What is the length of a radius of the circle represented by the equation

x2 + y2 - 4x - 4y + 4 = 0?


A) 2 units

B) 4 units

C) 8 units

D) 16 units

Answers

Answer 1

Answer:

A) 2 units

Step-by-step explanation:

Given;

x² + y² - 4x - 4y + 4 = 0

Consider general circle equation;

(x - h)² + (y - k)² = r²

where;

(h , k ) is the center of the circle

r is the radius of the circle

x² + y² - 4x - 4y + 4 = 0

subtract 4 from both sides of the equation

x² + y² - 4x - 4y  =  - 4

square half of coefficient of x and y, and add them to both sides of the equation

x² +  - 4x + (-2)² +  y² - 4y + (-2)² = - 4 +  (-2)² +  (-2)²

factorize x and y

(x - 2)² + (y - 2)² = - 4 + 4 + 4

(x - 2)² + (y - 2)² = 4

(x - 2)² + (y - 2)² = 2²

Compare this final equation to general equation of a circle

(x - 2)² + (y - 2)² = 2²  

(x - h)² + (y - k)² = r²

r = 2

Thus, the length of a radius of the circle is 2 units


Related Questions

In a study of cell phone usage and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 6965 subjects randomly selected from an online group involved with ears. There were 1330 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than​ 20%. Use the​ P-value method and use the normal distribution as an approximation to the binomial distribution. Identify the null hypothesis and alternative hypothesis. A. Upper H 0​: pequals0.2 Upper H 1​: pless than0.2 B. Upper H 0​: pgreater than0.2 Upper H 1​: pequals0.2 C. Upper H 0​: pequals0.2 Upper H 1​: pnot equals0.2 D. Upper H 0​: pnot equals0.2 Upper H 1​: pequals0.2 E. Upper H 0​: pless than0.2 Upper H 1​: pequals0.2 F. Upper H 0​: pequals0.2 Upper H 1​: pgreater than0.2 The test statistic is zequals nothing. ​(Round to two decimal places as​ needed.) The​ P-value is nothing. ​(Round to three decimal places as​ needed.) Because the​ P-value is

Answers

Answer:

Given:

Sample size, n = 6965

Sample proportion p' = [tex] \frac{1330}{6965} = 0.19 [/tex]

Let's claim that the return rate is less than​ 20%, ie, P = 0.2

Significance level = 0.01

The null and alternative hypotheses:

H0 : P = 0.2

H1 : P < 0.2

Option A is correct

_____________________________

For the test statistic, Z, let's use the formula:

[tex] Z = \frac{p'- P}{\sqrt{\frac{P(1-P)}{n}}} [/tex]

[tex] = \frac{0.19 - 0.2}{\sqrt{\frac{0.2(1 - 0.2)}{6965}}} = -1.887 [/tex]

Z = -1.887 ≈ -1.89

___________________________

The p-value.

This is a left tailed test.

Using z table,

P-value = P(Z ≤ -1.89) = 0.029

The pvalue is 0.029

Decision:

Because the pvalue, 0.029 is greater than level of significance, 0.01, we fail to reject null hypothesis, H0.

Conclusion:

There is not enough sufficient evidence to conclude that the return rate is less than 20%

Identify the equation of the line with the given slope and Y intercept,

Answers

Answer:

y = 6x - 7

Step-by-step explanation:

We can use the equation y = mx + b as a guide to help us solve this problem

The variables are given in the problem, so we just need to replace them with their respective variables, which give us:

y = 6x - 7

Answer:

The third one down is the correct answer.

cube of the number -13/15

Answers

Answer:

[tex]-\frac{2197}{3375}\\\mathrm{Decimal:\quad }\:-0.65096[/tex]

Step-by-step explanation:

[tex]-\left(\frac{13}{15}\right)^3\\\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}\\\left(\frac{13}{15}\right)^3=\frac{13^3}{15^3}\\=-\frac{13^3}{15^3}\\13^3=2197\\=-\frac{2197}{15^3}\\15^3=3375\\=-\frac{2197}{3375}[/tex]

Answer:

[tex] = \frac{ - 2197}{3375} [/tex]

Step-by-step explanation:

[tex]cube = {x}^{3} \\ (\frac{ - 13}{15}) ^{3} \\ \frac{ - 13}{15} \times \frac{ - 13}{15} \times \frac{ - 13}{15} \\ \\ = \frac{ - 2197}{3375} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

HElP asap GIVING BRAINLIST HELP!!!!

