Mathematics High School

The general form of the equation of a circle is x2 + y2 + 8x + 22y + 37 = 0.
The equation of this circle in standard form is

HELP WILL MEDAL,

Answers

Answer 1
The standard form of the equation for a circle is (x-a)^2 + (y-b)^2 = r^2 where (a,b) = center of circle r = radius. So let's do it. x^2 + y^2 + 8x + 22y + 37 = 0 Let's start with determining a. We know that (x-a)^2 will result in an x^2 term and an 8x term. Let's square (x-a) and we get x^2 - 2ax + a^2. The x^2 term is OK and we have 8x = -2ax So 8x = -2ax 8 = -2a -4 = a So we now know that part of the equation will be (x - -4)^2 = (x + 4)^2. Let's expand that, giving x^2 + 8x + 16 and since we're adding 16 to the left, we need to add that to the right as well. So our equation becomes (x + 4)^2 + y^2 + 22y + 37 = 16 Now let's work on the y terms. Using the same logic as above the equation to solve is 22y = -2by 22 = -2b -11 = b So (y - -11)^2 = (y+11)^2. And expanding gives us y^2 + 22y + 121 which means we need to add 121 to the right, so we have (x + 4)^2 + (y + 11)^2 + 37 = 16 + 121 (x + 4)^2 + (y + 11)^2 + 37 = 137 (x + 4)^2 + (y + 11)^2 = 100 And a simple rewrite of the right hand side gives us (x + 4)^2 + (y + 11)^2 = 10^2 So the final equation is (x + 4)^2 + (y + 11)^2 = 10^2 Which indicates a circle with a radius of 10 centered at (-4,-11)

Related Questions

A bag contains 8 black marbles, 16 white marbles, 14 red marbles, and 10 green marbles. A marble is drawn at random from the bag. What is the probability that the marble drawn will not be white? 13 23 34 1516

Answers

 add all of the marbles subtract from the white marbles and you get 34 out of 48

Answer: The answer is 2/3.

please help me please

Answers

Okay. By looking at the question, 2.75 is the distance ran for ½ an hour, because DeAngelo runs at 5.5 miles an hour, but he doesn't run the full 5.5 miles, because of the time. 2.75 is the base. He increases his speed for 1.5 hours for total of 13.25 miles. The equation would be set up as this:

2.75 + 1.5p = 13.25

How to solve it:

We will solve this by subtract 2.75.5 from both sides. 2.75 - 2.75 cancels out. 13.25 - 2.75 is 10.5. We will divide that number by 1.5 now. 1.5p/1.5 cancels out. 10.5/1.5 is 7. There. DeAngelo ran the last 1.5 hours at 7 miles per hour.

What percent of 82.5 is 21.12

Answers

100%/x%=82.5/21.12
(100/x)*x=(82.5/21.21)*x
100=3.90625*x
100/3.90625=x
25.6=x
x=25.6

Thus: 21.12 is 25.6% of 82.50

The 25.6 percentage of the number 82.5 is 21.12

Given data:

To find the percentage of 21.12 in relation to 82.5, the proportion is simplified as:

21.12 is to 82.5 as x is to 100.

This can be expressed as:

21.12/82.5 = x/100

On solving for x by cross multiplying:

21.12 * 100 = 82.5 * x

2112 = 82.5x

To isolate x, divide both sides by 82.5:

2112/82.5 = x

On simplifying:

25.6 ≈ x

Hence, 21.12 is approximately 25.6 percent of 82.5.

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Help Please!!!
A cylindrical pressure vessel has a height of 9 feet and a diameter of 6 feet. How much gas can the pressure vessel hold when full?

I know the answer is 81pi cubic ft

but not sure what formula to use to get that answer. It's not Volume of a cylinder.,

Answers

This is a volume of a cylinder question, so I wonder why you dismiss that. The equation is pi x radius^2 multiplied by height, which indeed comes to 81pi, which is somewhere in the neighborhood of 250 pounds per cubic foot.

Answer:

You would need to use the formula for the volume of cylinder in order to get this. That's how I got to the answer of 81 pi. Maybe you used a different/wrong formula but you do need the formula for the volume of a cylinder.

The probability that it'll rain tomorrow in Ohio is 30%
The probability that it'll rain tomorrow in both Ohio and Alaska is 12%
If it rains tomorrow in Ohio what is the probability that it will rain tomorrow in Alaska?

