If the point R (x, y) is equidistant from two points P (- 3, 4) and Q (2, – 1), prove that

y = x + 2.​

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Calculate the distance between (x, y) and the 2 given points and equate them.

Using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (x, y) and (x₂, y₂ ) = P(- 3, 4)

d = [tex]\sqrt{(-3-x)^2+(4-y)^2}[/tex]

Repeat with (x₁, y₁ ) = (x, y) and (x₂, y₂ ) = Q(2, - 1)

d = [tex]\sqrt{(2-x)^2+(- 1- y)^2}[/tex]

Equating both distances

[tex]\sqrt{(2-x)^2+(-1-y)^2}[/tex] = [tex]\sqrt{(-3-x)^2+(4-y)^2}[/tex]

Square both sides

(2 - x)² + (- 1- y)² = (- 3 - x)² + (4 - y)² ← expand and simplify both sides

4 - 4x + x² + 1 + 2y + y² = 9 + 6x + x² + 16 - 8y + y²

subtract x² + y² from both sides

5 - 4x + 2y = 25 + 6x - 8y ( add 8y to both sides )

5 - 4x + 10y = 25 + 6x ( subtract 5 from both sides )

- 4x + 10y = 20 + 6x ( add 4x to both sides )

10y = 10x + 20 ( divide all terms by 10 )

y = x + 2 ← as required


Related Questions

what is 3x+24+19x= what?

Answers

Answer:

is x 4.3 and would equal 98.6?

Step-by-step explanation:

triangle ABC is shown in the diagram. The links of the sides are in terms of the variable n, where n >4. complete the inquality

Answers

9514 1404 393

Answer:

  m∠B < m∠A < m∠C

Step-by-step explanation:

We can work with the triangle inequality to find that the side measures form a triangle when n > 5/4. For the given value of n ≥ 4, we don't need to be concerned with whether a triangle is formed or not.

For n = 4, the side lengths are ...

  a = 2(4) = 8

  b = (4) +3 = 7

  c = 3(4) -2 = 10

The longest side is opposite the largest angle, so the ordering of angles is ...

  m∠B < m∠A < m∠C

_____

The triangle inequality requires all of these inequalities be true:

a+b > c   ⇒   3n+3 > 3n-2 . . . always trueb+c > a   ⇒   4n+1 > 2n   ⇒   n > -1/2c+a > b   ⇒   5n-2 > n+3   ⇒   n > 5/4

That will be the case for n > 5/4. The attached graph shows the sides and angles keep the same order for n > 3.

Answer:

M- B     M-A      M-C

Step-by-step explanation:

yw

An 11-inch string is cut into 3 equal pieces. Which expression shows the length of each piece?

A. 11/3

B. 1/11 of 3

C. 3 divided by 11

D. 3÷11

Answers

Answer:

a

Step-by-step explanation:

11/3  (eleven divided by three)

Answer:a is the answer

Which shows the equation below written in the form ax2 + bx + c = 0?
x² + 6x+8=3
O A. x2 + 6x + 5 = 0
O B. x2 + 6x + 11 = 0
O C. x2 + 6x + 8 = 0
O D. x2 + 6x + 3 = 0

Answers

Answer:

A

Step-by-step explanation:

X^2 + 6X + 8 =3

TRANSPOSE 3 TO LEFT

X^2 + 6X + 8 - 3 = 0

CALCULATE

X^2 + 6 X + 5 = 0

This is not math but plz help here are some points

Answers

Answer:

the second one

Step-by-step explanation:

what do I need to know to ace my test on basic constructions for geometry

Answers

Answer:

Its important to ask your teacher this alot  of tests are different.  But just study the general idea of what you've learned so far.  

step-by-step explanation:

Answer:

perdón por no ayudar

Step-by-step explanation:

mucho texto

1
Find the slope of the following graph and write your result in the empty box.
Answer:

Answers

Answer:

y = 2x

Step-by-step explanation:

Slope = [tex]\frac{y}{x} =\frac{2}{1}[/tex]

13/14% of a quantity is equal to what fraction of the quantity?

Answers

The answer is 14 !!!

Help me please I need help with this

Answers

Answer:

A

You plug in the same x value for each and see the answer. So 2(5)*10^4= 100000. And for the other we do 4(5)*10^2 which is 200. Since is says that 2x10^4 is 50 times as great as 4x10^2, we know that a is right because 200 * 50 = 100000.

$4.50 plus $3.60 per mile. Patrick paid $28.80 to ride a shuttle bus into the city. How many miles did Patrick ride on the shuttle bus?

