In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2.

On a coordinate plane, circle Q is centered at the origin with radius r. Triangle P Q S is shown. Point Q is at (0, 0) and points P is at (x, y). The length of Q P is r, the length of P S is y, and the length of Q S is x. Angle P S Q is a right angle.

If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?

(h + x)2 + (k + y)2 = r2
(x – h)2 + (y – k)2 = r2
(k + x)2 + (h + y)2 = r2
(x – k)2 + (y – h)2 = r2 7-foot radius.

Answers

Answer 1

Based on the information provided, the equation of this new circle is equal to: B. (x - h)² + (y - k)² = r²

The equation of a circle.

Mathematically, the equation of a circle can be derived by using Pythagorean theorem;

x² + y² = r²

Where:

h and k represents the coordinates at the center.r is the radius of a circle.

After translating h units along the x-axis and k units along y-axis on a coordinate plane, the equation of this new circle is given by:

(x - h)² + (y - k)² = r²

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In The Diagram, A Circle Centered At The Origin, A Right Triangle, And The Pythagorean Theorem Are Used
Answer 2

Answer: B) (x – h)2 + (y – k)2 = r2

Step-by-step explanation:


Related Questions

Select the correct answer.
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship?
A.
12 miles per hour
B.
16 miles per hour
C.
45 miles per hour
D.
51 miles per hour

Answers

B 16 miles an hour

Hope this helps

9
If g = 8, what is the value of the expression 2+3?
OA.
B.
815
(11)
OC. 7
OD. 19

Answers

The value of the expression, g/2 + 3 when x = 8 is: 7.

How to Evaluate an Expression?

Given the expression, g/2+3, to find it's value when g = 8, plug in the value of g into the expression and solve.

g/2 + 3

8/2 + 3

Divide

4 + 3

= 7

The value of the expression is: 7.

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Determine whether each set of ordered pairs shown below is from a geometric sequence or from an arithmetic sequence.

{(-3, 7.5) , (-2, 10) , (-1, 12.5)}

Write the equation of the graph for the set of ordered pairs.

{(1, 150) , (2, 112.5) , (3, 84.375)}

Write the equation of the graph for the set of ordered pairs.

Answers

Using sequences concepts, it is found that:

The set of ordered pairs {(-3, 7.5) , (-2, 10) , (-1, 12.5)} is an arithmetic sequence with equation a(n) = 15 + 2.5d.The set of ordered pairs {(1, 150) , (2, 112.5) , (3, 84.375)} is a geometric sequence with [tex]a_n = 150(0.75)^{n-1}[/tex].

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a(n) = a(0) + nd[/tex]

The sequence {(-3, 7.5) , (-2, 10) , (-1, 12.5)} continues with points (0, 15), (1, 17.5), and so on, hence the first term and the common ratio are given, respectively, by:

a(0) = 15, d = 2.5.

Hence the equation is:

a(n) = 15 + 2.5n.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

For the sequence {(1, 150) , (2, 112.5) , (3, 84.375)}, the first term and the common ratio are given, respectively, by:

[tex]a_1 = 150, q = \frac{112.5}{150} = \frac{84.375}{112.5} = 0.75[/tex]

Hence the equation is given by:

[tex]a_n = 150(0.75)^{n-1}[/tex]

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please help me i need help quick

Answers

Answer:

x = -2

y = -6

Step-by-step explanation:

Equating the equations :

x - 4 = 4x + 23x = -6x = -2

y = -2 - 4y = -6
y=x-4y=4x+2

Equate both

x-4=4x+2-4-2=4x-x-6=3xx=-2

And

y=-2-4=-6

Graph attached

What is the expression for f(x) when we rewrite 36^x•6^(x-2) as 6^f(x)?
Answer: 3x-2

Answers

Using the given information, the expression for f(x) is 3x - 2

Writing an expression

From the question, we are to determine the the value of f(x)

The given expression is

36^x•6^(x-2)

That is

[tex]36^{x} \times 6^{x-2}[/tex]

This can be expressed as

[tex]6^{2x} \times 6^{x-2}[/tex]

Applying one of the laws of indices, we get

[tex]6^{2x+x-2}[/tex]

= [tex]6^{3x-2}[/tex]

Since the expression was rewritten as

[tex]6^{f(x)}[/tex]

By comparison,

f(x) = 3x - 2

Hence, the expression for f(x) is 3x - 2

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Sienna is solving the quadratic equation by completing the square.

