Answers
The answer is:
The center of the circle is located on the point (-9,-2) and the radius is 6 units.
Why?To solve the problem, we need to use the given equation which is in the general form.
We are given the circle:
[tex]x^{2}+y^{2}+18x+4y+49=0[/tex]
We know that a circle can be written in the following form:
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
Where,
h is the x-coordinate of the center of the circle
k is the y-coordinate of the center of the circle
r is the radius of the circle.
So, to find the center and the radius, we need to perform the following steps:
- Moving the constant to the other side of the equation:
[tex]x^{2}+y^{2}+18x+4y=-49[/tex]
- Grouping the terms:
[tex]x^{2}+18x+y^{2}+4y=-49[/tex]
- Completing squares for both variables, we have:
We need to sum to each side of the equation the following term:
[tex](\frac{b}{2})^{2}[/tex]
Where, b, for this case, will the coefficients for both terms that have linear variables (x and y)
So, the variable "x", we have:
[tex]x^{2} +18x[/tex]
Where,
[tex]b=18[/tex]
Then,
[tex](\frac{18}{2})^{2}=(9)^{2}=81[/tex]
So, we need to add the number 81 to each side of the circle equation.
Now, for the variable "y", we have:
[tex]y^{2} +4y[/tex]
Where,
[tex]b=4[/tex]
[tex](\frac{4}{2})^{2}=(2)^{2}=4[/tex]
So, we need to add the number 4 to each side of the circle equation.
Therefore, we have:
[tex](x^{2}+18x+81)+(y^{2}+4y+4)=-49+81+4[/tex]
Then, factoring, we have that the expression will be:
[tex](x+9)^{2}+(y+2)^{2}=36[/tex]
- Writing the standard form of the circle:
Now, from the simplified expression (after factoring), we can find the equation of the circle in the standard form:
[tex](x+9)^{2}+(y+2)^{2}=36[/tex]
Is also equal to:
[tex](x-(-9))^{2}+(y-(-2))^{2}=36[/tex]
Where,
[tex]h=-9\\k=-2\\r=\sqrt{36}=6[/tex]
Hence, the center of the circle is located on the point (-9,-2) and the radius is 6 units.
Have a nice day!
Related Questions
Which of the following are factors of the equation when written in factored form
Answers
Answer:
B and D
Step-by-step explanation:
Given
2a² + 8a - 15 = 3a - 3 ( subtract 3a - 3 from both sides )
2a² + 5a - 12 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the product of the a² term and the constant term which sum to give the coefficient of the a term, that is
product = 2 × - 12 = - 24 and sum = + 5
The factors are + 8 and - 3
Use these factors to split the a- term
2a² + 8a - 3a - 12 = 0 ( factor the first/second and the third/fourth terms )
2a(a + 4) - 3(a + 4) = 0 ← factor out (a + 4) from each term
(a + 4)(2a - 3) = 0 ← in factored form
colby and jaquan are growing bacteria in an experiment in a laboratory. Colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours. Jaquan starts with 80 of a different type of bacteria that doubles every 3 hours.
Let x equal number of days.
Colby’s experiment follows the model:
1) y=50*2^x
2) y=50*2^8x
3) y=50*2^12x
Jaquan’s experiment follows the model:
1) y=80*2x
2) y=80*2^8x
3) y=80*2^12x
20 POINTS*****
Answers
Answer:
3) y = 50 * 2¹²ˣ
2) y = 80 * 2⁸ˣ
Step-by-step explanation:
1 day = 24 hours
Number of 2-hour periods in 1 day = 24 ÷ 2 = 12
Number of 3-hour periods in 1 day = 24 ÷ 3 = 8
Colby's experiment:
y = 50 * 2¹²ˣ
Jaquan's experiment:
y = 80 * 2⁸ˣ
I need help i can not figure it out
Answers
Just times it all together, the same rules apply for finding the area.
