A certain circle can be represented by the following equation. x^2+y^2+8x-16y+31=0x 2 +y 2 +8x−16y+31=0x, squared, plus, y, squared, plus, 8, x, minus, 16, y, plus, 31, equals, 0 What is the center of this circle ? ((left parenthesis ,,comma ))right parenthesis What is the radius of this circle ? units

Answers

Answer 1

Answer:

center = [tex](-4,8)[/tex]

Radius = 7 units

Step-by-step explanation:

Given: Equation of circle is [tex]x^2+y^2+8x-16y+31=0[/tex]

To find: Radius and center of the circle

Solution:

Equation of circle is [tex](x-a)^2+(y-b)^2=r^2[/tex]

Here, [tex](a,b)[/tex] is the center and r is the radius.

[tex]x^2+y^2+8x-16y+31=0\\\left [ x^2+2(4)x+4^2 \right ]+\left [ y^2-2(8)y+8^2 \right ]+31=4^2+8^2[/tex]

Use formula [tex](u+v)^2=u^2+v^2+2uv[/tex]

[tex](x+4)^2+(y-8)^2=16+64-31\\(x+4)^2+(y-8)^2=49=7^2[/tex]

On comparing this equation with equation of circle,

center = [tex](-4,8)[/tex]

Radius = 7 units

Answer 2

Answer:

center: (4,-4)

Radius: 9

Step-by-step explanation:

KHAN ACADEMY


Related Questions

Which can be used to describe an equivalent expression for (s Superscript 6 Baseline) Superscript negative 3? Adding the exponents will create an equivalent expression. Dividing the exponents will create an equivalent expression. There are three factors of StartFraction 1 Over s Superscript 6 Baseline EndFraction. There are three factors of StartFraction 1 Over s Superscript 3 Baseline EndFraction.

Answers

Answer:

D

Step-by-step explanation:

i took the test

The equivalent expressions of [tex](x^{6} )^{-3}[/tex] will be [tex](x )^{-18}[/tex].

What are equivalent expressions?

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive the equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

The given expression is;

[tex](x^{6} )^{-3}[/tex]

Required to Determine the equivalent expression.

First, we need to evaluate the expression in the bracket:

Apply the following law of indices:

[tex](x^a)^b = x ^{ab}[/tex]

So:

[tex](x^{6} )^{-3}[/tex]

becomes

[tex](x )^{6 \times -3}\\\\[/tex]

[tex](x )^{-18}[/tex]

Hence: the equivalent expressions of [tex](x^{6} )^{-3}[/tex] will be [tex](x )^{-18}[/tex].

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please help! I will mark as branliest if you help

Answers

Answer:

B.180°

Step-by-step explanation:

The sum of supplementary angles are always equal to 180, as you can see, the angles form a half circle which is 360/2. Hope this helps :)

Answer:

180

Step-by-step explanation:

Supplementary angles sum to 180 degrees

PLZ HELP WILL MARK BRAINLIEST!!!
The graph of a proportional relationship passes through (3, 24) and (1, y).
Find y

Answers

Answer:

8

Step-by-step explanation:

If it is proportional 3/3=1

And 24/3=8

Answer: go up the origin maybe that would help

Step-by-step explanation:

What are our “cheat words” for finding slope?

Answers

mx+b=y ? that’s a formula

Answer: y-intercept

Step-by-step explanation:

what is w in the equation -20=5w

Answers

Divide each term by 5.
So, 5w/5=W and -20/5 =-4.

So,

W = -4

I hope that helps.

Answer:

-4

Step-by-step explanation:

Since this has an equals sign and in both sides it can be divisible. So you take 5 and divide it on both sides to get -4

Y = 3x -1 Y = 2x + 3

Answers

Answer:

x = 4

y = 11

Step-by-step explanation:

You can make the equations 3x - 1 = 2x + 3

x = 4

y = 11

Which point is located at (Negative 1, 1 and one-fourth)?

Answers

Answer:

(-1, 1 1/4) or (-1, 1.25)

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

Factor the expression
36x + 27 using the GCF.

Answers

Answer:

9(4x+3)     :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

the first step in factorising is to look for any common factors.

27

and

36

are both multiples of

3

and

9

.

We use

9

because it is the highest common factor:

Divide

9

out of each term:

27+36x=9(3+4x)

The reverse process would be to use the distributive law to multiply each term in the bracket by

9

.

This will give us the original expression:

9(3+4x)=27+36x

Nina recorded collected data on the number of tickets that people had received and how many accidents they had been in. She made a scatterplot of her data. What is the best line of fit for this data?

