A circle has the equation x2−12x+27=−y2+8y.
What is the equation of the circle in standard form, the location of its center, and the length of its radius?

The equation of the circle is (x−6)2+(y−4)2=25; the center is at (6,4), and the radius is 5 units.

The equation of the circle is (x−6)2+(y−4)2=5; the center is at (6,4), and the radius is 5–√ units.

The equation of the circle is (x−6)2+(y−4)2=5; the center is at (−6,−4), and the radius is 5–√ units.

The equation of the circle is (x−6)2+(y−4)2=25; the center is at (−6,−4), and the radius is 5 units.

Answers

Answer 1

Answer:

It's the first option.

Step-by-step explanation:

x^2 - 12x + 27 = - y^2 + 8y

x^2 - 12x + y^2 - 8y = -27    Completing the squares:

(x - 6)^2  - 36  + (y - 4)^2 - 16 = -27

(x - 6)^2 + (y - 4)^2 = -27 + 36 + 16

(x- 6)^2 + (y - 4)^2 = 25 is the standard equation.

The center is at (6, 4) and the radius is 5 units.

Answer 2

Answer:

first option

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² - 12x + 27 = - y² + 8y ( subtract - y² + 8y from both sides )

x² - 12x + y² - 8y + 27 = 0 ( subtract 27 from both sides )

x² - 12x + y² - 8y = - 27

Using the method of completing the square on both the x and y terms

add ( half the coefficient of the x/ y term )² to both sides

x² + 2(- 6)x + 36 + y² + 2(- 4)y + 16 = - 27 + 36 + 16

(x - 6)² + (y - 4)² = 25 ← in standard form

with centre = (6, 4 ) and r² = 25 ⇒ r = [tex]\sqrt{25}[/tex] = 5 → first option


Related Questions

Which statement is true about this question -4(2p+5)+8p=-11

A. The equation has one solution, p=2

B. The equation has one solution, p=-2

C. The equation has no solution

D. The equation has infinetly many solutions

Answers

Option C. The equation has no solution is correct.

Which statement is true about this question -4(2p+5)+8p=-11

What is equation?

Equation is the relationship between variable and represented as    is example of polynomial equation.

Since,  
The equation terminated while simplifying
-8p-20+8p=-11

-20≠-11


Thus the given equation has no solution at any point.

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3 - 2n = 7
Show work please

Answers

Answer:

-2

Step-by-step explanation:

3-2n=7

-3       -3

-2n=4

divide both sides by -2

n=-2

Answer & Explanation-

1. 3-2n=7

2. Subtract 3 from both sides to make x alone.

3. -2n=4

4. Divide both sides by -2

5. n=-2

Answer-

n=-2

The Cole family owns an above-ground circular swimming pool that has walls made of aluminum. ​ ​Find the length (l) of aluminum surrounding the pool as shown if the radius is 15 feet. ​(use π=3.14 )

Answers

Answer:

The length of aluminium surrounding the pool is 94.20 ft.  

Step-by-step explanation:

The picture represents the circular swimming pool that has walls of aluminium surround it.

The circumference of a circle is the distance around a circle. It is the curved line that goes round the circle. The question wants us to find the circumference of the aluminium surrounding the circular pool.  

circumference of a circle = 2πr

circumference of a circle = 2 × 3.14 × 15

circumference of a circle = 30 × 3.14

circumference of a circle = 94.2 ft

The length of aluminium surrounding the pool is 94.20 ft.  

In the figure, which angle has the same measure as Z2?
A. 21
B. 23
C. 24
D. 25

Answers

Answer:

I think it is D

Step-by-step explanation:

Is this right? if it isn't, what IS right?

Answers

Answer:

You are wrong and the correct answer is vaunted.

Step-by-step explanation:

Why? Because it would be the only applicable word for this sentence.

Omnipotent: Having unlimited power; able to do anything.

Overt: One or shown openly; plainly or readily apparent, not secret or hidden.

Annihilated: Destroy utterly; obliterate.

Vaunted: Praised or boasted about, especially in an excessive way.

Use simple interest to find the ending balance.
$53,300 at 4.7% for
3 3/4 years URGENT I will give you brainliest

Answers

Answer:

The ending balance would be:

EB = Money x (1 + rate)^year

     = 53300 x (1 + 4.7/100)^(3.75) = 63318.01

Hope this helps!

