Convert the equation x2 + 4y2 + 2x + 24y + 21 = 0 into standard form.

Answers

Answer 1

Answer:

(X+1)²+4(y+3)² = (√-20)²

Step-by-step explanation:

The standard form of expressing equation ic;

(x-a)²+(y-b)² = r²

Given the expression

x²+4y²+2x+24y+21 = 0

Collect the like terms

x²+2x + 4y²+24y+21 = 0

Completing the squares

x²+2x +(2/2)² + 4(y²+6y)+21 = 0+(2/2)²

x²+2x +(2/2)² + 4(y²+6y+(6/2)²)+21 = 0+(2/2)²

x²+2x +1 + 4(y²+6y+(3)²)+21 = 0+1

x²+2x +1 + 4(y²+6y+9)+21 = 0+1

x²+2x +1 + 4y²+24y+36+21 = 0+1

x²+2x +1 + 4(y²+6y+9)+21 = 0+1

x²+2x +1 + 4(y+3)²+21 = 0+1

(X+1)²+4(y+3)² = 1 - 21

(X+1)²+4(y+3)² = -20

(X+1)²+4(y+3)² = (√-20)²


Related Questions

A fan oscillates 250* and can be felt from a distance of 4 feet away . To the nearest tenth what area of the room can feel the wind from the fan? Use 3.14 for pi .

Answers

Answer:

[tex]A=256.67ft^2[/tex]

Step-by-step explanation:

From the question we are told that:

Fan oscillates [tex]\theta=250[/tex]

Distance [tex]d=>Raduis\ r=4 feet[/tex]

Since

 [tex]250\textdegree =180\textdegree +70\textdegree[/tex]

Generally the equation for the area A is mathematically given by

 [tex]Area=Area\ of\ semi\ circle\ + area\ of\ 70\textdegree sector[/tex]

 [tex]A=A_{sm}+A_{70\textdegree}[/tex]

Where

 [tex]A_{sm}=\frac{1}{2} \pi r^2[/tex]

 [tex]A_{sm}=\frac{1}{2} 3.14 4^2[/tex]

 [tex]A_{sm}=25.12ft^2[/tex]

 [tex]A_{70\textdegree}=\frac{1}{2}r^2 \frac{70\textdegree}{360\textdegree}[/tex]

 [tex]A_{70\textdegree}=\frac{1}{2}*4^2* \frac{70\textdegree}{360\textdegree}[/tex]

 [tex]A_{70\textdegree}=1.55ft^2[/tex]

Therefore the area A is given as

 [tex]A=A_{sm}+A_{70\textdegree}[/tex]

 [tex]A=25.12ft^2+1.55ft^2[/tex]

 [tex]A=256.67ft^2[/tex]

Grace’s garden is shown below. She is going to buy bags of soil that cover 75 square feet each. How many bags of soil will she need for her entire garden? Use 3.14 for pi.


A. 4 bags

B. 5 bags

C. 6 bags

D. 7 bags

Answers

Answer: C. 6 bags

Step-by-step explanation:

To solve this, you need to calculate the area of every shape in the garden and then sum them up.

Semi circle:

Area of semi-circle = (π * radius²) / 2

Radius = Diameter/ 2 = 18/2 = 9 feet

Area = (3.14 * 9²) / 2

= 127.17 ft²

Rectangle:

= Length * Width

= 18 * 8

= 144 ft²

Triangle

= 1/2 * base * height

= 1/2 * 18 * 18

= 162 ft²

Added up:

= 127.17 + 144 + 162

= 427.17 ft²

If each bag covers 75 ft² each, the number of bags needed is:

= Area to cover / Coverage per bag

= 427.17 / 75

= 5.7

= 6 bags

Choose all expressions that are equivalent to
to 5/7

Answers

Answer:

C,D,E are equivalent to 5/7

Solve 1/2x times 1/4x-18=6.

Answers

Answer:

The answer is 48

Step-by-step explanation:

Have a nice day

9272827292738hellp plssss

Answers

Answer: B. Each month, Zohal read more books than the month before

Step-by-step explanation: The bars went up each month getting higher and higher. Hope this helps!!

