Find the equation of locus of a point which moves such that its distance from (0,2) is one third distance from (-2,3). ( I WILL MARK BRAINLIEST FOR CORRECT ANSWER )

Answers

Answer 1

Answer:

\(8(x^2+y^2)-4x-30y+23=0\)

Step-by-step explanation:

Distance formula

\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Let P(x, y) = any point on the locus

Let A = (0, 2)    

Let B = (-2, 3)

If a point moves such that its distance from (0, 2) is one third distance from (-2, 3):

\(PA=\dfrac{1}{3}PB\)

Therefore, using the distance formula:

\(\implies \sqrt{(x-0)^2+(y-2)^2}=\dfrac{1}{3}\sqrt{(x-(-2))^2+(y-3)^2}\)

Square both sides:

\(\implies x^2+(y-2)^2=\dfrac{1}{9}[(x+2)^2+(y-3)^2]\)

\(\implies x^2+y^2-4y+4=\dfrac{1}{9}(x^2+4x+4+y^2-6y+9)\)

Multiply both sides by 9:

\(\implies 9x^2+9y^2-36y+36=x^2+4x+4+y^2-6y+9\)

\(\implies 8x^2+8y^2-4x-30y+23=0\)

\(\implies 8(x^2+y^2)-4x-30y+23=0\)


Related Questions

Negative eighteen divided by six is what number?

Answers

-18 divided six is -3.

Answer:

-18 divided six is -3.

Step-by-step explanation:

Hopefully this helped, if not HMU and I will get you a better answer

-Have a great day! :)

Which graph represents a linear equation?

Which graph represents a linear equation?

Answers

Graph B represents the linear function.

Given that,

4 curves on 4 individual graphs are shown,
Graph that has linear function is to be determined.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
The function in the graph A, C, and D are parabolic,  periodic, and cubic polynomial recpectively. And function in graph B shows the linear function because it is a straight line.

Thus, Graph B represents the linear function.

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if i have a b and then i get a 72% on a test that is 30% of my grade, what will my grade be?

Answers

Answer:

if you have about an 85 now than you shouldn’t go below a b

Step-by-step explanation:

As part of a science experiment, a student recorded 10 measurements of the temperature of a liquid. One of the measurements was an outlier when compared with the other 9 measurements. Which of the following must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements? (Note: An outlier is any number that is greater than the upper quartile or less than the lower quartile by at least 1.5 times the interquartile range.) (A) The median of the 9 measurements is less than the median of the 10 measurements. (B) The median of the 9 measurements is greater than the median of the 10 measurements. (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements. (D) The maximum of the 9 measurements is greater than the maximum of the 10 measurements. (E) The standard deviation of the 9 measurements is less than the standard deviation of the 10 measurements.

Answers

Among the given options, (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements.

An outlier is defined as a measurement that significantly deviates from the other measurements in a data set.

In this case, one of the measurements among the 10 is identified as an outlier.

When comparing the remaining 9 measurements with the entire set of 10 measurements, the maximum value of the 9 measurements cannot exceed the maximum value of the 10 measurements because the outlier, by definition, exceeds the upper quartile or lower quartile by at least 1.5 times the interquartile range.

It is important to note that the median of the 9 measurements can be either greater than or less than the median of the 10 measurements, depending on the specific values of the measurements.

The presence of the outlier does not necessarily determine the relationship between the medians of the two sets.

Similarly, the standard deviation of the 9 measurements may or may not be less than the standard deviation of the 10 measurements.

The inclusion or exclusion of the outlier can have an impact on the standard deviation calculation, but it is not guaranteed to be lower or higher in either case.

Therefore, among the given options, the only statement that must be true is (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements.

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TRY TO ANSWER THIS FAST

TRY TO ANSWER THIS FAST

Answers

Answer:

3/4(8-5y)

Step-by-step explanation:

Just like the first one

When does vertical asymptote occurs???

Answers

Answer:

When the bottom of the fraction equals zero

Step-by-step explanation:

2/(x-3) the VA would be at x=3 because when x does x=3 the bottom is 0

Please help! I will give Brainliest!

Please help! I will give Brainliest!

