Determine the equation of the circle with center (0,−1) containing the point ( − 8 , 10 )

Answers

Answer 1

To find the equation of the circle with center (0, −1) that contains the point (−8, 10), we can use the standard form of the equation of a circle:


(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.



Since the center of the circle is given as (0, −1), we have:


(x - 0)^2 + (y + 1)^2 = r^2


We still need to find the radius, r. We know that the circle passes through the point (−8, 10), so we can substitute these values for x and y and solve for r:


(-8 - 0)^2 + (10 + 1)^2 = r^2

64 + 121 = r^2

r^2 = 185

So the equation of the circle is:

x^2 + (y + 1)^2 = 185



Alternatively, we can expand the equation to get it in standard form:


x^2 + y^2 + 2y + 1 = 185

x^2 + y^2 + 2y - 184 = 0


So another form of the equation is:


x^2 + (y + 1)^2 =
185


Related Questions

Select the correct answer.
What are the zeros of g(x) = x³ + 6x² - 9x-54?
A. 1, 2,27
B.3, -3, -6
C.-6, 3, 6
D. 2, -1, 18

Answers

Answer:

The answer is C

Step-by-step explanation:

The zeros of g(x) = x³ + 6x² - 9x-54 are -6, 3, 6. Therefore, the correct answer is C.

Yes C is correct :) :)

CAN SOMEONE HELP WITH THIS QUESTION?

Answers

The number of cars that pass through the intersection between 6 am and 10 am is 4800.

To find the number of cars that pass through the intersection between 6 am and 10 am, we need to integrate the traffic flow rate function r(t) over the interval [0,4].

Integrating r(t) with respect to t, we get:

∫(400+ 600t - 150t²)dt = 400t + 300t² - 50t³ + C

where C is the constant of integration.

Evaluating this expression between t=0 and t=4 (since we are interested in the interval between 6 am and 10 am), we get:

(400(4) + 300(4)² - 50(4)³) - (400(0) + 300(0)² - 50(0)³) = 4800 cars

In summary, we can find the number of cars that pass through an intersection between two specific times by integrating the traffic flow rate function over that interval.

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Mathematics

Find the rate

What percent of 200 is 50?
What percent of 50 is 40?
What percent of 10 is 6?
200 is what percent of 200?
What percent of 800 is 200?

Show your solution, HELP PLS ASAP!!!

I'LL GIVE 20 POINTS!!

Answers

Answer:

Step-by-step explanation:

25%

80%

60%

100%

25%

1234-4566/45.44+67*755.34

Answers

Answer:

To solve this expression, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

The expression is:

1234 - 4566 / 45.44 + 67 * 755.34

First, we need to perform the division operation since it comes before addition and multiplication.

4566 / 45.44 = 100.50

Now, we can substitute that into the expression:

1234 - 100.50 + 67 * 755.34

Next, we need to perform the multiplication operation:

67 * 755.34 = 50,548.78

Now, we can substitute that into the expression:

1234 - 100.50 + 50,548.78

Next, we can perform the addition and subtraction operations:

1234 + 50,448.28 = 51,682.28

Therefore, the result of the expression is 51,682.28.

The table below shows different possibilities for the number of games a team would
need to win to maintain a certain percentage of wins.
A 18 20
B 30 20
POSSIBLE BASEBALL
GAMES WON
C 18 30
D 50 30
Number of
Games Won
6
24
36
42
Which ratio of the number of games won to the number of games played could also be
included in this table?
Number of
Games Played
10
40
60
70

Answers

The ratio that could also be included in this table is (c) 18 : 30

Calculating the ratio that could also be included in this table?

From the question, we have the following parameters that can be used in our computation:

Games won   Games played

6                    10

24                  40

36                60

42                70

From the above, we have the ratio of the number of games won to the number of games played to be

Ratio = 6 : 10

Simplify

Ratio = 3 : 5


From the options, we have

(c) 18 : 30

Simplify

Ratio = 3 : 5

Hence, the ratio that could also be included in this table is (c) 18 : 30

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a⃗ =⟨4, −3⟩ and b⃗ =⟨−1,−2⟩.

Represent a⃗ +b⃗ by using the head to tail method.

Use the Vector tool to draw the vectors, complete the head to tail method, and draw a⃗ +b⃗ . Do not draw any unnecessary vectors.

To use the Vector tool, select the initial point and then the terminal point.

Answers

The vector addition of vector a = < 4, - 3 > and b = < - 1, - 2 > is given by,

a + b = < 3, -5 >

The graph of the vector sum is given below.