Answers

Answer:

1. x = 0

2. x= 0

3. x = 10

4. x = -4

5. x = 0

6. x = -1

What is the factored form of 8x2 + 12x?

Answers

Answer:

Step-by-step explanation:

8x^2 + 12x

(x+4)^2

Answer:

4x( 2x + 3)

Step-by-step explanation:

8x2 + 12x = (4x) × (2x) + (4x) × (3)   ; we factor 4x out.

                = 4x( 2x + 3)

Jan says that a rhombus is a parallelogram and that every parallelogram is also a rhombus. Is Jan correct?

Part 2***

Explain why or why not.

Answers

Answer:

No

Step-by-step explanation:

Not all parallelograms are rhombuses, some parallelograms include rectangles, squares, hexagons, etc.

No. Jan is not correct. So, all parallelograms are not rhombuses.

What is a rhombus?

A rhombus is a parallelogram because the opposite sides are parallel but every parallelogram is not a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.

here, we have,

We need to identify the properties of the given figure in order to answer why one figure can not be the other one:

A rhombus has all sides equal as well as parallel but all angles might not be right angles.

A square has all four sides equal and has 4 right angles.

A rectangle has equal opposite sides and 4 right angles.

A parallelogram has opposite parallel sides.

Hence, a rhombus can be a parallelogram because the opposite sides are parallel but every parallelogram can not be a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.

A parallelogram has opposite sides parallel and equal in length. Also, opposite angles are equal. Squares, rectangles, and rhombuses are all parallelograms. So all parallelograms are not rhombuses.

Not all parallelograms are rhombuses, some parallelograms include rectangles, squares, hexagons, etc.

To know more about rhombus here

brainly.com/question/12665650

#SPJ3

Please answer this question ;(

Answers

Answer:

20 miles = 32 kilometers

64 kilometers = 40 miles

Step-by-step explanation:

please help ASAP :( ! which of the following is most likely to be the next step in the series?

Answers

D because the line is going clock wise

What is the measure of angle TQR?

Answers

Angle TQR equals to 70 degrees

First you have to find the value of x. An inscribed quadrilateral in a circle has it that opposite angles are supplementary.

So set the angles STQ and SRQ to 180.

3x+5+5x+15=180
8x+20=180
8x=160
x=20

Then find the angles of the three by substituting 20 as x.

Angle STQ=65
3(20)+5
60+5
65

Angle RST=110
4(20)+30
80+30
110

Angle SRQ=115
5(20)+15
100+15
115

Exterior angles of a quadrilateral equal to 360 when added together. So subtract the values from 360 to get the missing length.

360-115-110-65=70

So angle TQR=70

Find the value of the variable to the nearest tenth.

Answers

Answer:

Applying Pythagorean theorem:

r = sqrt(3^2 + (14/2)^2) = sqrt(9 + 49) = sqrt(58) = ~7.6 cm

Hope this helps!

:)

Mary signed up for a 5K race. It is called a 5K because it is 5 kilometers long. Mary doesn’t know how far a kilometer is and wants to visualize this distance in miles. How many miles will she have to run for the race?

Answers

Answer:

its 3.1 miles hope this helped :)

express x in term of y:x/7+2y=6​

Answers

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{x}{7}[/tex] + 2y = 6

Multiply through by 7 to clear the fraction

x + 14y = 42 ( subtract 14y from both sides )

x = 42 - 14y

Find the volume of the cone below. Round your answer to the nearest tenth if necessary. Use 3.14 for π. * PLS show work

Answers

Answer:

-The volume of the cone is 100.5[tex]in^3[/tex] .