Answer:
The formula for is Length x width x height so all you have to do it substitute length width and height.
Length= 14cm
Width= 7cm
Height= 16cm
so, 14cm x 7cm x 16cm= 1,568 cm
Please give me the brainliest answer?
:) Hope this helped!!! Have a good day!!! <3
lf 4 pounds of birdseed cost
$6.95, about how much does 1 ounce
cost?
Answers
Answer:
$1.01
Step-by-step explanation:
To find the cost of one ounce of birdseed, first convert the weight to ounces (4 pounds equals 64 ounces) and then divide the total cost by the total number of ounces. The result is approximately $0.11 per ounce.
First, we need to convert the weight from pounds to ounces since there are 16 ounces in 1 pound. So, 4 pounds is equivalent to 4 × 16, which equals 64 ounces.
Now, if 4 pounds (or 64 ounces) of birdseed cost $6.95, we want to find the cost of one ounce. To do this, we divide the total cost by the total number of ounces:
$6.95 / 64{ ounces} = approximately $0.10859375 { per ounce}
This result is the cost per ounce. So, the approximation for the cost of 1 ounce of birdseed is roughly $0.11 (rounded to 2 decimal places).
20 pts!!!Clarice wrote this expression to describe the total amount of fair tickets she has in her pocket. t + 12 Which situation could be described by this expression?
A.Clarice doesn't know how many tickets she used. She knows she had 12 tickets to start with.
B.Clarice doesn't know how many tickets she used. She knows they each cost $12.
C.Clarice knows she used 12 tickets. She doesn't know how many tickets she has left.
D.Clarice knows she bought 12 tickets. She doesn't know how many tickets her sister gave her.
Answers
Clarice started with 12 tickets and added more (t) to it. She doesn't know how many tickets she used, fitting situation A.
The expression t + 12 implies that Clarice started with 12 tickets and then added some more tickets ( t ) to it.
Among the given options, situation A best fits this expression. Clarice knows she had 12 tickets to start with, but she doesn't know how many additional tickets ( t ) she has acquired or used since then.
So, the correct situation described by the expression is A.
To enter a local fair, one must pay an entrance fee and pay for the number of ride tickets he/she wants. Admission to the fair is given by the equation f(x) = .50x + 10, where x represents the number of tickets purchased and f(x) represents the total price. How much does each ride ticket cost?
Answers
From the equation given, each ticket costs 50 cents as expressed in 0.50x. Every time you increase x by one, the total cost increases by 50 cents
Answer
A) $10
Step-by-step explanation:
Ms Redmond gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented
Answers
Answer:
The mean will decrease.
Answer:
The correct option is B.
Step-by-step explanation:
From the given dot plot we can create a frequency table.
x f
1.5 2
2 1
2.5 3
3 1
3.5 2
4 1
This data can be written as
1.5, 1.5, 2, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 4
The mean of the data is
[tex]Mean=\frac{\sum x}{n}=\frac{1.5+1.5+2+2.5+2.5+2.5+3+3.5+3.5+4}{10}=2.65[/tex]
The number of terms is 10 which is an even number. So, the median of the data is
[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{5th+6th}{2}=\frac{2.5+2.5}{2}=2.5[/tex]
If next student presents a monologue that is about 0.5 minutes long, then the new data is
0.5, 1.5, 1.5, 2, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 4
The mean of the new data is
[tex]Mean=\frac{\sum x}{n}=\frac{0.5+1.5+1.5+2+2.5+2.5+2.5+3+3.5+3.5+4}{11}=2.4545..\approx 2.45[/tex]
The number of terms is 11 which is an odd number. So, the median of the new data is
[tex]Median=(\frac{n+1}{2})th=6th=2.5[/tex]
Median of given data and new data is same but the mean of new data is less than the mean of original data. It means the mean will decrease.
Therefore the correct option is B.
How does the a value affect your tangent graph?