The addition of vectors suggests the addition of the corresponding components of the involving vectors.

Given the vectors are:

a = < 4, - 3 >

b = < - 1, - 2 >

So doing vector addition we get,

a + b = < 4, - 3 > + < - 1, - 2 > = < (4 + (-1)), (-3+(-2)) > = < (4 - 1), (-3 -2) > = < 3, -5>

Head to tail method is a method to draw vector addition, where the initial point of a vector involved in vector addition is started from tail point of another vector involved in vector addition.

Using vector tool we draw the vector addition of given vectors 'a' and 'b' we get,

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Answer: Look at the image below

Step-by-step explanation: I took the test.

Step 1: Select Vector

Step 2: Click on (0, 0), then click on (4, -3); (for every point your going to have to click on where you start then where you want to go.)

Step 3: Click on (4, -3), then (3, -5). Why?: ((4 - 1), (-3 - 2)) = (3, -5)

Step 4: To complete the problem and thus completing the "head to tail" method, you need to click on the origin (0,0) and finally click on (3, -5)

Your answer should now look like mine, now go get that A.

Please help!
Whoever answers right gets brainliest!!!!

Answers

Answer:

[tex]y - 4 = - 3(x - 2)[/tex]

Identify parallelograms, rectangles and squares

Answers

Answer:

figure A = square ( All sides are equal)

figure B = Rectangle (Two sides are equal)

Figure C = parallelogram (is a four-sided polygon (a quadrilateral) in which opposite sides are parallel and equal in length)

Given ƒ(x) = −2x² + x − 8, find ƒ (9)

Answers

Answer: -161

Step-by-step explanation: you solve by plugging 9 in for x so you get f(9) = -2(9)^2 +9-8 you solve using PEMDAS and you get -161

HELP PLS Triangle D has been dilated to create triangle D′. Use the image to answer the question.

Determine the scale factor used.

Scale factor of one third
Scale factor of 3
Scale factor of 4
Scale factor of one fourth

Answers

The scale factor will be one-third which is 1/3. Then the correct option is A.

Given that:

Dimension of a small triangle, 6, 8, and 10

Dimension of a giant triangle, 18, 24, and 30

Dilation is the process of increasing the size of an item without affecting its form. The object's size can be raised or lowered depending on the scale factor. There is no effect of dilation on the angle.

The scale factor is calculated as,

SF = 6 / 18

SF = 1 / 3

The scale factor will be one-third which is 1/3. Then the correct option is A.

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Answer:

1/3

Step-by-step explanation:

I took the test!

complete the following table , what’s C, AC, BC

Answers

Answer:

C = 45

AC = 1

BC = 2

Step-by-step explanation:

C: 180 - (90 + 45) = 45

AC: Because the angles are the same, it is equal to the other leg, 1 cm

BC: a^2 + b^2 = c^2, so 1 + 1 = 2

Find the sum of x+9 and 7x^- 2x+1.

Answers

The sum of given two expressions x+9 and 7x²-2x+1 results in the expression 7x² - x + 10.

To find the sum of two expressions, we simply add their like terms.

The given expressions are x+9 and 7x²-2x+1.

The first expression has two terms - x and 9.

The second expression has three terms - 7x², -2x, and 1.

We cannot add the terms of the two expressions directly since they are not like terms. However, we can simplify the expressions and then add the like terms.

First, we can simplify the second expression by combining the like terms -2x and 1.

7x² - 2x + 1 = 7x² - (2x - 1)

Now, we can add the like terms from both expressions.

(x + 9) + (7x² - 2x + 1) = x + 7x² - (2x - 1) + 9

= 7x² - x + 10

Note that we could also have added the two expressions without simplifying the second expression first. We would get the same result.

(x + 9) + (7x² - 2x + 1) = x + 7x² - 2x + 9 + 1

= 7x² - x + 10

In either case, the final answer is 7x² - x + 10.

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a. Find x. The figure is not drawn to scale. b. Is the triangle equilateral, isosceles, or scalene? Explain.

*

0 points

Captionless Image

Answers

Answer: Based on the given figure above, we can conclude that the triangle is an isosceles triangle. By definition, an isosceles triangle is a triangle that has at least two equal sides. Since this is an isosceles triangle, 8x-10 =6x. Now we can solve for x. So,

8x-10 =6x

8x-6x = 10

2x =10

x= 5.

Therefore, the value of x in the figure is 5. Hope this is the answer that you are looking for.

You start at (0,-4). You move left 1 unit and right 4 units. where do you end?