:)

Answer:

$62,694.125

Step-by-step explanation:

Interest = 53300 × (4.7/100) × 3.75

Interest = 9394.135

Balance = 53300 + 9394.135

= $62,694.125

An Ice Hockey rink is a rectangle with a perimeter of 174 meters. The length is 9 meters more than twice the width. What equation describes this problem? (Remember that the perimeter is twice the length plus twice the width)

Answers

Answer:

Let width be x metres

so, length is "9 metres more than twice the width" --> 9+2x

So, perimeter is x + x + (9+2x) + (9+2x) = 174

6x + 18 = 174

6x = 156

 

x = 156/6

x = 26m

width = 26m

length is therefore 9+2(26) --> 9+52 --> 61m

Step-by-step explanation:

Jan conducts an experiment and tosses a coin 40 times. She gets heads 30 times instead of the expected 20. What could be a reason for this difference?
A) She miscounted.
B) She needs more trials.
C) She needs a different coin.
D) She got 30 and that is close enough.

Answers

the answer is B. hope i helped

Solve x :
[tex]{(3 {x}^{2} - 8x + 5)}^{x + 1} = 1[/tex]

Answers

We want this expression to fall in one of the two cases:

[tex]\alpha ^ 0 = 1 = 1^\beta[/tex]

So, if the exponent is zero, the base can assume any value, because everything (expect zero) to the power of zero is one.

Similarly, if the base is 1, the exponent can be any number, becuase 1 raised to any exponent is still one.

If we are looking for the "zero exponent" strategy, we simply have to impose

[tex]x+1=0\iff x=-1[/tex]

In this case, the expression becomes [tex]16^0=1[/tex], so we avoided the [tex]0^0[/tex] case and we're good.

If we are looking for the "base equals one" strategy, we must impose

[tex]3x^2-8x+5 = 1 \iff 3x^2-8x+4=0 \iff x=\dfrac{2}{3}\lor x=2[/tex]

Answer:

x = -1, ⅔, 2

Step-by-step explanation:

3x² - 8x + 5

3x² - 3x - 5x + 5

3x(x - 1) - 5(x - 1)

(3x - 5)(x - 1)

[3x² - 8x + 5]^(x+1) = 1

The ourput is 1 when:

1) The power is 0

x + 1 = 0

x = -1

2) base is 1

3x² - 8x + 5 = 1

3x² - 8x + 4 = 0

3x² - 6x - 2x + 4 = 0

3x(x - 2) - 2(x - 2) = 0

(3x - 2)(x - 2) = 0

x = 2 , ⅔

Therefore, 3 solutions

x = -1, ⅔ , 2

Use either the square of a binomial or the
difference of two squares to find the area of
each rectangle.​

Answers

Answer:

9. 2916 sq. cm

10. 864 sq. in

Step-by-step explanation:

9.)  54 cm * 54 cm = area of square

   (50 + 4)*(50 + 4) =  50*50 + 8*50 + 16

= 2500 + 400 +  16 = 2916 sq cm.

10.  24 in *  36 in. = area of rectangle

get:   (30 - 6)*(30 + 6) = 30^2- 6^2

= 900 - 36 = 864 sq. in.

Find the parallelogram below. Use the formula: A = b x h.

Answers

Answer:A = b x h

Step-by-step explanation:

I can't see the problem but i can give help  u have to follow the formuls

Determine the area of a triangle with m

Answers

You could add ALOT more to your question

Answer:

I'm guessing they're asking about trig functions, topic test. Answer: B) 10 units^2

Step-by-step explanation:

just took the topic test on edge2021

How much concentrated 12 M sulfuric acid should be added to prepare a 250 mL of 1.5 m solution?

Answers

This will help you to get the answer

PLEASE HELP I NEED THE ANSWER ASAP

Jason wrote a computer program that randomly generate one of the letters of his name. He runs the program three times. What is the probability that it generates either a J or an N all 3 times?

Answers

Answer:

0.064

Step-by-step explanation:

(2/5) * (2/5) * (2/5)

= 0.064

Hope this is helpful!!! :)

The probability that it generates either a J or an N all 3 times would be 0.064.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Jason wrote a computer program that randomly generate one of the letters of his name. He runs the program three times.

The probability that it generates either a J or an N all 3 times

[tex](2/5) \times (2/5) \times (2/5)\\\\8/125\\\\0.064[/tex]

Thus, the answer is 0.064.

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DNA TAC ACC TTG GCG ACG ACT Write the mRNA strand then the Amino Acid sequence.

Answers

AUG UGG AAC CGC UGC AGU

what is the surface area of a storage box that measures 21 centimeters by 18 centimeters by 16 centimeters

Answers

Answer:

2004 cm²

Step-by-step explanation:

To solve this problem, you just need to plug your values into the rectangular prism formula: A=2(wl+hl+hw)

Assuming that the length is 21 cm, the width is 18 cm, and the height is 16 cm, your problem would look like this:

A=2((18x21)+(16x21)+(16x18))=2(378+336+288)=2x1002=2004 cm²

Ileana buys a large circular pizza that is divided
into eight equal slices. She measures along the
outer edge of the crust from one piece and finds it
to be 5 1/2 inches. What is the diameter of the pizza
to the nearest inch?