Answers
the value effects it by now much they have so you can determine who has the most and who has the least
Which situation is represented by the equation?
3n + 5 = 2n − 7
A) The product of a number and 3, decreased by 5, is 7 more than twice the number. What is n, the unknown number?
Eliminate
B) The product of a number and 3, increased by 5, is 7 more than twice the number. What is n, the unknown number?
C) The product of a number and 3, decreased by 5, is 7 less than twice the number. What is n, the unknown number?
D) The product of a number and 3, increased by 5, is 7 less than twice the number. What is n, the unknown number?
Answers
Answer:
D. should be the correct answer. Hope this helps.
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
took test
Find the 11th term 64,-32,16,-8
Answers
Answer:
0.025
Step-by-step explanation:
First you need to figure out the common pattern you see. What I saw was that we are dividing something.
I looked at the 16 and -8 and thought of -2. To make sure, you can use a calculator.
So -8 is the 4th term you can go back dividing -8 with -2 until you've reached the 11th term.
I don't know if my answer is right. I wasn't being organized as I could be. It would be better if you do it again to make sure it's correct.
what is the approximate area of the circle shown (please help first answer gets brainliest)
Answers
Answer:
The answer is B.
Step-by-step explanation:
Given: E, F, Q, D∈k(O),
O ∈ ED , m∠DFQ = 10°,
m EF = 28°
Find: Angles of △EFQ
Answers
Answer:
The angles are m∠EQF=14°, m∠EFQ=90° and m∠QEF=76°
Step-by-step explanation:
Given the figure in which m∠DFQ = 10°, m∠EOF = 28°
we have to find the angles of △EFQ
m∠EOF = 28°
By theorem angle subtended at the centre is twice the angle subtended at the circumference
⇒ m∠EQF=14°
As angle ∠EFQ is the angle in the semicircle
∴ ∠EFQ=90°
In ΔEFQ, by angle sum property of triangle
m∠EFQ+m∠FQE+m∠QEF=180°
90°+14°+m∠QEF=180°
m∠QEF=180°-90°-14°=76°
Hence, m∠EFQ=90° and m∠QEF=76°
To find the missing angle in triangle △EFQ, we used the fact that the sum of angles in a triangle is always 180°. Therefore, m∠EQF is found to be 142°, making the angles of the triangle 10°, 28°, and 142°.
Explanation:This problem deals with finding the measurements of angles in a triangle. In this case, the triangle is △EFQ, and we are given that m∠DFQ = 10° and m∠EF = 28°. The sum of the angles in a triangle always equals 180°. So, the third angle, m∠EQF, can be found by subtracting the given angles from 180°.
To calculate, follow these steps:
First, add the given angles: 10° + 28° = 38°.Next, subtract the sum of the given angles from 180°: 180° - 38° = 142°.Therefore, m∠EQF = 142°. So, the angles of triangle △EFQ are 10°, 28°, and 142°.
