Consider a circle whose equation is x2 + y2 + 4x - 6y - 36 = 0. Which statements are true? Check all that appl"
To begin converting the equation to standard form, subtract 36 from both sides.
mu To complete the square for the x terms, add 4 to both sides.

Answers

Answer 1

Answer:

To complete the square for the x terms, add 4 to both sides.

To convert the given equation of the circle to standard form we should do as follows.

1. Add 36 to both sides of the equation.

\(x^{2} +y^{2}+4x-6y-36+36=36\\ x^{2} +y^{2}+4x-6y=36\)

2. We order the terms according to their variables.

\(x^{2} +4x +y^{2}-6y=36\)

3. Divide the linear term by 2, then elevate it to the square power.

\(x^{2} +4x + (\frac{4}{2} )^{2} +y^{2} -6y+(\frac{6}{2} )^{2} =36\)

4. Solve operations, and add the same units to the other side of the equation.

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

5. Now, we sum costant terms, and factor both trinomials.

\((x+2)^{2} +(y-3)^{2} =49\)

As you can observe, the circle has center at (-2,3) and it has a radius of 7 units.

Notice that the second choice is correct, because we added 4 units to both sides to complete the square for the x terms.


Related Questions

Solve for x, given that the area is 120.

**Show work please(step by step)**

Solve for x, given that the area is 120.**Show work please(step by step)**

Answers

Answer:

x=20

Step-by-step explanation:

Solve for x, given that the area is 120.**Show work please(step by step)**

please help!
Try to solve the equation below.
2x^2+18=10
Explain why this equation has no real number solutions.

Answers

Answer:

Step-by-step explanation:

The discriminant of this equation, i.e, D=\(b^{2}-4ac\) is less than 0:

D= 0-(4*2*18)   --> which is clearly negative

When D is less than 0, the equation has no real number solutions.

Therefore, \(2x^{2}+18=0\) has no real roots

Answer:

Step-by-step explanation:

0 has no roots so thats one, and im just trying to complete a challenge so sorry if im wrong :( but make other person brainliest they did good job :)

Ava is buying 30 baseball caps and pays a total of $240. Each cap costs the same amount. Determine whether the situation below represents a direct proportion, and justify your reasoning. If so, find the constant of proportionality.

Pls find the answer winter break is almost ending

Answers

90% of people marry there 7th grade love. since u have read this, u will be told good news 2night. if u don't pass this on nine comments ur worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of ur life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you...

The answer is 8 so its a direct proportion

I think...

The constant of Proportionality is 8.

What is constant of Proportionality?

If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality. We can also express it as x is to y at times.

Given:

Total Baseball Caps= 30

Total amount of Cap= $240

let the number of caps sold be c.

Then, the equation is

30 c= 240

and, c= 240/30

c= 8

Hence, the constant of Proportionality is 8.

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please write a function for the points (1/3,0) (-2 3/4,0) and (0,-5) and explain the steps.
thank you!

Answers

The function for the points are  y = -15x - 5

How to determine the function

From the information given, we have that;

The points are;

(1/3,0) (-2 3/4,0) and (0,-5)

Using the point-slope form of a linear equation, we have;

y - y₁ = m(x - x₁)

Such that;

m is the slope of the liney - y₁ and (x - x₁) are the points

Using (1/3, 0) and (0, -5), we have that the slope is;

m = (0 - (-5))/0 -1/3)

expand the bracket

= 5 / (-1/3)

= -15

Now, take any of the given points and substitute the values

Using (1/3, 0), we get;

y - 0 = -15(x - 1/3).

y = -15x - 5.

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The function for the points solved by  (1/3,0) (-2 3/4,0) and (0,-5) solved by point slope form is \(a=-15b-5\)

We have given the points:

(1/3,0) (-2 3/4,0) and (0,-5)

Using the formula of linear equation

\(a-\)\(a_{1}\)\(=x[b-b_{1}]\)                                                          

Where we will consider (1/3,0) = \(a-a_{1}\) and (0,-5) = \(b-b_{1}\)

that is 1/3 = \(a\), 0 = \(a_{1}\) and

0 = \(b\), -5 = \(b_{1}\)

\(x\) refers to the slope of line (take any variable)

Now for finding the value of \(x\),

\(x=a-a_{1}/b-b_{1}\)

inserting the values,

\(x=[0-[-5]]/[0-1/3]\\x= -15\)

Substitute the value of \(x\) in the equation

\(a-0=-15[b-1/3]\)

By simplifying the equation, we get

\(a=-15b-5\)

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Joanna draws a scale model of a rectangular table for a carpenter to build.
On her drawing, 3/4 of an inch represents 1 foot. In the drawing, the table is 7 1/2 inches long. How long, in feet, will the table be when the carpenter builds it?