Answers

Answer:

A straight line dividng the data into two equal parts.

Step-by-step explanation:

A scatter plot is drawn by representing  the numbers with the dots on the specific points to interpret their values.The best line of fit for scatter plot data is a straight line. It divides the data  into two parts. Some points may lie above the  data and some below the data. Some points may lie on the line. All the points can also lie on the line and none of the points can also lie on the line.

bag of potatoes weighs 10 pounds what is the weight of the potatoes on ounce

Answers

Answer:

The potato is a root vegetable native to the Americas, a starchy tuber of the plant Solanum tuberosum, and the plant itself, a perennial in the family Solanaceae. Wild potato species, originating in modern day Peru, can be found throughout the Americas, from the United States to southern Chile.

Step-by-step explanation:

Answer:

160 ounces

Step-by-step explanation:

If the point (a,1) lies on the line y = 3x - 5, what is the value of a?

Answers

Answer:

a = 2

Step-by-step explanation:

Note that a point uses (x , y).

y = 1

x = a

Plug in 1 for y in the equation, and a for x:

y = 3x - 5

1 = 3a - 5

Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First add 5 to both sides:

1 (+5) = 3a - 5 (+5)

1 + 5 = 3a

6 = 3a

Next, divide 3 from both sides:

(6)/3 = (3a)/3

a = 6/3

a = 2

2 is your value for a.

~

Round to 2 decimal places
0.607

Answers

Answer:

Round to 2 decimal places

0.607 => 0.61

Hope this helps!

:)

What is the degree of
6x^5 – 4x^2 + 2x^2 - 3 + x?
A. 3
B. 5
C. 6
D.2

Answers

Hello!

Answer:

[tex]\boxed{ \bf The~degree~of~the~polynomial~is~B.~5}[/tex]

___________________________________________

Explanation:

The term with the greatest exponent determines the degree of the polynomial.

Let's list all the terms:

[tex]6x^{5}[/tex]-4x²2x²-3x

Out of all of these terms, the first one has the greatest exponent (5).

To rent a canoe costs $15 for the first hour and $12 for each additional hour or fraction of an hour. Which point is NOT included in the graph of this step function?

A. (2.5, 39)
B. (3.2, 51)
C. (3.0, 39)
D. (4.5, 51)

Answers

Answer:

A

Step-by-step explanation:

(2.5,39)

Answer:

(2.5, 39)

Person above me is correct. :)

13 POINTS!!!

In ΔJKL, j = 74 inches, k = 14 inches and l=67 inches. Find the measure of ∠L to the nearest degree.

Answers

Answer:

55°

Step-by-step explanation:

Using cosine law

67² = 74² + 14² - 2(74)(14)cos(L)

cos(L) = 169/396

L =55.18378419

The measure of angle L to the nearest degree is 55°.

What is Law of Cosines?

Law of cosines of triangle states that for three length of sides of the triangle, a, b and c opposite to the angles A, B and C respectively can be related as,

a² = b² + c² - 2bc cos(A)

Given, for a triangle JKL,

j = 74 inches, k = 14 inches and l = 67 inches.

We can use law of cosines to find the measure of angle L.

Using the law of cosines,

l² = j² + k² - 2jk cos(L)

67² = 74² + 14² - (2×74×14) cos(L)

4489 = 5476 + 196 - 2072 cos(L)

4489 = 5672 - 2072 cos(L)

-1183 = - 2072 cos(L)

cos (L) = 0.5709

L = 55.18° ≈ 55°

Hence the measure of angle L is 55°.

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Plz, help me!!!

How many solutions does the system of equations have?

Answers

Answer:

1 solution: x = 1 and y = 4

[tex] {75}^{2} + 25 - 750[/tex]

Answers

your answer is 4900

need help and an explanation!thanks!!​

Answers

Answer: A

Step-by-step explanation:

[tex]V=\frac{l*w*h}{3}[/tex]

[tex]V=\frac{(15in)(15in)(19in)}{3} \\V=1425in^3[/tex]

A company is designing a new cylindrical water bottle. The volume of the bottle will be 187 cmcubed. The height of the water bottle is 7.3 cm. What is the radius of the water​ bottle? Use 3.14 for pi.

Answers

Answer:

2.86cm

Step-by-step explanation:

Step 1:

Data obtained from the question. This includes the following:

Volume (V) = 187cm3

Height (h) = 7.3cm

Pi (π) = 3.14

Radius (r) =..?

Step 2:

Determination of the radius of the cylindrical water bottle.