Learn more about Triangle Angleshttps://brainly.com/question/12599487
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Find the standard form of the equation of the circle with the given characteristics. Center at origin; radius: 4√2
Answers
Answer:
x^2 + y^2 = 32
Step-by-step explanation:
The fact that the circle's center is at (0,0) tells you that the circles equation is of the form x^2 + y^2 = radius^2
radius = 4*sqrt(2) Given
r^2 = (4sqrt(2) )^2
r^2 = 16 * 2
r^2 = 32
So the entire equation is
x^2 + y^2 = 32
What is the cube root of 216x^9y^16
Answers
ANSWER
[tex]{ {6}{x}^{3} {y}^{ \frac{16}{3} } }[/tex]
EXPLANATION
We want to find the cube root of
[tex]216 {x}^{9} {y}^{16} [/tex]
This is the same as:
[tex] \sqrt[3]{216 {x}^{9} {y}^{16} } [/tex]
We rewrite as radical exponent to get;
[tex] {(216 {x}^{9} {y}^{16} )}^{ \frac{1}{3} } [/tex]
This implies that;
[tex] {( {6}^{3} {x}^{9} {y}^{16} )}^{ \frac{1}{3} } [/tex]
This simplifies to:
[tex]{ {6}^{ \frac{3}{3} } {x}^{ \frac{9}{3} } {y}^{ \frac{16}{3} } }[/tex]
Hence the cube root is:
[tex]{ {6}{x}^{3} {y}^{ \frac{16}{3} } }[/tex]
Answer:
The cube root of [tex]\sqrt[3]{216x^9y^{16}} \,\,is\,\,6x^3y^{16/3}[/tex]
Step-by-step explanation:
We need to find the cube root of 216x^9y^16
[tex]\sqrt[3]{216x^9y^{16}} \\can\,\, be\,\, written\,\, as\,\,\\=\sqrt[3]{216} \sqrt[3]{x^9} \sqrt[3]{x^{16}} \\=\sqrt[3]{6x6x6} \sqrt[3]{x^9} \sqrt[3]{x^{16}} \\we\,\, know\,\,\sqrt[3]{x} = x^{1/3}\\= (6^3)^{1/3} (x^9)^{1/3}(y^{16})^{1/3}\\= 6x^3y^{16/3}[/tex]
So, the cube root of [tex]\sqrt[3]{216x^9y^{16}} \,\,is\,\,6x^3y^{16/3}[/tex]
A fourth degree polynomial has real roots at 0,3 a double real root at -1 and passes through point 2,12 what is the equation for the function
Answers
Answer:
y=x^2-3x
Step-by-step explanation:
Final answer:
A fourth degree polynomial with real roots at 0, 3 and a double real root at -1 passes through the point (2, 12). The equation for the function is -2x(x - 3)(x - 3)(x + 1).
Explanation:
A fourth degree polynomial with real roots at 0, 3 and a double real root at -1 can be expressed as:
f(x) = a(x - 0)(x - 3)(x - 3)(x + 1)
To find the value of 'a', we can substitute the point (2, 12) into the equation:
12 = a(2 - 0)(2 - 3)(2 - 3)(2 + 1)
12 = -6a
a = -2
So, the equation for the function is:
f(x) = -2x(x - 3)(x - 3)(x + 1)
A bakery offers a sale price of $3.00 for 3 muffins. What is the price per dozen?
Answers
Answer:
$12 per dozen muffins
Step-by-step explanation:
3.00/3 = 1
1x = the price of one muffin
1(12) = 12
Step 1: Find what the price is per muffin. To do this you must divide $3.00 by 3 muffins (this will tell you dollar per muffin or $/muffin)
3 ÷ 3 = 1
This means that every muffin is $1
Since we know this, and we know that a dozen means 12 we can multiply 1 by 12 to find how much you would pay for a dozen muffins
12 × 1 = 12
It's $12 per dozen muffins
Hope this helped!
the length of a rectangle is 5 centimeters less than twice its width . the perimeter of the rectangle is 80 cm what
are the dimensions of the rectangle
A length = 25cm; width = 15cm
B length = 22cm; width = 18cm
C length = 23cm; width = 14cm
D length = 24cm; width= 16cm
Answers
B) is the answer because 22+22+18+18 will equal 80 and 22-18 is five
Which of the following could be the equation of the function below?
WILL MARK BRAINLIEST
Answers
Answer:
A: [tex]y=-3sin(2(x+\pi))+2[/tex]
Step-by-step explanation:
As all of the functions are sin functions, the option must be negative due to the shape of the graph.
This narrows down the options to A and B
When looking at b, it has a period of [tex]2\pi[/tex] which is not equivalent to the given graph that has a period of [tex]\pi[/tex]
Function A has a period of [tex]\pi[/tex] and is negative, so it is the correct option
Answer:
[tex]y=-3\sin(2(x+\pi)+2[/tex]
Step-by-step explanation:
The graph completes two cycles on the interval [tex][-\pi,\pi][/tex].