Step-by-step explanation:

To find the volume of cone, you need the formula:

[tex]V =\frac{1}{3} \pi r^2 h[/tex]

-Use the radius and the height for the formula:

[tex]V =\frac{1}{3} \pi 4^2 6[/tex]

-Then, you solve:

[tex]V =\frac{1}{3} \pi 4^2 6[/tex]

[tex]V = \frac{1}{3}\pi[/tex] × [tex]4^2[/tex] × [tex]6[/tex]

[tex]V = \frac{1}{3}\pi[/tex] × [tex]16[/tex] × [tex]6[/tex]

[tex]V = \frac{1}{3}\pi[/tex] × [tex]96[/tex]

[tex]V = \frac{96}{3} \pi[/tex]

[tex]V = 32\pi \approx 100.53[/tex]

-Round to the nearest tenth:

[tex]V \approx 100.5[/tex]

So, therefore, the volume of the cone is 100.5[tex]in^3[/tex] .

Solve for h.

0.8h − 11.49 = 5.67 + 12.9 − 15.9h

Answers

So the right answer is 1.8

Look at the attached picture

Hope it will help you

Good luck on your assignment

MATH HOMEWORK HELP PLEASE

Answers

Answer:

A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

[tex]r=\frac{\frac{4}{25} }{\frac{2}{5} } \\r=\frac{4}{25} \times \frac{5}{2} =\frac{2}{5} <1\\s_{\infty}=\frac{a}{1-r} =\frac{\frac{2}{5} }{1-\frac{2}{5} } =\frac{2}{5} \times \frac{5}{3} =\frac{2}{3}[/tex]

Renu wants to put a border of lace around a rectangular table cover 4 m long and 2 m wide..

Find the length of the lace required for the table cover..

Answers

Answer:12m

Step-by-step explanation:

The length of the lace required will be the same as that obtained by calculating the perimeter of that table, so p= (L+W)×2

Hence, P=(4m+2m)×2

P= 12m

Find the approximate perimeter of polygon CODIFYCODIFYC, O, D, I, F, Y plotted below.

Round your final answer to the nearest hundredth.

please helppp

Answers

Answer:

49.81

Step-by-step explanation:

the formula I used is distance=[tex]\sqrt{(x_{2}-x_{1})+(y_{2}-y_{1})}[/tex]

Lets say we are finding the distance from c to y

c=(-6,9)

y=(5,9)

cy=[tex]\sqrt{(5-(-6))^{2}+(9-9)^2 }[/tex]

cy=[tex]\sqrt{(11)^2+(0)^2}[/tex]

cy=[tex]\sqrt{121+0}[/tex]

cy=[tex]\sqrt{121}[/tex]

cy=11

And you can find the distance between y and i, i and d, d and o, o and c, using the same formula.

After solving the distance of all I got

yi=16.55294536

id=1

do=9.219544457

oc=12.04159458

After you add them all up you get 49.8140844 which rounded to the nearest hundredth is 48.81.

Thank you and I hope that is helpful.

Sorry that is actually wrong

Check out the other answer.

Answer:

51.53

Step-by-step explanation:

I need to know these answers fast please please help!!!!

Answers

Answer:

Step-by-step explanation:

y intercept please scroll down--i need to see the rest of the graph-- y intercept is where the graph intersects with the y axis

x intercepts are x=2 and x=6

greatest value of y is y=2 and it occurs when x=4

for x between... what are the options?

   if the options are greater than, equal to, or less than, the answer is greater than

please help me i really need help

Answers

Answer:

7t +5

Step-by-step explanation:

6t +7 -2 +t

Combine like terms

6t+t  +7-2

7t +5

Answer:

Relax. The answer is 7t +5

Step-by-step explanation:

Circle the 2 variables (T)

Next re-write the equation and put the varbiles equation 6t+t.

Then you have 7-2 left, you then put it next to the new equation but make sure when you do that it looks like this 6t+t+7-2.

Last you solve and your answer should be 7t+5.

Note: If a variable is alone like the t then make sure you put a one next to it

A figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of a vertex located at (3, 4)?

Answers

Answer:

(9,12).

Step-by-step explanation:

If a figure dilated by a scale factor of k and origin is the center of dilation, then the relation between point and its image is defined as

[tex]P(x,y)=P'(kx,ky)[/tex]

It is given that a figure is dilated by a scale factor of 3 and origin is the center of dilation. So,

[tex]P(x,y)=P'(3x,3y)[/tex]

We need to find the image of a vertex located at (3, 4). So, substitute x=3 and y=4 in the above rule of dilation.

[tex]P(3,4)=P'(3(3),3(4))[/tex]

[tex]P(3,4)=P'(9,12)[/tex]

Therefore, the image of a vertex located at (3, 4) is (9,12).

