Answers
The answer is:
The center of the circle is the point (-9,-2) and the circle has a radius of 6 units.
Why?To solve the problem, we need to use the given equation which is in the general form, and then, use it transform it to the standard form in order to find the center of the circle and its radius.
So,
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 (x and y):
[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 write 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 the point (-9,-2) and the circle has a radius of 6 units.
Have a nice day!
Related Questions
To the nearest hundred what is the value of X
Answers
Answer:
41.51
Step-by-step explanation:
We can find the value of x using the trigonometry identify.
Cos (41) = x/55
x = 55cos (41)
x = 41.51
ANSWER
[tex]x = 41.51[/tex]
EXPLANATION
The given triangle has a right angle.
We were given an acute angle that measures 41°
The hypotenuse of the given right triangle is 55.
Since x is adjacent to the given angle and we also know the hypotenuse, we use the cosine ratio to find x.
[tex] \cos(41 \degree) = \frac{x}{55} [/tex]
Therefore
[tex]x = 55 \cos(41 \degree) [/tex]
[tex]x = 41.509[/tex]
We round to the nearest hundredth to obtain,
[tex]x = 41.51[/tex]
john is asked to roll a fair numver cube, numbered 1 to 6, and tossed a balanced quarter simultaneously. What is the probability that he will roll a 2 and the quarter will come up tails? A.) 1/2 B.) 2/3 C.) 1/6 D) 1/12
Answers
Answer: B 2/3
Step-by-step explanation:
1/6 + 1/2
15. Cody and his wife are purchasing a home. The cost
of the home is $145,900. They will be required to
pay a down payment of 5% of the purchase price
and to pay closing costs of 6% of the purchase
price. How much cash will they need for the down
payment and closing costs?
$16,049
$8,754
$7,295
$145,900
$161,949
Answers
They would need $16,049!
Price of the home is $145,900.
Percentage of the down payment is 5%
Subtract 5% from $145,900 = $138,605
That mean 5% of $145,900 is $7,295
Percentage of the closing cost is 6%.
Subtract 6% from $145,900 = 137,146
That mean 6% of 145,900 is $8,754
Add the down payment ($7,925) and closing cost ($8,745)
$16,049!
Mark me Brainliest!! Please!
they will need to pay $16,049
multiply $145,900 by 5%
multiply $145,900 by 6%
now add the totals to get $16,049
Which of the following is the solution to the inequality below?
Answers
Answer:
C.
Step-by-step explanation:
distribute.
-3x+9 > 5-5x
put the x's to one side.
2x+9 > 5
put the number to the other side.
2x > -4
x > -2
Find the perimeter of the polygon ??
Answers
Answer:
35.5 m
Step-by-step explanation:
The perimeter of the polygon is the sum of all the sides of the polygon. The sides are given as
11 m , 5 m ,7.5 m , 5m and 7m
Hence the perimeter would be,
11+5+7.5+5+7
= 35.50 m
The manager of a company that sells movie tickets online releases a report. The report states that the company's customers do not want the option of reserving a seat when they buy tickets. The report was based on a survey of 200 customers chosen at random from the company's database. Participants were asked the question, "Are you willing to spend the extra time and effort to reserve a seat when you buy tickets?" Select all statements that correctly evaluate the report. The question is biased toward a Yes response.
A) The sample is biased because it does not represent the population.
B) The question is biased toward a No response.
C)The question is not biased.
D) The sample is not biased.
Answers
Answer:
the question is biased towards a no response, because they're asking participants "are you willing to spend the extra time to blah blah" obviously they're going to say no, and the second answer is the sample is not biased because they're not giving the consumers any reason to want the product they're selling.
Step-by-step explanation:
Answer:
The sample is not biased.
The question is biased toward a No response
Step-by-step explanation:
I took the test!
For the z-score for the 11.6 data point
Answers
Answer:
z = 1.3345
Step-by-step explanation:
The z-score for a given data point, say x, from a normal distribution with a given mean and population standard deviation is usually calculated using the formula;
[tex]z=\frac{x-mean}{standard deviation}[/tex]
The following information is available;
mean = 7
population standard deviation = 3.522
x = 11.7
We simply employ the above formula to determine the z-score associated with the 11.7 data point;
[tex]z=\frac{11.7-7}{3.522}=1.3345[/tex]
y = 3x-5
6x + 3y= 15
Answers
y = 3x - 5
So substitute 3x-5 for y:
6x + 3(3x-5) = 15
Simplify:
6x + 9x - 15 = 15
15x - 15 = 15
x - 15 = 1
x = 16
THEN find y by plugging the value of x back into the first equation:
y = 3(16) - 5
y = 48 - 5
y = 43
Carly wins 1282 tickets at a arcade. For each group of 65 tickets she will receive a prize. Carl solve the problem 1282÷65 and determines that she has enough tickets right now for 19 prices. What is the least number of additional tickets that current needs to win to have enough tickets for a 20th prize?