This implies that, the graph has a period of [tex]\pi[/tex].
The functions is a sine function that is reflected in the x-axis and shifted up by 2 units.
The range of the graph is -1 to 5.
This means that the amplitude is 6/2=3
The graph is also shifted to the right [tex]\pi[/tex] units
The function is
[tex]y=-3\sin(2(x+\pi)+2[/tex]
Alice has a photo of herself standing next to her dog. In the photo, she is 2.5 in. tall and her dog is 0.5 in. tall. Alice
is actually 66 in. tall.
How tall is her dog?
A. 13.2 in.
B. 22.0 in.
C. 26.4 in.
D. 33.0 in.
HELP ASAP PLZ!!
Answers
Answer:
a. 13,2 in.
Step-by-step explanation:
66 : 2.5 = 26.4
0.5 x 26.4 = 13.2
By creating a proportion based on the heights shown in the photo and Alice's actual height, we can calculate that Alice's dog's actual height is 13.2 inches, which is option A.
To find out how tall Alice's dog is in reality, we need to use the ratio of their heights in the photograph to determine the dog's actual height. In the photograph, Alice's height is 2.5 inches and her dog's height is 0.5 inches, while her actual height is 66 inches. This creates a ratio that we can use to calculate the dog's actual height.
First, we set up a proportion where the height of Alice in the photo is to her actual height as the height of the dog in the photo is to the dog's actual height:
2.5 inches / 66 inches = 0.5 inches / x inches
Now we solve for x, which represents the dog's actual height:
x = (0.5 inches * 66 inches) / 2.5 inches
After performing the multiplication and division, we get:
x = 13.2 inches
Therefore, the height of Alice's dog in reality is 13.2 inches, which corresponds to option A.
Help me answer this question please
Answers
Answer: it should be 3 units down
Think if it on a graph in your mind and plot points then use every choice to see which makes sense
For this case we have:
Let k> 0:
To graph [tex]y = f (x) + k,[/tex] the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
Let h> 0:
To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.
To graph [tex]y = f (x + h)[/tex], the graph moves h units to the left.
So, we have:
[tex]y = f (x) = \sqrt {x}\\h = 3\\y = f (x) = \sqrt {x + 3}[/tex]
It means that it was shifted 3 units to the left
Answer:
Option A
This week laptops are 25% off. If a laptop costs $340, what is its sale price?
Answers
Answer:
$25
Step-by-step explanation:
i have an odd method of solving these types of equations
25x=100
x=4
340/4 = 85
85 x 3 = 255
Answer:
13.6
Step-by-step explanation:
so i did 340 devided by 25 and thats how i got it i hope this is helpful
99/3 = Z/5 what is the value of z in this equation
Answers
The value 1/5 becuse you simplify
Answer:
165=z
Step-by-step explanation:
99/3 = z/5
We can solve this using cross products.
99*5 = 3z
495 = 3z
Divide each side by 3
495/3 = 3z/3
165 = z
Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance between points A and B is 264 miles. What is the speeds of the cars, if one of the cars travels 14 mph faster than the other?
Please help
This is the only problem of my homework that I don't understand
Answers
The answers are:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Why?To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to calculate one in function of the other.
So, let be the first car speed "x" and the second car speed "y", writing the equations we have:
For the first car:
[tex]x_{FirstCar}=x_o+v*t[/tex]
For the second car:
We know that the speed of the second car is the speed of the first car plus 14 mph, so:
[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]
Now, we already know that both cars met after 2 hours and 45 minutes, and the distance between A and B is 264 miles, so, we can calculate the relative speed between both cars.
If the cars are moving towards each other the relative speed will be:
[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]
So , since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we have:
[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]
Writing the equation:
[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]
Therefore, the speed of the first car is equal to 41 mph.
Now, for the second car we have that:
[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]
We have that the speed of the second car is equal to 55 mph.