Answers

If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

Calculating the endpoint of the point

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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Simplify each of the following exponential expressions. a. 7⁴= ? b. (–10)⁴= ? c. 5¹ = ? d. 0⁴= ? e. –6²= ? f. –3⁰= ?

Answers

The exponential expressions when simplified are 2401, 10000, 5, 0, 36 and 1

Simplifying each of the exponential expressions

From the question, we have the following parameters that can be used in our computation:

The exponential expressions a to f

The general rule is that

a^b = a * a * a..... in b places

Using the above as a guide, we have the following:

a. 7⁴ = 7 * 7 * 7 * 7 = 2401

b. (–10)⁴ = (–10) * (–10) * (–10) * (–10) = 10000

c. 5¹ = 5

d. 0⁴ = 0 * 0 * 0 * 0

e. –6² = -6 * -6 = 36

f. –3⁰ =  1

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Someone help please! I’m taking a test and just need some assistance

Answers

Answer: Given b=2√14 and c=9,

a = 5

Step-by-step explanation:

1/3 divided by 2/9 simplified?

Answers

Answer:3/2

Step-by-step explanation:

1/3 ÷ 2/9=

1/3 ×9/2=3/2

Answer:

3/2 u can also do 1 1/2 their equivalent fractions

Step-by-step explanation:

sorry about the handwriting :) not the best

Point A is at 0 radians with coordinates (1,0) on the unit circle. Point B is the result of point A rotating 7 pie/6 radians counterclockwise
around the unit circle. Name two other positive angles of rotation that take A to B.

Answers

Answer:

19π/6 radians and 31π/6 radians

Step-by-step explanation:

To rotate point A counterclockwise by 7π/6 radians, we can add this angle to the angle of point A, which is 0 radians, to get the angle of point B:

The angle of point B = angle of point A + 7π/6 radians

= 0 radians + 7π/6 radians

= 7π/6 radians

Angle of point B in degrees = (7π/6) * (180/π) degrees

= 210 degrees

To find two other positive angles of rotation that take A to B, we can add any multiple of 2π radians to the angle of point B. This is because adding 2π radians is equivalent to a full rotation around the unit circle, which brings us back to the same point. Therefore, we have:

angle of rotation 1 = angle of point B + 2π radians

= 7π/6 radians + 2π radians

= 19π/6 radians

angle of rotation 1 in degrees = (19π/6) * (180/π) degrees

= 285 degrees

angle of rotation 2 = angle of point B + 4π radians

= 7π/6 radians + 4π radians

= 31π/6 radians

angle of rotation 2 in degrees = (31π/6) * (180/π) degrees

= 465 degrees

So the two other positive angles of rotation that take A to B are (19π/6 radians and 31π/6 radians) or 285 degrees and 465 degrees respectively.

Note:

To convert the angles from radians to degrees, we can use the conversion factor:

1 radian = 180/π degrees

What is the domain of the function shown on the graph?

Answers

Answer:

A

Step-by-step explanation:

the domain is the values of x covered by the graph

on the left the graph → - ∞

on the right the graph tends to + ∞

there are no excluded values of x on the domain , so

domain is - ∞ < x < ∞

Write an equation for a parabola with vertex (1,8) and directrix y = 3.

Answers

i Got u Bro!

Ov=zo « = 192 +8 5 Or = 1/2 (x + 2)² – 8 20 Ov=« 2)2-4 DELL.

Find the length of each segment.

Answers

Answer:

1. 30; 2. 6.25.

Step-by-step explanation:

1. CE:CF=FD:DG; ⇒ 32/24=40/DG; ⇒ DG=30;

2. PQ:QM=RN:RM; ⇒ 5/8=RN/10; ⇒ RN=6.25.

Determine the equation of the circle graphed below.

Answers

The equation of the circle graphed is (x + 4)^2 + (y + 5)^2 = 16

Determining the equation of the circle graphed

From the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

Center = (a, b) = (-4, -5)

Radius, r = 4 units

The equation of the circle graphed is represented as

(x - a)^2 + (y - b)^2 = r^2

So, we have

(x + 4)^2 + (y + 5)^2 = 4^2

Evaluate

(x + 4)^2 + (y + 5)^2 = 16

Hence, the equation is (x + 4)^2 + (y + 5)^2 = 16

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Please im begging someone please help me this is so hard. If you help me ill give you 60 points. PLEASE ILL GIVE BRAINLIEST

Answers

Answer:  B, C, D

Step-by-step explanation:

Looking at the parabola, this is a width vs area graph.