A. 4 2/3 ft
B. 2 5/8 ft
C. 5 5/8 ft
D. 10 ft

Answers

Answer:

D

Step-by-step explanation:

just multiply the three over four inches with seven and a half to get the accurate measurements

the answer to this is D

An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $6100 and his stock in Company B was worth $6480. The stock in Company A has decreased 2% since last year and the stock in Company B has decreased 10%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).

Answers

Investment in Company A by investor = $6100

Investment in Company B by investor = $6480

The decrease in value of the stock of company A is 2%

The decrease in value of the stock of company B is 10%

Value of wealth that investor lost in company A = 6100× 2/100

= 61×2

= $122

The decline in the value of the stock of company B = 6480×10/100

= 648×1/1

= $648

The total decline in the wealth of the investor= 122+648

= $770

The combined wealth of investor in both companies= 6100+6480

= $12580

Percentage of decline in the stock account of investor= 770×100/12580

= 77000/12580

= 6.1%

The total percentage decline in investor's stock account is 6.1%

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Starting at sea level, a kingfisher flew to an elevation of 3714 feet. Spotting a fish below, the bird descended 4156 feet and caught the fish.What was the elevation of the fish?

Answers

Answer:

  -442 feet

Step-by-step explanation:

3714 -4156 = -442

The elevation of the fish was -442 feet, using the given numbers.

_____

Unfortunately, the bird died of the bends while surfacing from that depth.

Answer:

Step-by-step explanation:

a) 37.25 - 251/6

b) -27.5/6 feet, that is below sea level

factor the expression: -7a - 14b - 28

Answers

Answer:

-7 (a + 2b + 4)

Step-by-step explanation: hope this helps!

Answer: the answers  is -7 ( a + 2b + 4 )

Step-by-step explanation:

-7a - 14b - 28

you rewrite -28 as 4 * 7

you rewrite -14 as 2 * 7

-7a + 2 * 7b + 4 * 7

- & (a + 2b + 4)

question : ill mark brainlist

3. The ______ projection shows the size and shape of continents accurately but distorts water areas.

A. Conic

B. Mercator

C. Robinson

D. Interrupted

Answers

The correct answer is A. Conic projection.

A conic projection is a type of map projection created by projecting the surface of a globe onto a cone. The cone is then unrolled and flattened to create a two-dimensional map. Conic projections are best for mapping small areas, such as individual countries or states. They are also good for mapping areas that are located near the equator.

Conic projections show the size and shape of continents accurately, but they distort water areas. This is because the cone is tangent to the globe at one point, and the further away from that point you get, the more distortion there is.

Mercator projection is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. The map is thereby conformal. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles.

Robinson projection is a map projection presented by American cartographer Arthur H. Robinson in 1963. It is a compromise projection that attempts to balance the distortions of area, shape, and distance. The Robinson projection is neither conformal nor equal-area, but it is pseudocylindrical, which means that the meridians are straight lines and the parallels are circles.

Interrupted projection is a type of map projection that is interrupted at regular intervals. This is done to reduce the distortion of the map. The most common type of interrupted projection is the Mercator projection, which is interrupted at the equator and the prime meridian

The answer is B mercator hope it helps :)

You have a pizza with diameter 12
2
3 in., and a square box that is 12.65 in. across. Write 12
2
3 as a decimal. Can you fit the pizza inside the​ box?
What is the decimal expansion for 12
2
3​?
A.12.6
B.12.65
C.12.6
D.12.66
pls help me

Answers

Answer:

D is the right choice and no you cannot fit the pizza inside the box.