Answers

It raining in Alaska and raining in Ohio are independent events. One does not control the other or affect the other in any way.

For two independent events (let's call them A and B), the Probability of A and B both occurring is given by P(A and B) = P(B) x P(B).

For this problem, let A = rain in Ohio and B= rain in Alaska.

P(A and B) = P(A) x P(B)
[tex] \frac{12}{100} =(P(A))( \frac{3}{10} ) [/tex]
[tex]( \frac{12}{100}) ( \frac{100}{30} )=P(A)[/tex]
[tex]P(A)= \frac{12}{30}= \frac{2}{5} [/tex]

is 6km ( <, >, or =) 660m?

Answers

660 Meters is equal to 0.660 KM
6 KM is greater then 660 M
Is 6 km ( <, >, or = ).  660 m

Answer would be:  6 km is LESS THAN  660 m


Explanation:

Each Kilometer is 1000 meters

6 Kilometers is 6000 meters



Hope this helps.

Describe the relationship among the lengths of the segments formed by the secant, , and the tangent segment, .You may use words and/or an equation.

Suppose in. and in. Is it possible to find the length of ? If so, show how to find the length. If not, explain why not.

Answers

Answer: The relationship show in the picture is that TU squared is equal to ST multiplied by RT.

If we know that RT is 9 and ST is 4, we could write the following equation.

Let TU = x

x^2 = 9 x 4
x^2 = 36
x = 6

We found the length of TU to be 6 inches.

We can write the answers as -

TU² = TR x TSTU = 6

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the equation as -

3√x + 3 = 15

{ 1 } -

When a tangent and a secant are drawn from one single external point to a circle, square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment. We can write -

TU² = TR x TS

{ 2 } -

We can write -

TU² = TR x TS

TU² = 9 x 4

TU² = 36

TU² = ± 6

TU = 6                         {non - negative}

Therefore, we can write the answers as -

TU² = TR x TSTU = 6

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A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4pir2 for the surface area of a sphere.

Answers

Answer:
area = pi * (64x² + 32x + 4)
Using pi = 3.14:
area = 200.96 x² + 100.48 x + 12.56

Explanation:
We are given that:
area of sphere = 4 * pi * r²
radius = 4x + 1

Substitute with the radius in the given formula to get the area as follows:
area = 4 * pi * (4x+1)²
area = 4 * pi * (16x² + 8x + 1)
area = pi * (64x² + 32x + 4)

Using pi = 3.14:
area = 200.96 x² + 100.48 x + 12.56

Hope this helps :)

Two cones have the same radii but one has a height four times larger than the other. How many small cones would be needed in order to have the same volume as the larger cone?

4


8


16


64

Answers

since the radius is the same but the height changes, the volume would change by the multiple of the height.
 In this case the volume of the larger cone would be 4 times as large as the smaller cone so you would need 4 small cones

Fan for everyone who helps, medal for whoever helps the most! :)

1. What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)

2. Which expression can be used to find the difference of the polynomials?
(10m – 6) – (7m – 4)

3. Which expression can be used to find the difference of the polynomials?
(4m – 5) – (6m – 7 + 2n),

Answers

Answer:

1- The sum is: 2m + 2n + 7 = 2(m+n) + 7

2- The difference is: 3m - 2

3- The difference is: -2m - 2n + 2 = -2(m+n-1)

Explanation:

Before we begin, remember the following:

+ve * +ve = +ve

-ve * -ve = -ve

+ve * -ve = -ve

-ve * +ve = -ve

Also, remember that, we only add/subtract like terms. There are terms which have the same variable(s) raised to the same degree

Now, let's check the problems:

Problem 1:

Adding two polynomials:

(m + n + 3) + (m + n + 4)

We first start by getting rid of the brackets:

m + n + 3 + m + n + 4

Now, we add like terms:

2m + 2n + 7

As an additional step, we can take 2 as a common factor from the first two terms:

2(m+n) + 7

Problem 2:

Subtracting two polynomials:

(10m - 6) - (7m - 4)

We first start by getting rid of the brackets. Take care of the different signs while doing so:

10m - 6 - 7m + 4

Now, we add/subtract like terms:

3m - 2

Problem 3:

Subtracting two polynomials:

(4m - 5) - (6m - 7 + 2n)

We first start by getting rid of the brackets. Take care of the different signs while doing so:

4m - 5 - 6m + 7 - 2n

Now, we add/subtract like terms:

-2m - 2n + 2

As an additional step, we can take -2 as a common factor from the above expression:

-2(m+n-1)

Hope this helps :)

Given the function f(x) = 0.5(3)x, what is the value of f−1(7)?