Answer:

B.

is the answer

hope it helprd

PLEASE I NEED THE ANSWER IN THE NEXT MINUTE

Answers

Answer:

Step-by-step explanation:

A

Answer:

96

Step-by-step explanation:

:)

Tiara, a quality assurance inspector at a chocolate factory, checks for product quality using a random sample of 18 pieces of chocolate from a batch of 60, wity 17 white chocolate and 43 dark chocolates. Let p be the proportion of white chocolates in the sample. Part A: Is the 10% condition met in thjs case? Justify your answer. Part B: Is the Normal condition met in this case? Justify your answer.​

Answers

Answer:

Part A

The 10% rule is not met

Part B

The normal condition is not met

Step-by-step explanation:

The given data of the pieces of chocolate are;

The number of chocolates in the sample, n = 18

The number of white chocolate in the batch = 17

The number of dark chocolates in the batch = 43

Given that [tex]\hat p[/tex] is the proportion of white chocolates in the sample, we have;

The proportion of white chocolates in the batch, p = 17/60 = 0.28[tex]\overline 3[/tex]

Part A

The 10% condition states that the size of the sample should be less than or equal to 10% of the population because taking samples without replacing them does not result in independent Bernoulli trials

The given sample size, n = 18, which is 18/60×100 = 30% > 10% of the batch, therefore, the 10% rule is not met in the present situation

Part B

The normal approximation can be assumed when we have;

n·p > 10 and n·p·(1 - p) > 10

By plugging in the values for 'n' and 'p', we have;

p = 0.28[tex]\overline 3[/tex] = 17/60

n·p = 18 × 17/60 = 5.1 < 10

n·p·(1 - p) = 18 × 17/60 × (1 - 17/60) = 3.655 < 10

Therefore the normal condition is not met.

find the area of the irregular figure. PLEASE!!
The sides are: 3 in, 4 in, 4 in, 5 in, 7 in, 9 in
geometry

Answers

Answer:

A = [84]in^2

Step-by-step explanation:

5 x 3 = 15

4 x 2 = 16

9 + 4 = 13 x 4 = 52

52 + 15 + 16 = 84in

Classify the polynomial.

2x^5+x^2-2x+4

a. quintic polynomial
b. cubic polynomial
c. quadratic monomial

Answers

It would probably be A

HELP , TIMES ALMOST UP!!!!!!

Answers

Answer:

0.8660254 or √3/2

Step-by-step explanation:

Answer:

√3/2

Hope this helps

Ricky and Lucy are 40 miles apart on bicycles heading towards each other on the same road. Ricky bicycles at 8 mph and Lucy rides at 6 mph. In how many hours will they meet?

Answers

Answer:

2.86 hours

Step-by-step explanation:

Ricky and Lucy are 40 miles apart on bicycles heading towards each other on the same road. Ricky bicycles at 8 mph and Lucy rides at 6 mph. In how many hours will they meet?

Speed = Distance/time

Distance = Speed × time

t = ?

Hence,

8mph ×t + 6 mph × t = 40 miles

8t + 6 t = 40 miles

14t = 40 miles

t = 40/14

t = 2.86 hours

They will meet in 2.86 hours

Need help finding the length of AC

Answers

Answer:

I would have to say that the length of AC is 22.5

help pleass alot of points​

Answers

Answer:

44

Step-by-step explanation:

[tex]11 + 11 + 11 + 11 = 11 * 4 = 44[/tex]

The perimeter of the square is 44 kilometers

i need help please help asap

Answers

Answer:

Try 11

Step-by-step explanation:

11 -33+63-38=3

Please help and don’t put a random answer.

Answers

Answer:

The answer is 13/4

Step-by-step explanation:

I divides and cross miltiplied.

Which statement correctly describes gravity?

an attractive force that acts between all objects through contact
an attractive force that acts between all objects without contact
a repulsive force that acts between all objects through contact
a repulsive force that acts between all objects without contact

Answers

Answer:

an attractive force that acts between all objects without contact

Step-by-step explanation:

an attractive force that acts between all objects without contact

You are pulled down by gravity when you jump

Answer:

an attractive force that acts between all objects without contact

The force of gravity, first discovered by Isaac Newton, is one of the four fundamental forces. It is a force that is always attractive, and it is exerted between all objects that have mass. Also, the force is exerted even when the two objects are not in contact.

The magnitude of the force of gravity between two objects is given by where

G is the gravitational constant

m1 and m2 are the masses of the two objects

r is the distance between the two objects

Step-by-step explanation:

MRK ME BRAINLIEST PLPZZZZZZZZZZZZZZZZ

I don't know how to do this please help me!
Find the measure of an angle between 0 degrees and 360 degrees coterminal with an angle of -244 degrees in a standard position.