3x2 + 9x – 4 = 0

3x2 + 9x = 4

A(x2 + 3x) = 4

Answers

Answer:

See below

Step-by-step explanation:

3 (x^2 + 3x) = 4

3 ( x + 3/2)^2   = 4 + 27/4  

Solve the equation for x.
√x-5 = x-11

Answers

Your answer would be 14

Answer:

√x-5 = x-11 = 9.

Step-by-step explanation:

Isolate the radical, then raise each side of the equation to the power of its index.

x = 9 Solve the equation for x.

[tex]\sf\large\green{\underbrace{\red{Befikra*}}}:[/tex].

The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms​

Answers

First term f = 1

If first four terms are f, f + d, f + 2d, f + 3d

f + f + d + f + 2d + f + 3d = 100

4f + 6d = 100 (divided by 2 , both sides )

2f + 3d = 50

2 + 3d = 50

3d = 50 – 2

3d = 48

d = 48/3

d = 16

The arithmetic sequence is 1, 17, 33, 49, ………….

Answer:

[tex]\sf\large\blue{\underbrace{\red{itz \: jass*}}}:[/tex]

Step-by-step explanation:

[tex]\sf\large\green{\underbrace{\red{hlo \: \: sat \: shri \: akal \: ji \: \: \: *}}}:[/tex]

Which of the following angles are congruent?

Answers

Answer:

C

Step-by-step explanation:

if you rotate either of the triangles by 180 degrees, compare the angles and you will see that the answer is C

Figure B is a scaled copy of figure A.
What is the scale factor from figure A to figure B

Answers

Answer:

1/3

Step-by-step explanation:

We multiply 33(Figure A side) by 1 /3 to get 11(Figure B side).

Which angles are vertical angles select two options

Answers

The pair of the vertically opposite angles are ∠ABC = ∠DBE and ∠CBD = ∠ABE Then the correct options are B and E.

The complete question is attached below.

What is Vertically opposite angle?

When two lines intersect, then their opposite angles are equal.

The diagram is given below.

∠ABC = ∠DBE

∠CBD = ∠ABE

Then the correct options are B and E.

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What is the solution for the system of x - y = -1 and 2x - 5y = -5 ?
Show your work.

Answers

Step-by-step explanation:

please mark me as brainlest

x - y = -1 multiply by 5

we get 5x -5y = -5

subtract the equations:

5x - 5y = -5

-

2x - 5y = -5

5x - 5y -(2x - 5y ) = - 5 - - 5

5x - 5y - 2x + 5y =0

3x = 0

x = 0

2(0) - 5y = -5

- 5y = -5

y = 1

Let g be the piecewise defined function shown.

g(x)=
x + 4, −5 ≤ x ≤ −1
2 − x, −1 < x ≤ 5

Evaluate g at different values in its domain.

g(−4) =

g(−2) =

g(0) =

g(3) =

g(4) =

Answers

Answer:

g(4)= -2

g(-2)= 2

g(0)= 2

g(3)= -1

g(-4)= 0

Step-by-step explanation: See attachment, and don’t forget to check just in case ;)

Answer:

g(−4) = 0

g(−2) = 2

g(0) = 2

g(3) = -1

g(4) = -2

Step-by-step explanation:

Please Thank!

a fence is 2m high by 33m long, if a gallon of paint is enough to paint 2.5m^2, how many gallons will be used to paint the entire fence?

Answers

The number of gallons of paint needed to paint the entire fence is 26.4 gallons.

Area of rectangle

Length = 33 mWidth = 2 m

Area = length × width

= 33 m × 2 m

= 66 square meter.