This question has been asked before but the answer is unclear to me.

Answers

as you already know, to get the inverse of any expression, we start off by doing a quick switcharoo on the variables, and then solve for "y".

[tex]\bf \stackrel{f(x)}{y}=0.5(3)^x\qquad \stackrel{inverse}{\boxed{x}=0.5(3)^{\boxed{y}}} \\\\\\ log(x)=log[0.5(3)^y]\implies log(x)=log(0.5)+log[(3)^y] \\\\\\ log(x)-log(0.5)=log[(3)^y]\implies log(x)-log(0.5)=y\cdot log(3) \\\\\\ \cfrac{log(x)-log(0.5)}{log(3)}=\stackrel{f^{-1}(x)}{y}\\\\ -------------------------------\\\\ f^{-1}(7)=\cfrac{log(7)-log(0.5)}{log(3)}\implies f^{-1}(7)\approx 2.402173502732879697[/tex]

Two angles that are supplementary have a ratio of 7 to 5. what are their measurements?

Answers

7x + 5x = 180
12x = 180
x = 15
Therefore, the 2 angles equal (7*15) and (5*15) which equals
105 degrees and 75 degrees


Given cosx=1213 and sinx=513 .

What is ratio for ​ tanx ​ ?

leave answer as a fraction in simplest form

Remember to show all of you work

Answers

The answer to this question is 5/12

By using the tangent formula, we will see that:

tan(x) = 5/12.

How to get the tangent of x?

You just need to remember that we can write the tangent as:

tan(x) = sin(x)/cos(x).

In this case, we know that:

sin(x) = 5/13cos(x) = 12/13

We can just replace these two in the tangent equation, we will get:

tan(x) = (5/13)/(12/13) = (5/13)*(13/12) = 5/12

tan(x) = 5/12

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Please help

According to Cavalieri's principle,
A) the volume of the sphere is equal to the volume of the cones.
B) the volume of the sphere is equal to the volume of the cylinder.
C) the volume of the sphere is equal to two times the volume of the cones.
D) the volume of the sphere is equal to the volume of the solid between the cones and the cylinder.

Answers

Answer:

Step-by-step explanation:

The answer is d.

Answer:

d

Step-by-step explanation:

what is the value of x that equals 14 y=310-25(x)

Answers

If you want y = 14,
  x = (310 -y)/25 = (310 -14)/25 = 296/25
  x = 11.84

If you want x = 14,
  y = 310 -25*14 = 310 -350
  y = -40

How to find out how much you pay if there was a sale tax?

Answers

Money time tax owed

PLEASE HELP ME ON THIS AND SHOW UR WORK
THX

Answers

When an exponential function is given as 
f(x)=ab^x, and
knowing that b^0=1, that means that
f(0)=ab^0=a  value of function when x=0, or the initial value.
In the case of
f(x)=20.b^x, f(0)=20.b^0 = 20  (initial value)

If b=1.2, then the hourly growth rate is (1.2-1)=0.2=20%.
If b=1.85, then the hourly growth rate is (1.85-1)=0.85=85%. 

Which coordinate Gird shows the correct locations of P (1,2.5) Point Q which is a reflection Of point P across the Y-axis And R (2.-2.5)

Answers

The first thing we are going to do is define point Q
 "Point Q which is a reflection Of point P across the Y-axis"
 Therefore, we have:
 Q = (-1, 2.5)
 Now we graph each ordered pair.
 Note: See attached image.

What is the value of x?


20

40

45

85

Answers

2x+10=90
2x=80
x=40
the answer is 40.

Answer:

the answer i 40 hope this helps :)

Step-by-step explanation:



Find the slope of the line that contains the points named.
X(2, -1), Y(0, 4)
5/2
2/5
-5/2

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& -1~) % (c,d) &&(~ 0 &,& 4~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-1)}{0-2}\implies \cfrac{4+1}{0-2}\implies \cfrac{5}{-2}[/tex]
I believe following the slope formula the answer should be -5/2 
if I’m wrong I’m sorry.