Answer: 9,12

Step-by-step explanation:

Explain the difference between a nonnumeric growing pattern and a nonnumeric repeating pattern.

Answers

Answer: nonnumeric growing patteren: A repeating pattern has a pattern unit that repeats over and over again. nonnumeris repeating patteren: A growing pattern gets bigger in the same way over and over again.

a chord of a circle 8 cm long subtends an angle of 120 degree at the center find the radius of the circle​

Answers

Answer:

Chord = 2 • sine (Central Angle) • radius

radius = 8 cm / 2 * 0.86603

radius = 4.6187776405  cm

Step-by-step explanation:

is this the right answer for number 12?

Answers

Answer:

figure it out urself

Step-by-step explanation:

help me i dont understand


Answers

Answer:

4/8 +6/8 I just verfying the other person's. ok

Step-by-step explanation:

I did it on a calculator ;b

PLEASE MARK FallOutChild brainliest!!

Answer:

4/8 + 6/8 = 10/8 or 1 2/8, 1 1/4

Step-by-step explanation:

When it asks for like units, it's asking for the same denominator value. You can not add fractions together when they do not have a common denominator

if you multiply the denominator and numerator in 2/4 by 2, you get 4/8

Result of 4/8 + 6/8 gives you an improper fraction of 10/8

Hope this Helps!

From a group of 7 men and 6 women, five people are to be selected to form a committee. How many different committees can be formed from this group?

Answers

You can form 6 groups
I hope it was helpful

A company rents water tanks shaped like cylinders. Each tank has a diameter of 8 feet and a height of 3 feet. The cost is $5 per cubic foot. How much does it cost to rent one water tank?

Answers

Answer:

$754.05

Step-by-step explanation:

We have to find the volume of one tank and multiply it by the cost of renting the tank per cubic foot.

The volume of a cylinder is:

[tex]V = \pi r^2h[/tex]

where r = radius

h = height

Each tank has a diameter of 8 feet (radius = 4 feet) and a height of 3 feet.

The volume of the tank is therefore:

[tex]V = \pi * 4^2 * 3 = 150.81 ft^3[/tex]

The cost of renting is $5 per cubic foot.

Therefore, the cost of renting a tank is:

150.81 * 5 = $754.05

It costs $754.05 to rent a tank.

Rosanne is training for the Austin marathon, so she plans to run 10 miles in her neighborhood this weekend. It usually takes her an hour to run 6 miles. If she generally drinks 0.5 cups of water every 1 3 of an hour, how many cups of water will she drink on her run?

Answers

Answer:2.5 cups

Step-by-step explanation:

Given

Rosanne runs 6 miles in an hour

If she drinks 0.5 cups of water every  [tex]\frac{1}{3}[/tex]  of an hour

So in 1 hour Rosanne drinks 1.5 cups

So, for 6 miles Rosanne drinks 1.5 cups

i.e. For   [tex]1\ mile \quad \equiv \quad \frac{1}{4}\ \text{cup}[/tex]

for    [tex]10\ mile\quad \equiv \quad \frac{10}{4}\ \text{cup}[/tex]

[tex]=2.5\ \text{cup}[/tex]

Answer:

2.5

Step-by-step explanation:

Sharia surveyed students and teachers to determine how long it takes each person, in minutes, to get ready for school in the morning. The plots below show the results of the survey. Which statements accurately compare the two data sets? Select three options

Answers

Answer:

B),D),E)

Step-by-step explanation:

Trust

Answer:

B,D,E

Step-by-step explanation:

I got it correct on the quiz

Sean is in the science lab. He needs to divide 33 grams of salt into tiny vials that hold just gram each. He has one box that contains 48 empty vials. How many more vials does Sean need to divide all of the salt?

Answers

Answer:

-15

Step-by-step explanation:

Since each vial contains one gram. and he has 33 grams, so he has 33 vials of one gram each. since he has a box that has 48 vials. he needs 15 less vials to divide the salt into vials that contain one gram each

Please mark as brainliest

Pls help me with this question

Answers

Answer:

V = h·w·t cm³

Step-by-step explanation:

The volume is calculated no different than you would with a box.

V= length x width x height and yes centimeters cubed Answer:

Step-by-step explanation:

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