Identify the equation of the circle that has its center at (9, 12) and passes through the origin.

Answers

Answer 1

Answer:  [tex](x-9)^2 + (y-12)^2 = 225\\\\[/tex]

This is the same as writing (x-9)^2 + (x-12)^2 = 225

========================================================

Explanation:

Any circle equation fits the template of [tex](x-h)^2 + (y-k)^2 = r^2\\\\[/tex]

The center is (9,12) which tells us the values of h and k in that exact order.

h = 9

k = 12

To find the radius r, we need to find the distance from the center (9,12) to a point on the circle. The only point we know on the circle is the origin (0,0).

Apply the distance formula to find the distance from (9,12) to (0,0)

[tex]d = \sqrt{ (x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{ (9-0)^2+(12-0)^2}\\\\d = \sqrt{ (9)^2+(12)^2}\\\\d = \sqrt{ 81+144}\\\\d = \sqrt{ 225}\\\\d = 15\\\\[/tex]

The distance from (9,12) to (0,0) is 15 units. Therefore, r = 15

An alternative to finding this r value is to apply the pythagorean theorem. The distance formula is effectively a modified version of the pythagorean theorem.

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

Since h = 9, k = 12 and r = 15, we can then say:

[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-9)^2 + (y-12)^2 = 15^2\\\\(x-9)^2 + (y-12)^2 = 225\\\\[/tex]

which is the equation of this circle.


Related Questions

Write the equation in the point slope form for the line that contains the points (-2,-3), (4,3)

Answers

Answer:

Answer is 4 I think!!

Answer is 3.5-3.7i don’t haven’t any clue to the Braine amd I don’t know!!!!!

The product of two whole numbers is 588 and their sum is 49. What are the two numbers?

Answers

Answer:

Here is your answer. HOPE THIS HELPS YOU! STAY BLESSED.

Answer:

28,21

Step-by-step explanation:

let the numbers be x and y

x+y=49

y=49-x

xy=588

x(49-x)=588

49x-x²=588

x²-49x+588=0

[tex]x=\frac{49 \pm \sqrt{49^2-4*1*588} }{2*1} \\=\frac{49 \pm \sqrt{2401-2352} }{2} \\=\frac{49 \pm\sqrt{49} }{2} \\=\frac{49 \pm 7}{2} \\=\frac{49+7}{2} ,\frac{49-7}{2} \\=28,21[/tex]

Help please ASAP!!!!!

Answers

Answer:

answer is c because you gota tranlate it left

Step-by-step explanation:

Help!
Find the value of x for which ABCD must be a parallelogram.

Answers

3
In a parallelogram, the diagonals (the lines inside from corner to corner) bisect each other. That means the two halves of the diagonal are equal to each other.
So
-9-6x=x-30
-9-6x+6x=x-30+6x
-9=7x-30
21=7x
x=3

A display case of plastic bracelets are marked 13 for $3. If Nate has $60, how many plastic bracelets can Nate get? (assume no other taxes or fees)

Answers

Answer:

$4

Step-by-step explanation:

We can write a ratio to solve

15 stickers       30 stickers

----------------- = -------------

2 dollars           x stickers

Using cross products

15x = 2*30

15x = 60

Divide by 15

15x/15 = 60/15

x = 4

In a group 40% like football ,70% like cricket and 30% like both games

Answers

Answer:

40%

Step-by-step explanation:

40+30+70=140

180-140= 40

please answer this question​

Answers

Answer:

3

Step-by-step explanation:

[tex]log(3x^{3}) - log(x^{2}) = log(\frac{3x^{3}}{x^{2}})\\log(27) - log(x) = log(\frac{27}{x} )\\[/tex]

therefore,

[tex]\frac{3x^{3} }{x^{2} } = \frac{27}{x} \\3x=\frac{27}{x} \\3x^{2} =27\\x= +3\\x=-3[/tex]

however, since logarithms cannot have negative arguments, x can only be +3

i.e. log(-3) is impossible, and will return MATH ERROR on a calculator.

HELP PLEASE
Find the length of AB

Answers

Step-by-step explanation:

hopefully it makes sense and is visible

:)

if two adjacent sides of rectangle having perimeter 21 cm are in the ratio 3:4 what is the area of the rectangle is ...cm ?​

Answers

Let the length and breadth be l and b respectively.
Given,
l/b=3/4
=> l = 3b/4

We have,
P = 2(l+b)
=> 21 = 2(3b/4 + b)
=> 21*2= 7b
=> b = 6cm

Similarly,
l = 4.5cm
Thus, Area = l*b
=> Area = 4.5*6
=> Area = 27cm^2

please answer my question it's urgent​

Answers

a = 16

Solution:common ratio = (-1/8)/(1/16)=-2

a1 = 1/6

n=9

an = a1 (r n-1)a9 = a1

a9 = 1/16 (-2 9-1)

a9 = 1/16 (-28)

a9 = 1/16 (256)

a9 = 16

I hope this helps :)

I'm a little stuck on this, could I get some help? C:

How much would you need to deposit in an account each month in order to have $50,000 in the account in 10 years? Assume the account earns 5% annual interest compounded monthly.