Suzy likes to mix and match her 3 necklaces, 2 bracelets, and 6 hats. The colors are listed in the table. On Monday, she randomly picks a bracelet, a necklace, and a hat. What is the probability of Suzy choosing a red bracelet and silver hat? NECKLACE COLORS: RED ,GREEN ,GOLD BRACELET COLORS: RED AND BLACK HAT COLORS: SILVER, YELLOW, GREEN, GOLD, BLACK, AND WHITE A. one-half B. one-fourth C. start fraction 1 over 6 end fraction D. start fraction 1 over 12 end fraction

Answers

Answer: Option D. 1/12

We have:
3 Necklaces (red, green, and gold)
2 Bracelets (red and black)
6 hats (silver, yellow, green, gold, black, and white)

The number total of combinations is:
C=3x2x6→C=36 possible combinations

What is the probability of Suzy choosing a red bracelet and silver hat?
Possible combinations with a red bracelet and silver hat:
C1=1 (red bracelet) x 1 (silver hat) x 3 (necklaces: red, green, and gold)
C1=3 possible combinations with a red bracelet and silver hat

Probability of Suzy choosing a red bracelet and silver hat: P=C1/C
P=3/36

Simplifying the fraction dividing the numerator and the denominator by 3:
P=(3/3) / (36/3)
P=1/12

Answer: The probability of Suzy choosing a red bracelet and silver hat is 1/12

Answer:

The probability of Suzy choosing a red bracelet and silver hat is 1/12

Step-by-step explanation:

Each one of the red, green, and gold necklace have a probability of 1/3.

Each one of the red and black bracelet have a probability of 1/2.

Each one of the silver, yellow, green, gold, black, and white hat have a probability of 1/6.

Hence, the probability of Suzy choosing a red bracelet and silver hat becomes:

[tex]\frac{1}{2}*\frac{1}{6} =\frac{1}{12}[/tex]

So, the answer is 1/12.

Batteries for an MP3 player usually cost $8.00, but they are on sale for 40% off. What is the discount amount? What is the sale price for these batteries?

Answers

Let's think. What is 50% of 8.00? It's 4.00. So, 40% would be about 3.20.

Answer:

its b!

Step-by-step explanation:

discount is $8 = 40/100 to find that discout

is $3.20

sale price : $8.00 - $3.20 which is $4.80!

Your welcome! :D

Compare the properties of the diagonals of a kite with those of a square.

Answers

1.Two distinct pairs of adjacent sides are congruent (i. e they have the same angle)
2. Diagonals of a kite intersect at right angles
3. One of the diagonals is the perpendicular bisector of another.

While the square..
1. Diagonals are equal and are perpendicular bisectors of each other

Diagonals of square are congruent  while diagonals of kite are not congruent to each other.

What is diagonal?

" Diagonal is a straight line segment which connects the opposite vertices of any polygon or polyhedron."

Compare the properties of diagonal of square and kite

1) Diagonals of square are congruent while diagonals of kite are not of same length.

2) Diagonals of square bisect each other  while in kite longer diagonals bisects the smaller one.

3) Diagonals of square and kite are perpendicular to each other.

Hence, diagonals of square are congruent  while diagonals of kite are not congruent to each other.

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∆ABC has the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices.
The measure of the longest side of ∆ABC is ______ units. ∆ABC is_____ triangle.

If ∆ABD is formed with the point D(1, 2) as its third vertex, then ∆ABD is _____ triangle. The length of side AD is ______ units.

1. 
B.29^(1/2) . 
C.34^(1/2) 
D.6 
2.
A.equlaterial
B.isoclese
C.right
D.scalene
3. 
A.equilateral 
B.right isosceles 
C.right scalene 
D.non-right isosceles
E.non-right scalene

4.
A.3
B.5
C.8
D.10


Answers

1. D 6
2. B isosceles
3. C right scalene
4. B 5

The measure of the longest side of ∆ABC is 6 units. ∆ABC is a right scalene triangle. ∆ABD is also a right scalene triangle and the length of side AD is 5 units.

The measure of the longest side of ∆ABC can be found using the distance formula.

We calculate the distance between points A(1, 7) and B(-2, 2), between points B(-2, 2) and C(4, 2), and between points A(1, 7) and C(4, 2).

The longest distance is the measure of the longest side.

Using the distance formula, we find that the longest side is 6 units long.

∆ABC is a right scalene triangle.

This is because the lengths of its sides are all different and it has a right angle at point C, where the x-coordinate doesn't change but the y-coordinate does.