A gallon of paint = 2.5 m²

Number of gallons of paint needed = 66 square meter / 2.5 m²

= 26.4 gallons

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Base area = 18 ft²
Volume=
11 ft
7

Answers

Answer:

nhddhdbndbd

Step-by-step explanation:

jh h benrheoek

Can some help me with this, it’s urgent pls? It’s geometry

Answers

6. the name is circle x (due to the central point)
7. the diameter is segment WY
8. radius is 1/2 of the diameter so 1/2(15) = 7.5 meters
9. diameter is 2 times the radius so 2(4) = 8 cm
10. segment XW, segment XZ, segment XY
11. arc YW, arc WZ, arc ZY

The circle below is centered at the origin and has a radius of 7. What is its
equation?
A ²+2²=7
B. x²-y²=7
C. x²-²2²=49A
D. x² + y² = 49

Answers

Answer:

x² + y² = 49

Step-by-step explanation:

The equation for a circle is: x² + y² = r²

here, we know our circle's radius (r) to be 7

So, the equation for our circle is:                  {replace "r" with value}

x² + y² = 7²

which can be simplified to:

x² + y² = 49

hope this helps!! have a lovely day :)

help please
Find the sum or type
"impossible"
[3 -8] + [4 -5 -6]

Answers

The answer is negative 12

Consider the systems of equations below. determine the number of real solutions for each system of equations. system a has real solutions. system b has real solutions. system c has real solutions.

Answers

System A has 2 real solutions, System B has 0 real solutions and System C has 1 real solution.

Given a system of equations for A is x²+y²=17 and y=-(1÷2)x, a system of equations for B is y=x²-7x10 and y=-6x+5 and a system of equations for C is y=-2x²+9 and 8x-y=-17.

For system A,

The two systems of equations are

x²+y²=17            ......(1)

y=-1÷2x             ......(2)

Substitute the value of equation (2) into equation (1) as

x²+(-x÷2)²=17

x²+(x²÷4)=17

Simplify the above equation by taking L.C.M. as

(4x²+x²)÷4=17

5x²=68

x²=68÷5

x=±3.688

Find the value of y by substituting the value of x in equation (2).

When x=3.688 then y is

y=-(1÷2)×3.688

y=-1.844

And When x=-3.688 then y is

y=-(1÷2)×(-3.688)

y=1.844

Thus, the points where the equations of system A intersect each other is (3.688,-1.844) and (-3.688,1.844)

So, the system of equations of A has 2 real solutions.

For system B,

The two systems of equations are

y=x²-7x+10            ......(3)

y=-6x+5                ......(4)

Substitute the value of equation (4) into equation (3) as

-6x+5=x²-7x+10

x²-7x+10+6x-5=0

x²-x+5=0

Simplify the above quadratic equation using the discriminant rule,

x=(-b±√(b²-4ac))÷(2a)

Here, a=1, b=-1 and c=5

Substitute the values in the discriminant rule as

x=(1±√(1-4\times 5\times 1))÷2

x=(1±√(-19))÷2

x=(1±√(19)i)÷2

Here, the value of x goes into the complex.

So, the system of equations of B has 0 real solutions.

For system C,

The two systems of equations are

y=-2x²+9            ......(5)

8x-y=-17            ......(6)

Substitute the value of equation (6) into equation (5) as

8x-(-2x²+9)=-17

8x+2x²-9+17=0

2x²+8x+8=0

Simplify the above quadratic equation using factorization method as

2x²+4x+4x+8=0

2x(x+2)+4(x+2)=0

(2x+4)(x+2)=0

x=-2,-2

Find the value of y by substituting the value of x in equation (5).

When x=-2 then y is

y=-2(-2)²+9

y=-8+9

y=1

Thus, the point where the equations of system C intersect each other is (-2,1)

So, the system of equations of C has 1 real solutions.

Hence, the system of equations for A is x²+y²=17 and y=-(1÷2)x having 2 real solution, a system of equations for B is y=x²-7x10 and y=-6x+5 having 0 real solution and a system of equations for C is y=-2x²+9 and 8x-y=-17 having 1 real solution.

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What is the scale factor of this dilation?

Answers:
A. 1/2
B.3/5
C.1 2/3
D.2

Answers

Answer:

3/5

Step-by-step explanation:

scale factor of ab to A'B'

AB:A'B'

5 : 3

in fraction the scale

factor is 3

5

heance a reduction.

hope it helps thank me later

#galadohannadivine29

#carry on learning

What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning

Answers

Answer:

60 ft

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{AD}[/tex] = [tex]\frac{30}{AD}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

AD = 60 ft

Which expression is equivalent to (3^2) ^-2

Answers

[tex](3^{2} )[/tex]^-2=(9)^-2=1/9^2=1/81

hope it helps!