Hence, the answers are:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Have a nice day!
Bottled apple juice is sold in four different different sizes. Which is the best to buy?
Answers
Answer:
the bigger one ;)
Step-by-step explanation:
Answer:
C 24-ounce bottle
Step-by-step explanation:
WHAT IS THE AREA OF THE SQUARE????? Help me please
Answers
Answer:
9 units²
Step-by-step explanation:
we count the number of units for the length and Width.
Length = 3 units
Width = 3 units.
Area = 3 x 3 = 9 units²
Answer:
9 square units
Step-by-step explanation:
The area of the square will be the length*width.
Because there are 3 square boxes going horizonally (length), and 3 square boxes going vertically (width), you multiply it together.
Express the product of 2x^2+6-8 and x+3 in standered form ASap plz !!!!
Answers
1095 to the second power is what google told me!
Can someone tell me how to do this ??
Answers
Answer:
See step-by-step
Step-by-step explanation:
A prism is named by the shape of its bases. That makes this an octagonal prism
The shape of the bases are octagons.
The vertices are all the letters
The lateral edges are all the vertical lines connected by the vertices. RQ, WN, VM, are all examples.
The rectangles making up the sides are called lateral faces.
The altitudes are the same as the lateral edges. They all represent the height of the prism.
which of these operations is not closed for polynomials?
A. subtraction
B. Division
C. Multiplication
Answers
Answer:
B. Division
Step-by-step explanation:
Subtraction is closed for polynomials subtracting two polynomials will result in another polynomial. Same goes with multiplication. However, if you divide polynomials, you are able to get a result that is not always a polynomial. Therefore, division is the answer.
Answer: division
Step-by-step explanation: a p e x 2020
find the volume of a cylinder with diameter 8 inches and height 9 1/2 inches
Answers
Answer:
[tex]V=152\pi in^{2}[/tex] in terms or pi
[tex]V=477.52in^{2}[/tex] simplified
Step-by-step explanation:
To solve this, we are using the Cylinder's volume formula:
[tex]V=\pi r^{2} h[/tex]
where
[tex]V[/tex] is the volume of the cylinder
[tex]r[/tex] is the radius of the cylinder
Remember that radius is half the diameter, so we can divide the diameter of our cylinder by 2 to find its radius: [tex]r=\frac{d}{2} =\frac{8in}{2} =4in[/tex]. Now, 9 1/2 inches is 9 and a half inches, so [tex]h=9.5in[/tex].
Replacing values:
[tex]V=\pi (4in)^{2} (9.5in)[/tex]
[tex]V=\pi (16in^{2})(9.5in)[/tex]
[tex]V=152\pi in^{2}[/tex]
[tex]V=477.52in^{2}[/tex]
We can conclude that the volume of our cylinder is [tex]V=152\pi in^{2}[/tex] in terms of pi, or [tex]V=477.52in^{2}[/tex] simplified.
Answer:
[tex]V=477.5in^3[/tex]
Step-by-step explanation:
The volume of a cylinder can be calculated using the formula;
[tex]V=\pi r^2h[/tex]
where the radius is half of the diameter of the circle.
[tex]r=\frac{8}{2} =4in.[/tex]
The height of the cylinder is
[tex]h=9\frac{1}{2}=\frac{19}{2}in.[/tex]
We substitute the values into the formula to obtain;
[tex]V=\pi\times 4^2\times \frac{19}{2}[/tex]
[tex]V=477.5in^3[/tex]
correct to the nearest tenth
What is the equation for the line of symmetry in this figure?
Answers
Answer:
Characteristics of the axis of symmetry include the following: It is the line of symmetry of a parabola and divides a parabola into two equal halves that are reflections of each other about the line of symmetry. It intersects a parabola at its vertex. It is a vertical line with the equation of x = -b/2a.
Step-by-step explanation:
Answer: i need a pic to know what your asking for.