∆ABD is also a right scalene triangle.

The length of side AD can be found using the distance formula between points A(1, 7) and D(1, 2).

The length of side AD is 5 units.

What is the sum of the geometric series

Answers

Which one theres many!! :)

Answer:

Hence, the sum of the geometric series is:

                                      259

Step-by-step explanation:

We are given a geometric series as:

[tex]\sum_{i=1}^4 6^{i-1}[/tex]

i.e. we are asked to fnd the sum of first four terms of the geometric series with first term as 1

Since, the series is:

[tex]6^0+6^1+6^2+6^3[/tex]

Also, the common ratio of the series is: r=6

Since, each of the term of the series is 6 times it's preceding term.

Also we know that sum of a finite geometric series with n-terms and common ratio r is calculated by the formula:

[tex]S_n=a(\dfrac{r^n-1}{r-1})[/tex]

Here we have: a=1 and r=6 and n=4

Hence,

[tex]S_4=1(\dfrac{6^4-1}{6-1})\\\\\\S_4=\dfrac{1295}{5}\\\\\\S_4=259[/tex]

                        Hence, the sum of the series is:

                                     259

One inch on a map equals 300 miles. it is 1/4¨ from el paso texas, to bismarck north dakota. how many miles would it be?

Answers

if 1in=300 miles, then 1/4 of an in would be 75miles. because there are four 1/4ths in an inch. 300/4=75

The value of 1/4 inch in miles from the given map is; 75 miles

How do you convert the measurement?

We are given that;

1 inch on the map = 300 miles

Now, we want to find what 1/4 inch will give us in miles from the given conversion. Thus;

1/4 inch in miles = 1/4 * 300

⇒ 75 miles

Thus, we will conclude that 1/4 inch will yield 75 miles on the map.

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Jim and Gail invested a total of $3,600 in a stock, in a ratio of 5:7. The stock made $6,450 on top of the initial capital. If the payoff is done in the same ratio, how much does Gail get?

Answers

"Since the ratio is 5:7 you can think in total there was 12 equal blocks of money invested. 5 of those blocks belonged to Jim and 7 of those blocks belonged to Gail. Since they invested $3,600 and then made $6,450 in total there is $10,050. Divide that total into 12 equal blocks of $837.50 and 5 of those blocks belong to Jim. So he will get $4,187.50"

The amount that Gail will get is $5862.5.

What is Ratio?

A ratio is a comparison of two quantities produced by dividing the first by the second. If a and b are two values of the same kind and with the same units, and b is not equal to zero, then the quotient a/b is known as the ratio between a and b. The colon sign is used to denote ratios (:). This means that the ratio a/b has no unit and can be expressed as a: b.

Given:

Jim and Gail invested a total of $3,600 in a stock, in a ratio of 5:7.

The stock made $6,450 on top of the initial capital.

Total they made

= 3600+ 6450

= $10, 050

The pay off Jim get

= 10, 050 x 5/12

= 4187.5

and, the pay off Gail  get

= 10, 050 x 7/12

= $5862.5

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Choose the graph that matches the following system of equations:
Explain to me why I got this wrong!!! Please
8x + 5y = −5
7x − 3y = 3 (6 points)

Answers

In intercept form, the equations are
.. x/(-5/8) +y/(-1) = 1
.. x/(3/7) +y/(-1) = 1

The first line has intercepts (-5/8, 0) and (0, -1).
The second line has intercepts (3/7, 0) and (0, -1)

In the second graph, the (blue) line with positive slope has an x-intercept greater than 1/2. Neither line matches that. The intercepts match those of the first graph.

On the rectangular coordinate system, what is the shortest distance between points (−4, 3) and (−2, −1)?

Answers

Shortest Distance = [tex] \sqrt{ (-4+2)^{2} + (3+1)^{2} } [/tex]
Shortest Distance = [tex] \sqrt{ (-2)^{2} + (4)^{2} } [/tex]
Shortest Distance = [tex] \sqrt{20} [/tex]
Shortest Distance = [tex]4.47 units[/tex]

Answer:

In other words to what the dude above me said, the answer is "a''

Step-by-step explanation:

Write an equation to represent, "sum of eight and a number is one hundred". What is the number?

Answers

The equation is "8 + x = 100" and the number is "92". You get 92 by subtracting 8 from each side which leaves "x = 92"
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