A)    Incorrect.  the greatest possible area is not 10.  Area goes higher

B) True.  The highest possible area, highest point for area is 100

C) True.  The area is 0 when width is 0

D)True.  The area is also 0 when the width is 20

marcus deposits $500 in an account that pays 6.8% simple annual interest. if he keeps the money in the account for 5 years how much interest will he earn

Answers

Marcus will earn $170 in interest after keeping his $500 in the account for 5 years.

To calculate the interest Marcus will earn, we can use the formula:

I = P * r * t

where I is the interest earned, P is the principal amount deposited, r is the annual interest rate as a decimal, and t is the time period in years.

In this case, Marcus deposited $500 and the annual interest rate is 6.8%, which is 0.068 as a decimal. He kept the money in the account for 5 years.

So we can plug in these values into the formula:

I = 500 * 0.068 * 5

I = $170

This is simple interest, which means that the interest is only earned on the original principal amount and not on any accumulated interest.

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For many years, businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent survey showed that 52% of employers are likely to require higher employee contributions for health care coverage this year relative to last year. Suppose the survey was based on a sample of 900 companies likely to require higher employee contributions for health care coverage this year relative to last year.

1. At 95% confidence, compute the margin of error for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answer to four decimal places.)

2. Compute a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answers to four decimal places.)

Answers

The margin of error for the proportion of companies likely to require higher employee contributions for health care coverage is 0.0344. The 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage is ( 0.4823, 0.5577.).

To compute the margin of error for the proportion, we use the formula:

Margin of error = z*√((P(1-P))/n)

where z is the z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96), P is the sample proportion, and n is the sample size. From the information given, we have

P = 0.52 (sample proportion)

n = 900 (sample size)

z = 1.96 (for 95% confidence level)

Substituting these values into the formula, we get

Margin of error = 1.96√((0.52(1-0.52))/900) ≈ 0.0344

Therefore, the margin of error is approximately 0.0344, or 3.44%.

To compute the confidence interval, we use the formula:

Confidence interval = P ± z*(√((P(1-P))/n))

where P, z, and n are the same as in part 1. Substituting these values into the formula, we get

Confidence interval = 0.52 ± 1.96*(√((0.52*(1-0.52))/900)) ≈ (0.4823, 0.5577)

Therefore, we can say with 95% confidence that the true proportion of companies likely to require higher employee contributions for health care coverage this year relative to last year is between 0.4823 and 0.5577.

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A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?

Answers

The volume of this rectangular prism is equal to: B. 8 in³.

How to calculate the volume of a rectangular prism?

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.

Since this rectangular prism is filled with 16 cubes and each cube is a 1/2 inch cube, the dimensions of the rectangular prism is given by;

Dimensions = 16 × (1/2)³ = 2inches.

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 2 × 2 ×  2

Volume of rectangular prism = 8 cubic inches.

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Complete Question:

A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?

A. 2 in³

B. 8 in³

C. 16 in³

D. 32 in³

A circle has an area of 45 square meters. What is the area of a sector with an arc measure of 70 degree?

______m^2

Answers

The area of a sector is 8.75 [tex]m^{2}[/tex].

What is a sector?

A sector is a part of a given circle which is bounded by two radii and an arc. The area of a sector can be determined by;

area of a sector = (θ/ 360)π[tex]r^{2}[/tex]

where r is the radius, and θ is the central angle.

Given a circle whose area is 45 sq. m.; then;

area of a circle = π[tex]r^{2}[/tex]

45 = π[tex]r^{2}[/tex]

r = [tex]\sqrt{\frac{45}{\pi } }[/tex]

Then,

area of a sector = (θ/ 360)π[tex]r^{2}[/tex]

                  = ([tex]\frac{70}{360}[/tex])*π*[tex][\sqrt{\frac{45}{\pi } }] ^{2}[/tex]

                  = [tex]\frac{7}{36}[/tex]*π*45/π

                  = [tex]\frac{7}{36}[/tex]*45

                  = 8.75 sq. m.

The area of the sector is 8.75 [tex]m^{2}[/tex].

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Suppose that the demand of a certain item is x=-0.7p+10.
Evaluate the elasticity at 6.

Answers

The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.

What is the item's demand if elasticity is at 6?

The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)

The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.