Step-by-step explanation:

D is the answer because to turn 2/3 into a decimal you would divide 2 by 3 and the answer you would get would be 0.66666666666...You would then add 12 to the answer and get 12.6666... Once you get this answer you would round it to the hundredths to get 12.67 but since that is not an option you could use D, 12.66 inches.

Answer:

I believe the answer is D.

Step-by-step explanation:

GOOGLE

Hello! I just have a simple math equation lol
Please put yout answer in a mixed number =)

Hello! I just have a simple math equation lolPlease put yout answer in a mixed number =)

Answers

-6 1/2 x 7 5/6
-13/2 x 47/6
13x 47=611
2x6=12
-611/12
Answer:-50 11/12

If x is 6, then 7x =

Answers

Answer:42

Step-by-step explanation:

if x=6 u change the x with 6 then the equation would be 7x6= 42

A piece of cheese is shaped like a triangle. It has a height of 2.5 inches and a base that is 3.75 inches long.

If 1 inch = 2.54 centimeters, find the area of the cheese in square centimeters. Round the answer to the nearest square centimeter.

Answers

3.690944881889764 square centimeters. (Not sure what place you wanted it rounded to, so I put the whole number.)
3.7 square centimeters

Write this number in scientific notation.
Thank you!

Write this number in scientific notation.Thank you!

Answers

Answer:To write the number 0.0000149 in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of 10.

First, we move the decimal point to the right until there is only one non-zero digit to the left of the decimal point, which gives us:

1.49 × 10^-5

Since we moved the decimal point 5 places to the right, the exponent of 10 is negative 5.

Therefore, the scientific notation of 0.0000149 is 1.49 × 10^-5.

Step-by-step explanation:

Answer:

1.49×10^-5

Step-by-step explanation:

0.0000149=1.49×10^-5

it's to the power of -5 because it's a decimal number not a whole number

A hat at the store is being offered at a 15% discount. If the original price of the hat is x, which answer choice shows an expression that represents the discounted price of the hat?

Answers

.85x is the discounted price of the hat

The discounted price of the hat is 0.85x.

What is discounted price?

Discount is the difference between the marked price (list price) and the selling price of an article. Therefore, the formula used for discount calculation is: Discount = List price - selling price.

Given that, a hat is at 15% discount price, we need to find the expression that represents the discounted price of the hat,

The discount = x - SP

15% of x = x - SP

SP = 85% of x

SP = 0.85x

Hence, the discounted price of the hat is 0.85x.

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I NEED THIS RIGHT NOW

I NEED THIS RIGHT NOW

Answers

Answer:

x - y

Step-by-step explanation:

if x is greater than y subtraction will be the result with a positive number.

ANSWER PLEASE BEFORE 2/14!!!!

Tamara likes to go hiking and tries to hike for at least 30 minutes every week. On Tuesday, she hiked for 1 mile in the morning and 3 miles in the evening. On Thursday, she hiked with a friend for 4 miles. On Saturday she hiked for 5 miles. On Sunday, she hiked for 4 miles. She also hiked for an extra 10 minutes on Sunday night. If she hiked for a total of 350 minutes all week and it takes her the same amount of time to hike each mile, how many minutes does it take her to hike each mile?

Answers

Answer:

20 minutes

Step-by-step explanation:

1+3+4+5+4=17

350-10=340

340÷17=20

What operation can you use to solve the equation?

A. addition
B. division
C. subtraction
D. multiplication

Answers

Answer:

C

Step-by-step explanation:

24+m=56

You would want to subtract 24 from 56 to get the answer to m

24+m=56

-24      -24

m=32

Answer - C
Step by Step -
24+m=56
-24. -24
m=32

please help me on this :DD

please help me on this :DD

Answers

So all you do is the first number goes on the bottom and the second number on the coordinates goes on the top.

So if you had 5,4 you would move it over to 5 on the bottom and 4 on the top. It’s actually super easy!

Answer:

parallelogram

Step-by-step explanation:

As you can see in the pic the shape is a parallelogram.

:)

please help me on this :DD

i need help with this question please help me

i need help with this question please help me

Answers

Answer:

The answer is D.

Step-by-step explanation:

y = mx + b

C = 5/9 (F - 32)

C = 5/9F - 5/9 (32)

Option (D) is correct.