The radius of the cylindrical water bottle can be obtained as follow:

V = πr^2h

187 = 3.14 x r^2 x 7.3

Divide both side by 3.14 x 7.3

r^2 = 187 / (3.14 x 7.3)

Take the square root of both side

r = √[187 / (3.14 x 7.3)]

r = 2.86cm

Therefore, the radius of the cylindrical water bottle is 2.86cm

Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing!

Answers

Answer: A

Step-by-step explanation:

Answer:

I'm sorry what grade level is this

What is the Volume of the triangular prism, in cubic centimeters?

Answers

Answer: the answer is approximately 45.6

Step-by-step explanation:

Michael has 4 red shirts, 3 green shirts, and 5 blue shirts in his closet. If he randomly selects a shirt, what is the probability that he chooses green or red?

Answers

First add
4 red + 3 green + 5 blue = 12

Then add the likelihood that you will choose a green or red
4 + 3 = 7

The answer is 7/12

Answer:

First add

4 red + 3 green + 5 blue = 12

Then add the likelihood that you will choose a green or red

4 + 3 = 7

The answer is 7/12

Step-by-step explanation:

USA TESTPREP

Enter the division problem 15 ÷11 as a fraction.

Answers

Answer: 15/11

Step-by-step explanation:

Answer:

15 ÷ 11 as a fraction is 15/11. As a mixed number it is 1 4/11.

Step-by-step explanation:

An economy package of cups has 750 green cups. If the green cups are 30% of the total package, how many cups are in the package?

Answers

Answer:

2500 cups

Step-by-step explanation:

Let c = total cups

c*30% = green cups

c*.30 = 750

Divide each side by .30

.30c/.30 = 750/.30

c =2500

Which steps should be taken to solve the equation 2x+3=x+5. Check all that apply

Answers

Answer:

Remove 1 x tile and 3 unit tiles from each side

Step-by-step explanation:

technically you can do any of them, but I don't think that's what your teacher wants.

Please answer this question

x^2 = 11x

Answers

[tex] {x}^{2} = 11x \\ {x}^{2} - 11x = 0 \\ x(x - 11) = 0[/tex]

Product is equal to 0 when one of multipliers is equal to 0, so

[tex]x = 0[/tex]

Or

[tex]x - 11 = 0 \\ x = 11[/tex]

Answer: x=0 or x=11

Answer:

Step-by-step explanation:

x^2 = 11x

x ( x − 11 ) = 0

x = 0  (by transposing)

x − 11 = 0

x=11  (by transposing)

therefore, x= 0,11

Hope it Helps...pls Mark as Brainliest!!

Eduardo is filling containers with water to make lemonade. He filled 4 containers in 29 minutes, and each container holds 8.7 gallons. At what rate did Eduardo fill the containers?

Answers

Answer: 7.25 minutes per container.

Step-by-step explanation:

Your looking for a ratio of time per container. 29/4 is the given ratio it was simplified to 7.25/1. Or simply 29 divided my 4.

1) Find the volume of the triangular prism.
5 yd
5 yd
3 yd
6 yd
8 yd
27 yd
72 yd
240 yd
360 yd

Answers

Answer:

I am not completely sure but I believe that it is C) 240 yd^3

Step-by-step explanation:

Select ALL the correct answers.
Consider the following quadratic equation.
y=x²-8x+4
Which of the following statements about the equation are true?

When y = 0, the solutions of the equation are x=8±2√2.
The extreme value of the graph is at (8,-4).
When y = 0, the solutions of the equation are x=4±2√3.
The extreme value of the graph is at (4,-12).
The graph of the equation has a minimum.
The graph of the equation has a maximum.

Answers

Answer:

Statements 3, 4 and 5 are true.

Step-by-step explanation:

x^2 - 8x + 4

Using the quadratic formula:

x = [ -(-8) +/- √((-8)^2 - 4*1*4)] / 2

= (8 +/- √(64 - 16)) / 2

= 4 +/- √48 / 2

= 4 +/- 4√3/2

= 4 +/- 2√3.

So the third statement is true.

Converting to vertex form:

x^2 - 8x + 4

= (x - 4)^2 - 16 + 4

= (x - 4)^2 -12

So the extreme value is at (4, -12)

So the fourth statement is true.

The coefficient of the term in x^2 is 1 (positive) so the graph has a minimum.

Find the mean for each data set.

Number of Flowers




<-----I-----I-----I-----I-----I-----I-----I-----I-----I----->
10 11 12 13 14 15 16 17 18

Answers

Answer:

14

Step-by-step explanation:

you add them all up and divide by how much there are

(10+11+12+13+14+15+16+17+18)=126

(126/9)=14

Answer:

14

Step-by-step explanation:

first you add them all up and then divide alll of them again

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