Answers

Answer:

1/8

Step-by-step explanation:

a

E = {1,02,03} and F= {T155295 3} be bases for a vector space V in R", and suppose f = 2d, -d, +d3 , = 3d, +d, & =-3d, +2d, = = a. Find P the change of basis matrix from F to D. b. Find [] for x = 1

Answers

The change of basis matrix from F to D is [0 -1 0; 2 1 -3; 1 0 0]b and  the value of [] for x = 1 is [] = P⁻¹[]_F .

The given vector space V in R² has bases E = {1, 02, 03} and F = {T155295 3} and some vectors defined as follows:

f₁ = 2d, -d, +d³f₂ = 3d, +d₃f₃ = -3d, +2d³a.

To find the change of basis matrix from F to E, we need to express the basis vectors of F as linear combinations of E.

Therefore, T₁ = 1*1 + 5*02 + 5*03 + 2d*T₂ = 5*1 + 2d*T₃ = 3*1

The vectors f₁, f₂, and f₃ can be written as linear combinations of the E basis as follows:

f₁ = -d + 2(02) + 1(03)f₂ = 3d + 1(02) + 0(03)f₃ = 2d³ - 3(02) + 0(03)These can be represented in a matrix form asf₁ f₂ f₃  0 -1  0  2  1 -3  1  0  0

Thus, the change of basis matrix P from F to E is given by:

P = [0 -1 0; 2 1 -3; 1 0 0]b.

To find the coordinate vector [] for x = 1,

we need to express 1 as a linear combination of the basis E. This is simple since 1 is already a member of the basis E.

Therefore,[] = [1; 0; 0]

Using the change of basis matrix from F to E, we can find the coordinate vector [] for x = 1 in terms of the basis F as follows:

[] = P⁻¹[]_F

Where []_F is the coordinate vector of x with respect to the basis F.

Therefore, the change of basis matrix from F to D is [0 -1 0; 2 1 -3; 1 0 0]b and  the value of [] for x = 1 is [] = P⁻¹[]_F .

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PLEASE HELP URGENT WILL MARK AS BRAINLIEST PLUS POINTS!!

PLEASE HELP URGENT WILL MARK AS BRAINLIEST PLUS POINTS!!

Answers

It think I would be 4.5 if it’s the same order as the left side

Answer:

x = 3.5

Step-by-step explanation:

i don't really know how to explain it but that is the answer btw love ur username

find the area of the given circle​

find the area of the given circle

Answers

Answer:

Area of white circle = 346.36 cm²

Step-by-step explanation:

Area of a circle = πr² where r is the radius

r = diameter/s

For the green circle, d = 42, r = 21

A = π(21)² = 1,385.44 cm²

The white circle has a diameter half of the green circle = 42/2 = 21 cm
So radius of white circle = 21/2 = 10.5 cm

Area of white circle = π (10.5)² = 346.36 cm²

The perimeter of the rectangle is 32 inches. what is the formula that shows the length of side c?

Answers

Answer:

Step-by-step explanation:

2(x+y)=32  means :

x+y =16

A certain food has a gluten ratio of 13\,\text{mg}13mg13, start text, m, g, end text of gluten per \text{L}Lstart text, L, end text of the food. What is the gluten ratio in micrograms per milliliter

Answers

Given the gluten ratio of 13 mg/L in the food, the gluten ratio is micrograms per milliliter can be shown as 13 μg/mL.

In the question, we are given that a certain food has a gluten ratio of 13 mg/L.

We are asked to find the gluten ratio in micrograms per milliliter.

We know the conversion rates:

1 milligram (mg) = 1000 micrograms (μg).

1 Liter (L) = 1000 milliliters (mL).

Applying these conversion rates to the given gluten ratio for the food, we get:

13 mg/L

= 13 (1 mg)/(1 L)

= 13 (1000 μg)/(1000 mL)

=  13 μg/mL.

Thus, given the gluten ratio of 13 mg/L in the food, the gluten ratio is micrograms per milliliter can be shown as 13 μg/mL.

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Charmaine worked 27 hours last month and earned $9 per hour. She spent $19 of her earnings since then. How much money does she have left?

Answers

Answer:

224

Step-by-step explanation:

(27x9) - 19

243 - 19 = 224

Someone please help me ​

Someone please help me

Answers

Answer:

C. 5^10

Step-by-step explanation:

You can add the exponents together (3+7) if they have the same base (5)!