Answers
18 is correct because 1300/65=20 1300-1282=18.
The ratio of red cars to blue cars in a parking lot was 5:3.if there were 40 red cars, how many blue cars were there??
Answers
Every 5 red cars there are 3 Blue cars,
So if there are 40 red cars,
there are going to be 24 Blue cars
40 divided by 5 which is 8
Multiply 3 × 8 which is ( 24 blue cars )
Answer:
24
Step-by-step explanation:
The 5 part of the ratio represents 40 cars, thus
40 ÷ 5 = 8 cars ← value of 1 part of the ratio
3 parts = 3 × 8 = 24 ← number of blue cars
A ________ is a transformation of a figure by turning it around a given point.
A. dilation
B. reflection
C. rotation
D. translation
Answers
Answer:
Translation
Step-by-step explanation:
given f(x)=x+2 and h(x)=1/x-1 evaluate the following function at x=2
[h(x)]^2/f(x)
Answers
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Substitute x = 2 into both h(x) and f(x)
h(2) = [tex]\frac{1}{2-1}[/tex] = 1 ⇒ (h(2))² = 1
f(2) = 2 + 2 = 4
Hence
[tex]\frac{h(x)^2}{f(x)}[/tex] when x = 2
= [tex]\frac{1}{4}[/tex]
1/4 is the following function at x=2
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and co domain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Given
Substituting x = 2 into both h(x) and f(x)
h(2) = 1(2-1) = 1 ⇒ (h(2))² = 1
f(2) = 2 + 2 = 4
Hence
h(x)²/f(x) when x = 2
=1/4
To know more about domain refer to :
https://brainly.com/question/11787743
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Brainliest + Points Please help!!!
A force of 100 newtons will stretch a spring 0.25 meters. How far will a force of 80 newtons stretch it?
Use Hooke's law F = kx.
A.
0.04 meters
B.
0.2 meters
C.
0.4 meters
D.
2 meters
Answers
Answer:Your Answer would be B 0.2 meters
Step-by-step explanation:
In the figure, angle A measures 41° and angle D measures 32°. What is the measurement of angle E?
Answers
triangles angles always add up to 180° that being said,
41+32=73
180-73=107
angle e= 107°
hope this helps!
Which of the following statements is false regarding randomization
Answers
Answer:
Randomization can be replaced by accurately matching the sample to the population
You should never replace Randomization, its important. Thats why this is false (I just took this quiz)
What is the value of x?
Answers
x = 16.
Hope this helps!
Answer:
x = 16
Step-by-step explanation:
Since the triangles are similar then the ratio of corresponding sides are equal, that is
[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] ( cross- multiply )
5x = 80 ( divide both sides by 5 )
x = 16
Tell whether each equation represents a direct proportion. If so, identify the
constant of proportionality.
1. 0.4y = x
2. x = 1 - 2y
Answers
Answer:
Step-by-step explanation:
1. 0.4y = x is a direct proportion. It'd be more appropriate to write this as
y = x / 0.4, or y = 2.5x, in which case 2.5 is the constant of proportionality.
2. x = 1 - 2y is not a direct proportion because of the offset (1). A line representing a direct proportion must go through the origin (0, 0); this particular line does not do that.
The first equation, 0.4y = x, represents a direct proportion with the constant of proportionality being 2.5. The second equation, x = 1 - 2y, does not represent a direct proportion since it does not have the form y = kx.
When we talk about two quantities being directly proportional, we mean that as one quantity increases, the other increases by a constant rate, and vice versa. This relationship can be represented by the equation y = kx, where k is the constant of proportionality.
For the first equation, 0.4y = x, this is rearranged as y = (1/0.4)x or y = 2.5x. This is indeed a directly proportional relationship, with the constant of proportionality being 2.5.
The second equation x = 1 - 2y does not describe a directly proportional relationship because it is not of the form y = kx. Instead, it shows that x decreases as y increases, which is suggestive of an inverse relationship, rather than a direct one.