- 4 inches
- 7 inches
- 8 inches
- 14 inches

Answers

Answer:

14

Step-by-step explanation:

the edge of one slice of pizza is 5.5 and there are eight slices so i multiplied 5.5 by eight to get the circumference

the circumference is 44 so i divided that by pi to get the diameter which was 14 after you round

if your more of a numbers/formula person this might be more helpful:

circumference: 5.5 x 8 = 44

formula for diameter is  [tex]d=\frac{C}{\pi }[/tex]

so, [tex]d=\frac{44}{\pi }[/tex]

     [tex]d=14[/tex]

The diameter of the pizza is 14 inches.

Given that the pizza is divided into 8 equal slices and one of the outer edges measures 5 1/2 inches.

When need to find the diameter of the pizza.

What is the formula to find the circumference of the circle?

The formula to find the circumference of the circle is 2πr.

Since a pizza is divided into 8 equal parts.

So, the circumference of 1 part=2πr/8=πr/4

πr/4=5.5 inches.

⇒πr=22

⇒r=7 inches.

Then, diameter=14 inches.

Therefore, the diameter of the pizza is 14 inches.

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What quadrants is csc less than 0.

Answers

Answer:

Quadrant 2

Step-by-step explanation:

The baker made 27 pies. Nine of the pies were cherry pies and the rest were pumpkin pies. The baker placed the pumpkin pies in rows of 3 pies each. How many rows of pumpkin pies did the baker make?

Answers

27-9=18. The baker made 18 pumpkin pies.

To prove our answer,,

18 divided by 3 is 6, so it is possible to place them in rows by three.

Your confirmed answer is 18.

I hope this helps!

Brainliest?

The two dot plots below compare the forearm lengths of two groups of schoolchildren:

Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length in inches. There are markings from 10 to 13 on each line at intervals of one. For the top line there are 4 dots above the first mark, 4 dots above the second mark, and 2 dots above the third mark. For the bottom line there are 2 dots above the second mark, 3 dots above the third mark, and 5 dots above the fourth mark.

Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?

A. Group B, because five children have a forearm length longer than 12 inches.
B. Group B, because a child in the group has the least forearm length of 10 inches.
C. Group A, because no child in the group has a forearm length longer than 12 inches.
D. Group A, because four children in the group have the least forearm length of 10 inches.

Answers

Answer:

The corect answer is : Group A because 4 children have a forarm length longer than 12 inches.

Step-by-step explanation:

I did the test and got it right!    :D

Answer:

D. Group A, because four children in the group have the least forearm length of 10 inches.

Step-by-step explanation:

It can be seen that more children in group B have forearm length more than 12 inches and there are no children who have forearm length greater than 12 inches in group A. So, based on the visual inspection of the dot plots, group A, appears to have longer average forearm length.In order to verify the claim let us find the mean

Mean of Group A

[tex]\dfrac{10\times 4+11\times 4+12\times 2}{10}=10.8\ \text{inches}[/tex]

Mean of Group B

[tex]\dfrac{11\times 2+12\times 3+13\times 5}{10}=12.3\ \text{inches}[/tex]

So, group A has shorter average forearm length.

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what is the median 3 2 -9 9 -3 -4 -1

Answers

Answer:

the median is -1

-9 -4 -3 (-1) 2 3 9

stay safe and have a good day

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⊕ΘΞΠΤ⊕

∵∴∵∴∵∴∵∴∵

Answer:

-1

Step-by-step explanation:

First put the numbers in order from smallest to largest

-9 -4  -3 -1 2 3 9

The median is the middle number

The middle number is -1

5 in
Q
2 in
R
PQ =
Using Pythagorean theorem

Answers

By applying Pythagorean's theorem to right-angled triangle PQR, the length of segment PQ is equal to [tex]\sqrt{29}[/tex] units.

In Mathematics and Geometry, Pythagorean theorem is an Euclidean postulate that can be modeled or represented by the following mathematical equation:

[tex]c^2=a^2+b^2[/tex]

Where:

a is the opposite side of a right-angled triangle.b is the adjacent side of a right-angled triangle.c is the hypotenuse of a right-angled triangle.

By applying Pythagorean's theorem to right-angled triangle PQR, the length of segment PQ can be calculated as follows;

[tex]PQ^2=QR^2+PR^2\\\\PQ^2=2^2+5^2\\\\PQ^2=4 + 25\\\\PQ=\sqrt{29}[/tex]units.