Given line AC is tangent to circle O.
If m(arc BY)= 44, enter the m∠YAC.
(The figure is not drawn to scale.)

Answers

The measure of <YAC from the figure is. 68 degrees

Circle theorem

The given figure is made up of line and angles.

Since the line AC is tangential to the circle, hence <BAC = 90 degrees and;

<BAY + <YAC = 90degrees

Determine the measure of <BAY

<BAY = 1/2(arcBY)

<BAY = 1/2(44)

<BAY = 22degrees

From the expression above;

<YAC = 90 - 22

<YAC = 68 degrees

Hence the measure of <YAC from the figure is. 68 degrees

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If anyone could help me, it would be greatly appreciated!

Answers

Answer: [tex]x=65^{\circ}, y=65^{\circ}, z=65^{\circ}[/tex]

Step-by-step explanation:

All radii of a circle are congruent, so by the base angles theorem

z = y = (180-50)/2 = 65.

Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.

If side c measures 32.3 units long, how long is side a?

Answers

Answer:

16.15

Step-by-step explanation:

sin(30) = a / c

a = c * sin(30)

a = 32.3 * 0.5

a = 16.15

40. Se desea distribuir las bancas dentro de un salón de clases cada 1.5 m como
se muestra en la imagen, ¿de qué forma se puede saber el área requerida para
conservar la separación de las bancas?
1.5m

Answers

La forma adecuada para saber el área requerida para conservar la separación de las sillas es multiplicar (7.5) (4.5) opción B.

¿Cómo calcular el área requerida para mantener la separación?

Para identificar la operación necesaria para calcular el área requerida para ubicar las sillas con su respectiva separación de 1.5 metros es:

7.5 × 4.5 = 33.75

Esta expresión nos va a permitir calcular el área necesaria debido a que la separación entre sillas es 1.5 metros y tenemos 6 sillas a lo largo y 4 sillas a lo ancho, es decir:

1.5 × 5 = 7.5 distancia a lo largo1.5 × 3 = 4.5 distancia a lo ancho

Nota: Esta pregunta está incompleta porque falta la imagen y las opciones. Aquí está la información faltante:

Opciones:

A. Multiplicar (6)(4)

B. Multiplicar (7.5)(4.5)

C. Multiplicar (9)(6)

D. Multiplicar (9.5)(4.5)

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2 3/5t + 5 1/4t + 4t

Answers

Answer:

11 17/20t

Step-by-step explanation:

add the whole numbers first then add the numbers in fraction then there you get your answer.

The expression 55 + 14m - 2n + 3p has _________ terms.

1. 3
2. 4
3. 2
4. 5

Answers

The expression has 3 terms

Select the correct answer.
Which value of x makes this equation true?
-12x2(x + 9) = 5(x + 4)
O A.
OB.
O C.
O D.

Answers

Answer:

B. -2

Step-by-step explanation:

-12x -2(x+9) = 5(x+4)

*ALWAYS REMEMBER YOUR BODMAS*

-12x -2x - 18 = 5x + 20

*group the like terms*

-14x - 5x = 20 + 18

-19x = 38

x = -2

The value of x that makes the equation true is: x = -2.

B. -2.

Here, we have to find the value of x that makes the equation true, we need to solve for x.

Let's solve the equation step by step:

-12x - 2(x + 9) = 5(x + 4)

Distribute the -2 and 5 on the right side of the equation:

-12x - 2x - 18 = 5x + 20

Combine like terms on both sides:

-14x - 18 = 5x + 20

Move the variable terms (5x) to one side of the equation and the constant terms to the other side.

Let's subtract 5x from both sides:

-14x - 5x - 18 = 5x - 5x + 20

-19x - 18 = 20

Move the constant term (-18) to the other side of the equation.

Let's add 18 to both sides:

-19x - 18 + 18 = 20 + 18

-19x = 38

Finally, divide both sides by -19 to isolate x:

x = 38 / -19

x = -2

So, the value of x that makes the equation true is: x = -2.

B. -2.

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Select the correct answer.
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship?
A.
12 miles per hour
B.
16 miles per hour
C.
45 miles per hour
D.
51 miles per hour

Answers

B 16 the boat is traveling 16 miles an hour
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