Answers

I'm very sorry but i don't know the answer to this queshtion

PLEASE HELP, I WILL UP POINTS AND VOTE BRAINLIEST! DONT MAKE ME WASTE MY 88 POINTS.
Convert the equations in #4-6 to standard form.
#4. y = 9/7x + 1/7
#5. y = -6/5x - 3
#6. y = 1/3x - 2

Answers

Answer:

Ok im  using a standered form calculator:

1. 9/7x + 1/7 = -8

2. y = -6/5x - 3 =  -11

3. y = 1/3x - 2 = -10

Step-by-step explanation:

I will be glad to help more

The Marine Discovery Aquarium sells ocean-themed cookies in their gift shop. Last month, they sold 65 shark cookies and 85 clown fish cookies. The cookies were so popular that they want to order more cookies this month. They plan to order 170 clown fish cookies this month. If they keep the same ratio, how many shark cookies should they order this month?

Answers

Answer: 130 shark cookies.

Step-by-step explanation: If you divided 170 clown fidh cookies by 85 clown fish cookies you get 2. So same as 85 times 2. Then do the same with the shark cookies. 65 times 2, that equals 130.

What is the domian of y=4[x+2]

Answers

Answer:

I'm pretty sure The domain of y=4[x+2] is (-infinity, infinity)

( − ∞ , ∞ )  ,  { x | x ∈ R }

write 0.63 repeating as a fraction in simplest form​

Answers

Answer:

2

Step-by-step explanation:

8=

Answer:

63/100 (the simplest form)

Step-by-step explanation:

1. Covert decimal into fraction:

0.63 = 63/100

2. Simplify (1 is the greatest common divisor of 63 and 100. The result can't be further reduced):

63/100

I NEED HELP ASAP, I'LL GIVE BAINLIEST
Find the value of each expression. SHOW YOUR WORK.

(3.4)2

33 + 10 – 2 • 6

102 ÷ 22

Answers

Answer:

Step-by-step explanation:

3.4 times 2 is 6.8

pemdas for the second one. 2 times 6 is 12. 33+10-12, 31

102/22

4.3636

Answer:

1: 6.8

Work: 3.4 divided by 2 equals 6.8

2: 246

Work: 33 plus 10 minus 2 times 6 equals 246

3: 4

Work: 102 divided by 22 equals 4

Step-by-step explanation: I hope this helps! :)

Write an equation of a line that is (a) parallel to the given line and (b)
perpendicular to the given line.
can you answer 7 too ?

Answers

Answer:

for question 7 : I think it is no

Step-by-step explanation:

if you plot the points on a quick rough sketch you will find that none of the coordinates are on the same line (which they would have to be for a straight line). No points in those 3 coordinates are the same so the there cannot be two points on the same x or y coordiante therefore there is no right-angles triangle.

If you plot the points roughly there will not be two perpendicular lines so there is no right-angles triangle.

sorry I realise   this is confusing :(

Also for Question 5:

Parallel should be anything y= for example, y=6

Perpendicular should be anything x= for example x=6 as y=7 is a horizontal line and x=6 is a vertical line. Y=6 would be parallel because y=(any number with no gradient e.g. 1,2,3,4,etc.) is horizontal.

a line containing the points (4,4) and (8,9)

Answers

Answer:

im assuming slope : 5/4 is slope

Step-by-step explanation:

the formula (y₂ - y₁) / (x₂ - x₁) is how you get slope. plug stuff in and you get (9 - 4) / (8 - 4) and thats 5/4

Answer:

y=1.25x-1

Step-by-step explanation:

Hope this helps! PS I'm not assuming anything

(-2,0) is a solution of the equation 2x - 3y = 6
Is that true or false

Answers

Answer: False

Step-by-step explanation:

To see if (-2,0) is a solution to the given equation, we can plug in the point and solve. If we get the same answer, then it is a solution.

2(-2)-3(0)=6            [multiply]

-4-0=6                     [subtract]

-4≠6

Now, the doesn't equal sign tells us that -4 is not equal to 6. This means the given point is not a solution to the equation, making it false.

what is the least common denominator of2/3and 5/8​

Answers

Answer:

16

Step-by-step explanation:

3 and 8 can both go into 16

Instructions: Find the missing angle in the image below. Do not include spaces in your answers. If you are using a screen-reader, please consult your instructor for assistance. m∠DCF= ∘

Answers

its the angle of a s ss

1/4 ( x − 12 ) + 1/3 ( x + 9 )

Answers

Answer: 7/12x

Step-by-step explanation:

Answer:

7x/12

Step-by-step explanation:

brainleist please

The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is . The solution to the inequality is . Sal's mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.