Answers

Answer:

to find the equivalent positive angle of a negative angle, just add 360 to it until it becomes positive and is between 0 and 360 degrees. -244 + 360 = 116.

Step-by-step explanation:

Which equation represents the line that is perpendicular to and passes through (-6,-9)?
A.
x = -9
B.
x = -6
C.
y = -9
D.
y = -4

Answers

Answer:

y = -9

Step-by-step explanation:

Complete question;

Which equation represents the line y = 1/4 that is perpendicular to and passes through (-6,-9)?

The equation of the line in point slope form is y-y0 = m(x-x0)

Given the equation y = 1/4, the slope of the line is zero

Substitute the slope and the point into the formula;

y -(-9) = 0(x-(-6)

y + 9 = 0

y = -9

Hence the required equation is y = -9

Answer:

C.y = -9

Step-by-step explanation:

Reduce each of the following fractions to its simplest form. a. 12⁄18 b. 48⁄54 c. 27⁄90 d. 63⁄77 e. 24⁄32 f. 73⁄365

Answers

Answer: A. 2/3 B. 8/9 C. 3/10 D. 9/11 E. 3/4 F. 1/5

Step-by-step explanation:

What is the overlap of Data Set 1 and Data Set 2?


high

moderate

low

none

Answers

Answer: Low

The overlap of data set 1 and data set 2

Please help! I'll give you brainliest if you get it right!
Write the piecewise function for the graph.

Answers

Answer:

In the picture

Step-by-step explanation:

First, find a function for each line.

-2x - 2 fits the green line because for every x value, y is -2(x) - 2.

2x + 1 fits the red line because for every x value y is 2(x) + 1.

You also need to include "if." -2x -2 if x < 0.

For the red line, the dot is closed so if x ≥ 0.

Find the missing sign.
Solve for X

Answers

Answer:

x = 17.9

Step-by-step explanation:

sin 42° = 12/x

x = 12/sin 42°

x = 17.9

Answer:

17.9

Step-by-step explanation:

> sin 42° = 12/x

> x = 12/ sin 42°

> x = 17.9

a day in the month of january is randomly selected. what is the probability of selecting a prime number?

Answers

Answer:

70 percent susheeiiesoosos

Ms. Powell bought 12 cookies for $4.00 and Ms. Malley bought 8
cookies for $3.50. How much did each person pay for a cookie? And who
had the better deal?

Answers

Answer:

Ms. Powell paid around 33 cents for each cookie

Ms. Malley paid around 43 cents for each cookie

Ms. Powell had the better deal

Step-by-step explanation:

Divide the amount paid with the amount of cookies bought so 4 ÷ 12 = 0.3333... and 3.50 ÷ 0.4375...

I hope this helped!

1) Approximately ¢33 per cookie

2) Approximately ¢29 per cookie

Ms. Powell had a better deal

ressions, Equations, and Relationships - Readines
What is the approximate value of x in this equation?
6x + 14 = 7 - X

Answers

Answer:

x=-3

Step-by-step explanation:

Henry takes out a $20,250 student loan to pay for college tuition this year. The interest rate he pays is 6% for 15 years. How much interest will he owe?

Answers

Answer:

$1215 x 15 = $18225 This is over 15 years.

You start at (9, 3). You move right 1 unit. Where do you end?

Answers

Answer:

(10, 3)

Step-by-step explanation:

What is the distance between the points (7, -3) and (-5, 6)?

Answers

Answer:

The distance between the two points is: √145≈12.04 to 2 decimal places.

Step-by-step explanation:

If using a grid it will make the answer easier to solve.

Answer:

21units

12 units + 9 units

ASAP someone please help. Given the following angle measurements for a triangle, find the remaining angle.
a. 53, 58
b. 28, 47
c. 65, 25

Answers

Answer:

c

Step-by-step explanation:

use the figure below to answer the question

Answers

Answer:

Sin(Ф) = Opposite / Hypotenuse

We know that Opposite = 6, and

Hypotenuse = 3/4 or 0.75

So,

Sin(Ф) = 6 / 0.75

Sin(Ф) = 8

So the value of sin of Ф would be 8

Hope this helps!

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