by-step explanation:

im not sure so sorry if wrong

The probability of choosing a ten, a nine, an eight, or a seven in order is 3.9 10⁻⁵.

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that 4 cards are chosen at random from a deck of 52 cards without replacement.

The probability of choosing a ten, a nine, an eight, or a seven in order is calculated as,

Probability = ( 4 / 52 ) x ( 4 / 51 ) x ( 4 / 50 ) x ( 4 / 49 0

Probability = 3.9 x 10⁻⁵

To know more about probability follow

https://brainly.com/question/24756209

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What Is The Distance Between Point G (4,2) And The Line Through The Points E(1,-2) And F(7, -2)? Help (2024)
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