Thank you, and I am eternally grateful.

Answers

9514 1404 393

Answer:

  $321.99

Step-by-step explanation:

Use the annuity formula and solve for P.

  A = P(12/r)((1 +r/12)^(12t) -1) . . . . value of a series of deposits P earning rate r compounded monthly for t years.

  50,000 = P(12/0.05)((1 +0.05/12)^(12·10) -1) = P(240)(0.64700950)

  P = 50,000/155.282279 = 321.99

You would need to deposit $321.99 in the account each month to have $50,000 in 10 years.

3.0040916 to the nearest hundred thousandth

Answers

Answer:

3.004

Step-by-step explanation:

If you were to round it like this: 3.0041, the thousands place would still be 4, so it would come out to be 3.004. Hope that helps!!

Does this picture indicate that < JAC =

Answers

Answer:

No

Step-by-step explanation:

<JAC = 93

< DBE = 90

The two angles are not equal

Help!
Which expression is equivalent?
On edge

Answers

Answer: Choice B

[tex]x^{1/8}y^{8}[/tex]

======================================================

Explanation:

The two rules we use are

[tex](a*b)^c = a^c*b^c[/tex]

[tex](a^b)^c = a^{b*c}[/tex]

When applying the first rule to the expression your teacher gave you, we can say that:

[tex]\left(x^{1/4}y^{16}\right)^{1/2} = \left(x^{1/4}\right)^{1/2}*\left(y^{16}\right)^{1/2}[/tex]

Then applying the second rule lets us say

[tex]\left(x^{1/4}\right)^{1/2}*\left(y^{16}\right)^{1/2} = x^{1/4*1/2}*y^{16*1/2} = x^{1/8}y^{8}[/tex]

Therefore,

[tex]\left(x^{1/4}y^{16}\right)^{1/2} = x^{1/8}y^{8}[/tex]

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

In short, we just multiplied each exponent inside by the outer exponent 1/2.

So that explains why the exponents go from {1/4,16} to {1/8,8} for x and y in that exact order.

help plz answer quickly

Answers

Answer:

plane EBG

Step-by-step explanation:

plane C is also named plane EBG

Answer:

[tex]\\ \sf\longmapsto Plane EBG[/tex]

We can't name it EBF as it is a axis and coplanar points

Also nEF is not a satisfactory name .

So the correct option is C

Jimmy's dog weighed 60 pounds 4 months ago. Since then his weight has increased by 6% How much does Jimmy's dog weigh now

Answers

Answer: 3.6

Step-by-step explanation:

Answer:

63.6 pounds

Step-by-step explanation:

Jimmy's dog's weight was 60 pounds 4 months ago and now it is weighing 6% heavier.

So 6% of 60 is

[tex]\frac{x}{60} *100=6[/tex]

x=360/100

x=3.6

So Jimmy's dog weighs 60+3.6=63.6 pounds

evaluate the expression

Answers

Step-by-step explanation:

13

[tex]3 + (20 \div 5) - ( {2}^{2}) [/tex]

[tex]3 + 4 - 4 = 3[/tex]

15

[tex] \frac{10 - {3}^{2} }{20 - (3 \times 4)} [/tex]

[tex] \frac{10 - 9}{20 - 12} [/tex]

[tex] \frac{1}{8} [/tex]

A trapezoid has one base measuring 12', and the other measuring 13'8". What is the area in square feet if the height of the trapezoid is 9'4"?

(Remember for trapezoids A= (b1 + b2)/2 x h

Answers

Answer:

Step-by-step explanation:

buzhou一=12212+13。8.12+13.8=25.8          25.8x9.4=?242.52242.522

The area of the trapezoid is given by A = 121.26 feet²

What is a trapezoid?