Help please asap!!!

please:(

Help please asap!!!please:(

Answers

it would be D because when adding them together the only one that makes sense would be D. adding the exponents 5+4 = 9 so it would be 10^9
The answer for this question is D

Can someone pls help me with this first right answer gets brainlist

Can someone pls help me with this first right answer gets brainlist

Answers

116.

116.
you add the m<1 and the m<3 and make them equal to 180. the value of x can then be substituted into the m<3 making the answer 116.
i believe the answer is 116.2

What is the y-intercept of the following equation? y = 3x - 1

Answers

Answer:

-1

Step-by-step explanation:

Because in this equation the -1 doesn't have any variables (x,g,etc.) it makes it the y intercept, therefore your y intercept is y= -1

Answer:

(0, -1)

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

y = 3x - 1

Step 2: Break Function

Identify Parts.

Slope m = 3

y-intercept b = -1

The price of a pair of slacks is 29 dollars. What is the price after a 30% discount

Answers

Answer:

The pair of slacks would be

C. $20.30

Step-by-step explanation:

The price with the discount is $20.3

Multiply 29 by 0.7 (70 percent)

("._.) ................................................. >(-.-)>

("._.) ................................................. &gt;(-.-)&gt;

Answers

Answer: C

Step-by-step explanation:

Type the integer that makes the following addition sentence true:

___ + -27 = –79

Answers

Answer:

-105

Step-by-step explanation:

Answer: -52

Step-by-step explanation:

-50 + -20 = -70,    -0 + -9 = -9,     -70 + -9 = -79

I suck at math so be nice n help:)

I suck at math so be nice n help:)
I suck at math so be nice n help:)

Answers

Answer: See explanation

Step-by-step explanation:

1. ∠WOV and m∠30° are complementary angles so they should add up to 90°

∠WOV + 30 = 90

Subtract 30 from both sides

∠WOV = 60°

I used the relationship of complementary angles.

2. ∠YOZ and ∠WOV are vertical angles so they're congruent.

∠YOZ ≅ ∠WOV

∠YOZ ≅ 60°

∠YOZ = 60°

I used the relationship of vertical angles.

I hope this helped!

There’s nothing here

Men and women (ages 22–40) were surveyed to choose a favorite free-time activity: playing sports, dancing, or watching movies/TV.

The survey showed the following frequencies:
Men—playing sports: 11; dancing: 3; watching movies/TV: 6
Women—playing sports: 5; dancing: 16; watching movies/TV: 9

Which of the following is a correct two-way frequency table for the data?


Men and Women Leisure Time Activity Preferences
Playing Sports Dancing Watching movies/TV Row totals
Men 0.22 0.06 0.12 0.12
Women 0.10 0.32 0.18 0.60
Column totals 0.32 0.38 0.30 1

Men and Women Leisure Time Activity Preferences
Playing Sports Dancing Watching movies/TV Row totals
Men 11 3 6 20
Women 5 16 9 30
Column totals 16 19 15 50

Men and Women Leisure Time Activity Preferences
Playing Sports Dancing Watching movies/TV Row totals
Men 0.55 0.15 0.30 1
Women 0.17 0.53 0.30 1
Column totals 0.32 0.38 0.30 1

Men and Women Leisure Time Activity Preferences
Playing Sports Dancing Watching movies/TV Row totals
Men 0.69 0.16 0.40 0.40
Women 0.31 0.84 0.60 0.60
Column totals 1 1 1 1

Answers

Answer:

Hello how are you the answer is b

the answer should be letter b based on what you explained the final answer is B

can u help me pls and ty a lott :)

can u help me pls and ty a lott :)

Answers

Answer: The table on the left is s direct variation. The equation is y = x/2

The table on the right is indirect.

Step-by-step explanation:

See if the output y changes by the same amount for each x-value. The equation describes the amount of change for the values you see and predicts the ones you can't see.

The table on the left is direct.

The table on the right is indirect.

Please help me with acellus

Please help me with acellus

Answers

X would be 15
Process:

X + 6 - 2x = x - 24

6 - x = x - 24

30 - x = x

30 = 2x

2x = 30

X = 15
i think that is 0.273 , srry if im not right
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