Choose the correct answer

Answers

Answer:

Option D

Step-by-step explanation:

Assuming you're referring to slope, the rule is rise/run or "rise over run" so as i look at this line i see it rises 1 unit and then runs back or negatively 4 units, therefor the answer is D 1/-4

Please mark as brainliest :)

A certain shampoo is available in two sizes. A 23.7-ounce bottle costs $4.97 . A 33.8 -ounce bottle costs $7.48 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Unit price for the 23.7 Price per ounce
33.8 Price per ounce

Answers

Answer:

23.7 ounce = 20 cents per ounce

33.8 ounce = 22 cents per ounce

The 23.7 ounce bottle is a better deal because it is only 20 cents per ounce, rather than 22 cents per ounce.

3.Can we multiply a 2x3 matrix by a 3x2 matrix? If yes, what dimensions will the product matrix AB have ?

Answers

Answer:

Yes, the dimensions will be 2x2

Step-by-step explanation:

When multiplying matrices you have AxB by CxD. You can only multiply matrices if the inner number is the same.

Ex. 2x3 by 3x2 or QxD by DxW

The dimensions of the result will depend on the outer numbers.

Ex. 2x3 by 3x2 has a 2x2 result or QxD by DxW has a QxW result  

Final answer:

Yes, you can multiply a 2x3 matrix by a 3x2 matrix. The result will be a 2x2 matrix because the number of rows in the first matrix and the number of columns in the second matrix define the dimensions of the product matrix.

Explanation:

Yes, it is possible to multiply a 2x3 matrix by a 3x2 matrix. When multiplying matrices, the number of columns in the first matrix must be the same as the number of rows in the second matrix. Therefore, in this case, where we have a 2x3 matrix and a 3x2 matrix, the 3 columns in the first matrix and the 3 rows in the second matrix make multiplication possible.

The resulting product from the multiplication of these two matrices will be a new matrix whose dimensions are determined by the number of rows in the first matrix and the number of columns in the second matrix. In this case, as the first matrix has 2 rows and the second matrix has 2 columns, the resulting matrix will have dimensions of 2x2.

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Lin says that the inequalities h>150 and h<160 describe her height in centimeters. what do the inequalities tell us about her height?

Answers

Answer:

Her height is in between 150 and 160

Step-by-step explanation:

Given

h > 150

h < 160

Required

What do these represent?

First, the inequalities need to be combined.

If h < 160, then this means that 160 > h.

So, h > 150 and 160 > h can be combined to form an inequality in the following form;

160 > h > 150

This.meeans 160 is greater than h and h is greater than 150.

If this is related to her height, it means 160 is greater than her height and her height is greater than 150;

In other words, her height is in between 150 and 160

What is the volume of this rectangular pyramid?
3 yd
5 yd
5 yd
cubic yards

Answers

5yd si the volumen of the rectangular pyramid

PLEASE HELP!
put the following fractions in order from smallest to biggest

1/2, 3/4, 3/8, 5/8, 5/16, 7/16, 9/16 and 11/16 inches

Answers

5/16
3/8
7/16
1/2
9/16
5/8
11/16
3/4

:)

HURRY PLEASEEEEE!!!!

Use r = 2 and r = 5 to determine if the two expressions are equivalent.
r + 4(2 + r) – 12    8 + 2r – 6

Complete the statements.
1.When r = 2, the first expression is ?.
2.When r = 2, the second expression is 6.
3.When r = 5, the first expression is 21.
4.When r = 5, the second expression is .?
5.The expressions are not equivalent.

Answers

The two expressions are not equivalent to each other at r =2 and r = 5.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Use r = 2 and r = 5 to determine if the two expressions are equivalent.

r + 4(2 + r) – 12    8 + 2r – 6

First put r = 2 in both the expressions:-

E1 = 2 + 4 ( 2 + 2 ) -12

E1 =6

E2 = 8 + ( 2 x 2 ) - 6

E2 = 6

Secondly, put r = 5 in both the expressions.

E1 = 2 + 4 ( 2 + 5 ) - 12

E1 = 30

E2 = 8 + ( 2 x 5 ) -6

E2 = 12

The two expressions are not equivalent at r = 2 and r =5.

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Answer: 6, 12

Step-by-step explanation:

proof :)

The data to represent average test scores for a class of 16 students includes an outlier value of 91. If the outlier is included, then the mean is 80. Which statement is always true about the new data when the outlier is removed?

The median would decrease.

The median would increase.

The mean would decrease.

The mean would increase.

Answers

Answer:

c the mean would decrease

Step-by-step explanation:

Answer:

C) The mean would decrease!!

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