Answer:

C

Step-by-step explanation:

All you have to do is add the exponents

Jesse has four friends over to study. He bakes four pizzas to share equally for lunch. His father takes half of one when the pizzas come out of the oven. Jesse still has to divide the remaining pizza equally among the study group. Use this information for Parts A and B below.

Answers

Answer:

they each get 1 slice because the father took half the pizza.

ASAP PLEASE HELP I WILL GIVE BRIANLEST (precalc) unit circle

ASAP PLEASE HELP I WILL GIVE BRIANLEST (precalc) unit circle

Answers

The trigonometric ratios for the angle A are given as follows:

sin(A) = 0.86.cos(A) = 0.51.tan(A) = 1.69.sec(A) = 1.96.csc(A) = 1.16.cot(A) = 0.59.

What are the trigonometric ratios?

The six trigonometric ratios are defined as follows:

Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.Secant = one divided by the cosine.Cossecant = one divided by the sine.Cotangent = one divided by the tangent.

Applying the Pythagorean Theorem, the hypotenuse of this triangle is given as follows:

c² = a² + b²

c² = 10² + b²

c = sqrt(10² + 6²)

c = 11.66.

For angle A, we have that:

The opposite side is of a = 10.The adjacent side is of b = 6.

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In Crosby's model collection, 5/16 of the models are trains and 7/16 of the models are cars. What part of Crosby's model collection is trains and cars?

Answers

Answer:

3/4.

Step-by-step explanation:

5/16 + 7/16

= (5+7)/16

= 12/16

= 3/4.

PLEASE I NEED HELP WITH ONLY TWO QUESTIONS THIS IS DUE ON SATURDAY

PLEASE I NEED HELP WITH ONLY TWO QUESTIONS THIS IS DUE ON SATURDAY
PLEASE I NEED HELP WITH ONLY TWO QUESTIONS THIS IS DUE ON SATURDAY

Answers

Answer:

due on saturday? psshttt anyways i have the answer lol im gonna put the link below

Step-by-step explanation:

https://pnrtscr.com/ziyaselcukistifa

A car rental agency charges $15 a day for driving a car 200 miles or less. If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven. Which of the following functions represents the cost to drive a car from this agency miles x a day?

A car rental agency charges $15 a day for driving a car 200 miles or less. If a car is driven over 200

Answers

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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A line passes through the points (14.5) and (19.15) determine an equation for a perpendicular line that passes through the point (19.15)

Answers

The equation of the perpendicular line that passes through the point (19,15) is y = -(1/2)x + 24.5.

To find the equation of a line perpendicular to a given line, we need to use the fact that the slopes of perpendicular lines are negative reciprocals (opposite signs and flipped) of each other. Therefore, we first need to find the slope of the given line that passes through the points (14,5) and (19,15):

slope = (change in y)/(change in x) = (15 - 5)/(19 - 14) = 2

The slope of the perpendicular line will be the negative reciprocal of 2:

perpendicular slope = -1/2

Now we can use the point-slope formula to find the equation of the perpendicular line that passes through the point (19,15):

y - 15 = -(1/2)(x - 19)

y - 15 = -(1/2)x + 9.5

y = -(1/2)x + 24.5

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the amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1800 hours and a standard deviation of 95 hours. out of 530 freshly installed light bulbs in a new large building, how many would be expected to last between 1620 hours and 1920 hours, to the nearest whole number?

Answers

The expected number of light bulbs that would be expected to last between 1620 hours and 1920 hours, to the nearest whole number, is 459.Given the mean is 1800 hours and the standard deviation is 95 hours, the amount of time a certain brand of light bulb lasts is normally distributed.

We need to find out how many light bulbs out of 530 freshly installed light bulbs in a new large building would be expected to last between 1620 hours and 1920 hours, to the nearest whole number.According to the empirical rule, approximately 68% of the observations fall within one standard deviation of the mean, and 95% fall within two standard deviations.

Since the light bulb's lifespan is normally distributed, we can utilize the empirical rule to find the number of light bulbs expected to last between 1620 and 1920 hours.We first determine the z-score of both 1620 hours and 1920 hours. z = (x - μ) / σWhere, x = 1620 hours, μ = 1800 hours, σ = 95 hours.