What is the answer to this?
Answers
Answer:
90°
Step-by-step explanation:
The angles at the intersection of a kite will always be 90°
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
22 feet
26 feet
33 feet
44 feet
Answers
22 feet is the answer I hope this helps
Answer:
Longest rope is 44 feet. 1 piece is 1/2(44)=22. 22+44=66
Step-by-step explanation:
a penny is dropped from the top of the statue of liberty which is 305 feet tall . the height of the penny, (h,) at time (t) seconds can be repesented by the equation h(t) = -16t^2 + 305. After 4 seconds how much further does the penny need to travel before it hits the ground.
Answers
Answer: Penny need to travel 49 feet before it hits the ground.
Step-by-step explanation:
Since we have given that
[tex]h(t)=-16t^2+305[/tex]
Here, h denotes the height of the penny
t denotes the time in seconds.
Now, t = 4 seconds
So, the penny needs to travel before it hits the ground is given by
[tex]h(4)=-16(4)^2+305\\\\h(4)=-16\times 16+305\\\\h(4)=256-+305\\\\h(4)=49\ feet[/tex]
Hence, Penny need to travel 49 feet before it hits the ground.
After 4 seconds, the penny needs to travel an additional 49 feet before it hits the ground.
Explanation:The equation h(t) = -16t^2 + 305 represents the height of the penny at time t seconds. To find out how much further the penny needs to travel before it hits the ground after 4 seconds, we need to substitute t = 4 into the equation and solve for h.
h(4) = -16(4)^2 + 305
h(4) = -256 + 305
h(4) = 49 feet.
Therefore, the penny needs to travel an additional 49 feet before it hits the ground.
Learn more about Height of a penny here:https://brainly.com/question/35873705
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Convert 7pi/5 to degrees.
Answers
Answer: 252 degrees!
7pi/5 is 252degrees.
What is radians?The standard unit of angular measure used in many branches of mathematics is the radian, indicated by the symbol rad. The radian is the SI unit for measuring angles. The radian has replaced the unit as a SI derived unit, which was previously a SI supplementary unit.
Given
To convert radians to degrees, multiply by 180/π, since a full circle is
360° or 2π radians.
(7π/5)⋅180°/π
Cancel the common factor of π.
Rewrite the expression.7/5⋅180
7⋅36
Multiply 7 by 36.
252
To know more about radians refer to :
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write the equation for an exponential function, in the form axb^x, whose graph passes through the coordinates points (1, 7.5) ( 3, 16.875)
Answers
Answer:
see explanation
Step-by-step explanation:
The equation of the exponential function in the form
y = a[tex]b^{x}[/tex]
Substitute the given points into the equation and solve for a and b
Using (1, 7.5), then
7.5 = ab → (1)
Using (3, 16.875), then
16.875 = ab³ → (2)
Divide (2) by (1)
[tex]\frac{ab^3}{ab}[/tex] = [tex]\frac{16.875}{7.5}[/tex], hence
b² = 2.25 ( take the square root of both sides )
b = 1.5
Substitute b = 1.5 into (1)
1.5a = 7.5 ⇒ a = 5
The exponential function is y = 5[tex](1.5)^{x}[/tex]
what is the difference r+2/r+4-3/r+1
Answers
Answer:
[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]
Step-by-step explanation:
We want to evaluate:
[tex]\frac{r+2}{r+4}-\frac{3}{r+1}[/tex]
We collect the least common multiple of the denominators to get:
[tex]\frac{(r+2)(r+1)-3(r+4)}{(r+4)(r+1)}[/tex]
Expand the numerator:
[tex]\frac{r^2+3r+2-3r-12}{(r+4)(r+1)}[/tex]
[tex]\frac{r^2-3r+3r+2-12}{(r+4)(r+1)}[/tex]
[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]
Answer:
[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]
Step-by-step explanation:
[tex]\frac{r+2}{r+4} - \frac{3}{r+1}[/tex]
To simplify the fractions we take common denominator
LCD is (r+4)(r+1)
we try to get same denominator on both fraction
multiply the first fraction by r+1 and second fraction by r+4
[tex]\frac{(r+2)(r+1)}{(r+4)(r+1)} - \frac{3(r+4)}{(r+1)(r+4)}[/tex]
(r+2)(r+1) becomes r^2 +3r+2
3(r+4) becomes 3r+12
[tex]\frac{ r^2 +3r+2}{(r+4)(r+1)} - \frac{3r+12)}{(r+1)(r+4)}[/tex]
[tex]\frac{ r^2 +3r+2-3r-12}{(r+4)(r+1)}[/tex]
combine like terms
[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]
The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1. The events are not independent because the .