Let say Initial quantity demanded is:

x = -0.7(6) + 10

x = 5.8

Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:

= -0.7(6.01) + 10

= 5.793

The % change in quantity demanded will be:

= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%

= [(5.793 - 5.8) / 5.8] x 100%

= -0.12%

As price has changed from 6 to 6.01, we can calculate the percentage change as follows:

% change in price = [(new price - initial price) / initial price] x 100%

= [(6.01 - 6) / 6] x 100%

= 0.17%

Elasticity of demand = (% change in quantity demanded) / (% change in price)

= (-0.12% / 0.17%)

= -0.71

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Triangle D has been dilated to create triangle D′. Use the image to answer the question. image of a triangle labeled D with side lengths of 24, 32, and 40 and a second triangle labeled D prime with side lengths of 6, 8, and 10 Determine the scale factor used. Scale factor of one half Scale factor of 4 Scale factor of 2 Scale factor of one fourth

Answers

The scale factor used is 1/4.

We have,

Length of sides of triangle D 24, 32, and 40.

Length of sides of triangle D' 6, 8, and 10.

So, scale factor

= length of corresponding side in D' / length of corresponding side in D

= 6/24

= 1/4

Thus, the scale factor used is 1/4.

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Ben's Barbershop has a rectangular logo for their business that measures 7(1)/(5) feet long with an area that is exactly the maximum area allowed by the building owner. Create an equation that could be used to determine M, the unknown side length of the logo.

Answers

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Suppose you are a manager of a firm that operates in a duopoly. Recently, the state attorney general fined you and your competitor for price fixing. In your market, firms only set prices, not total quantities to sell. From previous experience you know your competitor has a marginal cost of $4.34. Further, your marginal costs are $4.32. The previous cartel price was $10.00 (when you and your competitor were price fixing). What price level do you now choose to maximize profits? How does minimizing the supernatural impact thie story? Hercules movie 2014 which of the following best explains the mechanism that caused this speciation event in the giant kangaroo rats of population a? Tech outsourcing, inc. , registers a domain name that is the same as, or confusingly similar to, the trademark of tech resourcing corporation and then offers to sell the domain name back to tech resourcing. This is:. What did the rivalry between the U.S. and the Soviet Union stem from ? PCR stands forA. polymerase copy reaction.B. polymerization copying rapidly.C. polymerase chain reaction.C. polymerase chain reaction. A web server has a planned firmware upgrade for Saturday evening. During the upgrade, the power to the building is lost, and the firmware upgrade fails. Which of the following plans should be implemented to revert to the most recent working version of the firmware on the webserver?Alternative planBackout planContingency planBackup plan In a concentration cell, what drives the movement of electrons from the anode to the cathode?. PART B If the survey has a margin oferror of 2.5%, what is the differencebetween the minimum and maximumestimates of the total number ofstudents at the university that useonline tutoring services?A.60B.121C.504D.1007 if one side of the lens is flat, what must the radius of curvature of the other side of the lens be? although los angeles is infamous for its air pollution and smog, there are many parts of los angeles where the air is quite nice, especially in the mountains and by the sea. however, the people who live in these places are disproportionately white; the people who live in the places with the worst air quality are disproportionately likely to be racial and ethnic minorities. this is an example of a. environmental racism. b. conservation. c. environmental justice. d. sustainable development. What things did Muhammad Ali do to reform Egypt? When will social security offices reopen to the public 2022. If 6. 02x10^1c9 he atoms are found in 2. 0 mol of gas, what is the he mole fraction in ppm?. Diagnosis: Alteration in fetal tissue perfusion related to maternal position, epidural, oxytocin, rupture of membranes.Provide: 2nd intervention an employee stock ownership plan represents a. a harvest method of choice. b. an effort to ease investor concerns. c. an opportunity for employees to acquire an ownership interest in their company. d. a good way for a business founder to build his/her position in the company. to ensure antibody-mediated immunity, which actions would the nurse instruct an older client to implement? select all that apply. one, some, or all responses may be correct. To increase the money supply, the federal reserve could. which xxx would make the class people an abstract class?class people { protected: string name; int age; public: xxx};class teacher : public people { private: int experience; public: void printinfo();};class student : public people { private: int grade; public: void printinfo();};group of answer choicesvoid abstract people() const;virtual void printinfo() const;void abstract people() Please please helppp Using the two maps what changes occurred to China between the year 1900 and after the1911 Nationalist Revolution? Select all changes that apply.A.China was conquered by RussiaB.Neighboring Provinces such as Tibet, Mongolia, and Manchuria became larger distinctterritories in 1911.C.Korea is divided between north and south in 1911.D.European Influence was reduced by eliminating the "spheres" of Influence after 1911.