Therefore, z = (1620 - 1800) / 95 = -1.89.For 1920 hours,z = (1920 - 1800) / 95 = 1.26.Now, we find the area under the curve between these two z-scores using the standard normal distribution table.

Using the standard normal distribution table, we get the area as follows:Z-value 0.10 0.11 0.12 ... 1.26.Area 0.5398 0.5371 0.5344 ... 0.8962Z-value -1.89 -1.90 -1.91 ... -3.99.Area 0.0294 0.0293 0.0292 ... 0.0001.Therefore, the area between z = -1.89 and z = 1.26 is: 0.8962 - 0.0294 = 0.8668.

Thus, the percentage of light bulbs expected to last between 1620 and 1920 hours is 86.68%.Finally, we calculate the number of light bulbs that would be expected to last between 1620 hours and 1920 hours, to the nearest whole number.

Out of 530 light bulbs, 86.68% is expected to last between 1620 hours and 1920 hours.Therefore, the expected number of light bulbs that will last between 1620 hours and 1920 hours is given by:Number of light bulbs = (86.68 / 100) x 530 = 459 (to the nearest whole number).

Thus, the expected number of light bulbs that would be expected to last between 1620 hours and 1920 hours, to the nearest whole number, is 459.

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If f(x)=-9x-3, find f(-5)

Answers

Answer:

42

Step-by-step explanation:

f(-5) = -9 × (-5) - 3 = 45 - 3 = 42

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)

HELP GIVING BRAINLIEST Carlene is selling T-shirts for a fundraiser. The T-shirts cost $20.50 each. To date, she has raised $900. Her goal is to raise more than $9,100. How many more T-shirts, x, does Carlene need to sell to reach her goal?

Select the number line that includes the fewest number of T-shirts Carlene can sell and still meet her goal.

Answers

FYI:

Sorry, I can't answer your second question because I can't see any number-lines in your question. But yes, I can answer the first one.

Answer:

400 T-Shirts

Step-by-step explanation:

If each T-Shirt is $20.50, that means that Carlene has to sell lots of them in order to earn the amount of money she wants. So, to find how many T-Shirts she needs to sell in order to get $9,100, we have first remove $900 dollars from the $9,100, because she ALREADY earned it!

9,100-900=8,200

Now we have to divide $8,200 by $20.50. like this...

8,200÷20.50=400

Now, that's our answer. 400.

Carlene has to sell 400 more T-Shirts in order to earn to her goal!

Thank You! Please mark me brainliest so that I can get encouraged to make more great answers like this one!

Write the equation of a circle where the endpoints of a diameter are (4,9) and (4,-3).

Answers

The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.

The "center" of circle is called as midpoint of diameter.

The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and

The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.

So, center of circle is (4,3),

The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:

⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.

⇒ distance = √((4 - 4)² + (9 - (-3))²)

⇒ √(144) = 12.

So, radius is 6.

The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,

Substituting the values

We get,

⇒ (x - 4)² + (y - 3)² = 6²,

⇒ (x - 4)² + (y - 3)² = 36,

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.

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solve this maths problem​

solve this maths problem

Answers

Answer:

hope you find it helpful

solve this maths problem

The correlation in error terms that arises when the error terms at successive points in time are related is termed _____. a. autocorrelation b. leverage c. multicorrelation d. parallel correlation

Answers

The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

Correlation is the mutual connection between two or more variables. These variables can be dependent or independent but there should be random variables.

Autocorrelation is the degree of correlation between the values of the same variables across different data.

Instead of correlation between two different variables, the correlation is between two values of the same variable at times i and i + k.

It is used for the following two purposes:

- To detect non-randomness in data.

- To identify an appropriate time series model if the data are not random.

Therefore, The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

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this is the numbers 14-15

this is the numbers 14-15

Answers

Answer:

14: (-3,-5)

15: (1,0)

Step-by-step explanation:

this is the numbers 14-15

Which
expression is equivalent to
(x^6y^8)^3/x^2y^2

Answers

Answer: \(x^{16}y^{22}\)

Step-by-step explanation:

\(\frac{(x^6 y^8)^3}{x^2 y^2}=\frac{x^{18}y^{24}}{x^2 y^2}=x^{16}y^{22}\)

Use prime factorization to find the LCM and the HCF of 210 and 112​

Answers

Answer:

HCF = 14

LCM = 1680

Step-by-step explanation:

Factorizing the given values

210 = 2 * 3 * 5 * 7

112 = 2 * 2 * 2 * 2 * 7

Since 2 * 7 is common to both factors

Hence the HCF = 2 * 7 = 14

For LCM, we we will multiply all the prime factors that are in both

LCM = 2* 2 * 2 * 2 * 3 * 5 * 7

LCM = 112 * 15

LCM = 1680

Hence the LCM is 1680

The scale of a map says that 8cm represents 5km what is the actual number of kilometers that is represented by 5 centimeters on the map

Answers

Answer:

8 km

Step-by-step explanation:

It is given that, the scale of a map says that 8 cm represents 5 km. We need  to find the  actual number of kilometers that is represented by 5 centimeters on the map.

8 cm = 5 km

1 cm = (8/5) km

For 5 cm, multiply (8/5) km by 5.

So,

x = 8 km

So, 8 km is represented by 5 centimeters on the map.

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methylation is decreasing transcription rates. where are those methyl tags likely to be most prevalent? A company contributes money towards a profit-sharing fund for its employees. Every 2 years, employees are free to withdraw money from their account without penalty. This benefit indicates which type of reinforcement schedule?. The onset of the Greek Dark Ages led toA. All of the aboveB. Rise of strong men and warlordsC. Collapse of citiesD. Loss of written language Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. is parallel to . and are perpendicular to and .The ratio of the lengths of and is : . Change the following mixed number to an improper fraction. Reduce if possible.7 81/1000 Which of the following is a rational number?v1, v2, v3, v5 0.789x10^5 is this correct scientific notation On 12 March 2022 Heidrun bought a 180-day $100 000 bank bill for $97 500. She sold this bank bill on 12 May 2022 at 4.59% p.a. (simple interest). [2 marks] What was the (simple interest) purchase yield Heidrun paid (expressed as a percentage and rounded to three decimal places)? a. 5.199% p.a. b. 5.348% p.a. c. 13.182% p.a. d. 15.343% p.a. [2 marks] What was Heidruns selling price (rounded to four decimal places)? a. $98 525.598 2 b. $98 403.676 7 c. $98 647.822 1 d. $99 238.743 7What was Heidruns holding period yield, expressed as a percentage and rounded to three decimal places? a. 10.671% p.a,b. 3.226% p.a.c. 6.294% p.a.d. 7.044% p.a The figure below shows a line graph and two shaded triangles that are similar:Which statement about the slope of the line is true?A. It is 2 throughout the line.B. It is fraction negative 1 over 2 throughout the line.C. The slope from point O to point A is one-half times the slope of the line from point A to point B.D. The slope from point O to point A is two times the slope of the line from point A to point B. Which is a correct first step in solving 5 - 2x < 8x - 3?5 < 6x-33x < 8x-35 < 10x - 32 - 2x < 8x Linking verbs help make a(n) __________ (appearance, statement, action, or structure) not express the ___________ (appearance, statement, action, or structure) 10 points how do agency relationships affect businesses and the business world? choose 2 answer choices. The Moore family received 23 pieces of mail on July 28 . The mail consisted of letters, magazines, bills, and ads. How many letters did they receive if they received five more ads than magazines, three more magazines than bills, and the same number of letters as bills? two major unanticipated problems that occurred as a result of deinstitutionalization involve Tickets for a concert were \$5$5dollar sign, 5 for each child and \$8$8dollar sign, 8 for each adult. Ports M and N are 162 mi apart. A ship left port M for port Nat a speed of 45 mph. Forty-five minutes later, a second ship leftport N and steamed toward the first ship at a speed of 36 mph.How long after the departure of the first ship will the two shipsmeet? Please answer the following prompts regarding advertising andpublic relations:A) Post a link to one of your favorite ads. Does it persuadeyou? How? Why do you like it? Is there anything problematic If two vehicles arrive at an intersection with stop signs on all four corners, which driver must yield? a) Briefly explain the role of accounting staff in budgeting b) What is the significance of budgeting in any business organization c) Briefly discuss the benefit of using variable costing as a basis of management reporting d) A chemical process has a normal wastage of 10% of input. In a period, 2,500bags of material were input and there was abnormal loss of 75 bags. What quantity of good output was achieved? application control objectives do not normally include assurance that