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be represented as A

Now , the equation will be

Let the height of the trapezium be H = 9.4 feet

The shorter base of the trapezium a = 12 feet

The longer base of the trapezium b = 13.8 feet

Now , Area of Trapezoid = ( ( a + b ) h ) / 2

On simplifying the equation , we get

Area of Trapezium A = ( ( 13.8 + 12 ) 9.4 ) / 2

Area of Trapezium A = 121.26 feet²

Hence , the area of trapezium is 121.26 feet²

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Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) {-4, 8/3, -16/9, 32/27, -64/81, . . . } an =

Answers

Step-by-step explanation:

a1 = -4 = -4/1, a2 = 8/3

r = a2/a1 = (8/3) / (-4/1) = -2/3

the formula :

an = a1. r^(n-1)

so,

an = (-4). (-2/3)^(n-1)

Step-by-step explanation:

[tex]-4, \dfrac{8}{3}, -\dfrac{16}{9}, \dfrac{32}{27}, -\dfrac{64}{81},..., (-1)^n\dfrac{2^{n + 1}}{3^{n - 1}}, ...[/tex]

Two cars start at the same point. One travels north at 65 km/h and the other travels east at 50 km/h. How far are they apart after 30 minutes?​

Answers

Answer:

1they are 15 kilometers apart

2. A doctor treated 2000 patients over a period of time. If he worked for 5 hours a day and spent 15 minutes on each patient how many days did the doctor spend to treat all patients?

Answers

Answer:

The answer is 6000 days.

Find the area of the shaded region.​

Answers

Step-by-step explanation:

find the area of the big semicircle and the small semicircle.minus the area of the small semicircle from the big semicircle.

now find the area of the other semicircle on top of the big semicircle.

add your results

area of semicircle=1/2(pir^2)

What is the area of a circle with a diameter of 8 meters? Use 3.14 for pi, nothing else. Express in pi term and number term.

Answers

The two answers you are looking for are 16π m² and 50.24 m².

Solution:

Finding the area of the circle,

First, knowing what the area of a circle formula is:

A=πr²

Since knowing that the radius is half the length of the diameter,

If the diameter is 8, then the radius must be 4.

A=π(4)²

A=16π m²

Now, you have the first answer. If you want to express it differently,

Using 3.14 as pi,

So, therefore,

A=16(3.14)

A=50.24 m²

So, now, we can conclude that the two answers you are looking for for the area of this circle are 16π m² and/or 50.24 m².

Answer:

16pi and 50.24 m squared

Step-by-step explanation:

six quarts of paint is equally shared among 9 artists. how many quarts of paint does each artist get?

Answers

Answer:

2/3 quarts

Step-by-step explanation:

Paint used by 9 artists = 6 quarts

So, paint used by 1 artist if shared equally among the 9 artists

= 6 quarts/9

= 2/3 quarts

= 0.6666...... quarts

Rounding to the nearest hundredth, each artist would get approximately 0.67 quarts of paint.

To determine how many quarts of paint each artist gets when six quarts of paint are equally shared among nine artists, we can divide the total amount of paint by the number of artists. 6 quarts ÷ 9 artists = 0.6667 quarts per artist

To "equally share" means to divide or distribute something equally among a group of individuals or entities. It implies that each person or entity involved receives an equal portion or share of the item being distributed. This division ensures fairness and equal opportunities for everyone involved. The goal is to ensure that each recipient receives an equal amount or proportion of the item being shared.

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Use a number line or place value to round each number to the place of the underlined digit

Answers

you didn't put a picture in,

Solve using substitution.


6x + y = 7

8x + 9y = 17

(_,_)


Please help me I really need it

Answers

You take the first equation and make a value for y. So 6x + y =7 change it to :
y = -6x + 7
Now in the second equation replace the “y” with -6x +7 this is what it means to use substitution method . Your combined equation will now be :
8x + 9(-6x + 7) =17
Now do distributive property and you get :
8x + -54x +63 =17
Now combine like terms ;
-46x +63 =17
-46x =-46
x = 1
Now replace 1 for X value and we can get the value of Y .
Y=1
X=1

Find NL. Not sure to to solve this.

Answers

Answer:

NL= 2 × HI

x+24 =2 × (X+16)

x+24=2x + 32

2x-x= 24-32

x= – 8

NL=x+24 = –8 +24= 16

So ; NL= 16

I hope I helped you^_^

X+24 =2(x+16)
X +24 = 2x +32
24-32= 2x-x
X = -8
NL = x+24
NL = -8+24
NL = 16

One week, Rachel earned $250. She spent $120 on food, $30 on miscellaneous items, and saved the rest.

If Rachel makes a pie chart showing how she spends her money, the central angle for the food sector would be __________.


187°


173°


90°


144°

Answers

250 is the total
120 is 48% of 250
A pie chart is a complete circle which is 360 degrees and 48% of 360 is 172.8 round that up to 173 degrees

The answer is 173

What is the value of X minus Y if x equals 9 and Y equals -20

Answers

x-y = (9)-(-20) =29

doneeee

1 year is what fraction of a decade?

Answers

Answer:

It is 1/10

Step-by-step explanation:

One decade has 10 years

[tex]{ \sf{1 \: decade = 10 \: years}} \\ { \sf{ \frac{1}{10} \: decade = 1 \: year}}[/tex]

Answer:

10% , 1/10, or 10/100

Step-by-step explanation:

There are 10 years in a decade

1/10 represents the 1 year out of the 10!

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