Answers

Question:

Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage.

The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is .

The solution to the inequality is .

Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.

Answer:

a. [tex]150 + 51x < 100 + 55x[/tex]

b. [tex]x > 12.5[/tex]

c. At least 13 months

Step-by-step explanation:

Given

First Phone;

[tex]Cost = \$100[/tex]

[tex]Additional = \$55[/tex] (monthly)

Second Phone;

[tex]Cost = \$150[/tex]

[tex]Additional = \$51[/tex] (monthly)

Solving (a): The inequality

Represent the number of months with x

The first phone is expressed as:

[tex]100 + 55x[/tex]

The second phone is expressed as:

[tex]150 + 51x[/tex]

For the second to be less expensive that the first, the inequality is:

[tex]150 + 51x < 100 + 55x[/tex]

Solving (b): Inequality Solution

[tex]150 + 51x < 100 + 55x[/tex]

Collect Like Terms

[tex]51x-55x<100 - 150[/tex]

[tex]-4x<-50[/tex]

Solve for x

[tex]x > -50/-4[/tex]

[tex]x > 12.5[/tex]

Solving (c): Interpret the solution in (b)

[tex]x > 12.5[/tex] implies 13, 14, 15....

Hence, She'll keep the second phone for a period of at least 13 months

Answer:

I'm terrible at explaining so here's a screenshot

- Ripper

Step-by-step explanation:

Help!! Its a photo but I need help on it quick!!! Ty if you help me!

Answers

Answer:

36

Step-by-step explanation:

the answer should be 36

Which ordered pair is the solution to the system of equations? {−3x+4y=−20y=x−4 (−4, −8) (4, 8) (−2, −6) (0, −5)

Answers

Answer:

Step-by-step explanation:

-3x + 4y = -20

y = x - 4

Put the second equation into the first equation in place of y.

-3x + 4 (x - 4) = -20

Multiply everything in the parenthesis by 4.

-3x + 4x - 16 = -20

Combine like terms.

x - 16 = -20

Add 16 to both sides.

x = -4

Put this into the second equation in place of x.

y = -4 - 4

y = -8

Your solution set is (-4,-8).

Hope this helps!

Answer:

(-4,8)

Step-by-step explanation:

h+9.5= -9.5

find h. help pls, thank you

Answers

H=-19

That’s the answer
The Answer is -19
Reason: -19+9.5=9.5

I put 37 points in this pls this is urgent!! I’ll give brainliest to best answer... PLEASEE

Answers

uhh I think it’s 2,650 I’m not sure I tried doing all the math and that’s what I got

Answer:

19x + 550n + 200

Step-by-step explanation:

Total cost of the skirts

[tex]7x + 150n + (2n + 1) \times 200 + 4 \times 3x \\ \\ = 7x + 150n + 400n + 200 + 12x \\ \\ = \purple{ \bold{19x + 550n + 200}}[/tex]


The diagram is not drawn to scale.

​ answer as m2

Answers

Answer:

Area = 76[tex]m^{2}[/tex]

Step-by-step explanation:

you can cut into two rectangles

first one:

top and bottom sides = 4m

two sides = 9m

Area = b*h = 9m * 4m = 36 [tex]m^{2}[/tex]

second one

top and bottom sides = 8m

two sides = 14m - 9m = 5m

Area = b*h = 8m * 5m = 40[tex]m^{2}[/tex]

Now add both rectangle areas for the total shaded Area = 36 + 40 = 76[tex]m^{2}[/tex]

Find the quotient: (16x + 24x2) = 2x

Answers

Answer:

48x=2x

Step-by-step explanation:

im big brain can i get brainilest

What is the decimal equivalent of 5/11? (round to the hundredths place)

Answers

Answer:

0.45

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

5 ÷ 11  or 5.0 ÷ 11 = 0.45

Hope this helped!!! Pls mark me brainliest if you want more math answers like this! Also pls thank me!

What is the value of x in the equation 2(x-3)+9=3(x+1)+x?
O x = -3
OX=-1
O x = 0
O x = 3

Answers

Answer:

I think Its x=0

just did it on edg lol hope

The value of x in the expression is,

⇒ x = 0

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 2 (x - 3) + 9 = 3 (x + 1) + x

Now, We can simplify the expression as;

⇒ 2 (x - 3) + 9 = 3 (x + 1) + x

⇒ 2x - 6 + 9 = 3x + 3 + x

⇒ 2x + 3 = 4x + 3

⇒ 4x - 2x = 3 - 3

⇒ 2x = 0

⇒ x = 0

Thus, The value of x in the expression is,

⇒ x = 0

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ7

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