Answers
Answer:
The events are not independent because the product of their marginal probabilities is not equal to their joint probability
Step-by-step explanation:
Two events A and B are said to be independent with respect to probability if the product of their marginal probabilities is equal to their joint probability. In the question presented we have;
Pr(A) = 0.4
Pr(B) = 0.2
Pr(A n B) = 0.1
The product of their marginal probabilities is;
Pr(A) * Pr(B) = 0.4 * 0.2 = 0.08
Their joint probability is given as;
Pr(A n B) = 0.1
Clearly, Pr(A) * Pr(B) ≠ Pr(A n B) and thus the events are not independent.
Answer:
Product of P(A) and P(B) is not equal to P(A and B)
Step-by-step explanation:
it would be option C on E2020
If the mean of this distribution is 7, which could be the median? A) 1.5 B) 5 C) 8 D) 10
PLEASE HELP
Answers
Answer:
Tationia Rolon
Step-by-step explanation:
I think its C because the median is the number in the middle
Answer
6
Step-by-step explanation:
I got is correct on usatestprep
How many terms are in the arithmetic sequence 7, 1, −5, …, −161?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
27
28
29
30
Answers
Answer:
29
Step-by-step explanation:
The n th term of an arithmetic sequence is
• [tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
d = 1 - 7 = - 5 - 1 = - 6 and a₁ = 7, [tex]a_{n}[/tex] = - 161, hence
7 - 6(n - 1) = - 161 ← solve for n
7 - 6n + 6 = - 161
13 - 6n = - 161 ( subtract 13 from both sides )
- 6n = - 174 ( divide both sides by - 6 )
n = 29
There are 29 terms in the sequence
What is the surface area of the cylinder in term of pi? Radius of 11 and height of 23
Answers
Answer:
The surface area of the cylinder is [tex]748\pi[/tex].
Step-by-step explanation:
Given : Radius of the cylinder is 11 unit and height of the cylinder is 23 unit.
To find : What is the surface area of the cylinder in term of pi?
Solution :
The formula of surface area of cylinder is
[tex]A=2 \pi r^2+2\pi rh[/tex]
Where, r is the radius of the cylinder r=11 unit.
h is the height of the cylinder h=23 unit.
Substitute the value in the formula,
[tex]A=2 \pi r^2+2\pi rh[/tex]
[tex]A=2\pi(r^2+rh)[/tex]
[tex]A=2\pi(11^2+11(23))[/tex]
[tex]A=2\pi(121+253)[/tex]
[tex]A=2\pi(374)[/tex]
[tex]A=748\pi[/tex]
Therefore, The surface area of the cylinder is [tex]748\pi[/tex].
FIRST CORRECT ANSWER GETS BRAINLIEST!! (Please don't rush to answer, I've gotten a lot of incorrect answers from people who answer within the minute)
Which table shows a proportional relationship between x and y?
Answers
Answer:
B
Step-by-step explanation:
y is 3 times the x
Answer:
B
Step-by-step explanation
1/3=3
6/2=3
12/4= 3
15/5=3
Find the value of X in the circle
Answers
Answer:
x=7 units
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The triangles AMN and APQ are congruent by SAS similarity postulate
The include angle
∠MAN=∠PAQ
Because
Arc MN=Arc PQ
therefore
MN=PQ
substitute the values
38=4x+10
solve for x
4x=38-10
4x=28
x=7 units
x would be 7 units because 4 × 7 = 28 And 28 + 10 = 38
Can someone help me on 8,12 please
Answers
Step-by-step explanation:
8.
[tex]\triangle CHF\sim\triangle YWS\\\\\angle C\cong\angle Y\\\angle H\cong\angle W\\\angle F\cong\angle S\\\\\dfrac{CH}{YW}=\dfrac{HF}{WS}=\dfrac{CF}{YS}[/tex]
Although it does not look like the picture.
From the picture ∠F ≅ ∠Y...
We must stick to the correct writing:
Δ → Δ
C → Y
H → W
F → S
12.
ΔMLK and ΔYWZ are not similar because they have different angles (different shape).