What is the general form of the equation for the given circle centered at O(0, 0)? x2 + y2 + 41 = 0 x2 + y2 − 41 = 0 x2 + y2 + x + y − 41 = 0 x2 + y2 + x − y − 41 = 0
Answers
x^2 + y^2 = 41
The general form of the equation for the given circle centered at O(0, 0) is:
[tex]x^2+y^2-41=0[/tex]
Step-by-step explanation:We know that the standard form of circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where the circle is centered at (h,k) and the radius of circle is: r units
1)
[tex]x^2+y^2+41=0[/tex]
i.e. we have:
[tex]x^2+y^2=-41[/tex]
which is not possible.
( Since, the sum of the square of two numbers has to be greater than or equal to 0)
Hence, option: 1 is incorrect.
2)
[tex]x^2+y^2-41=0[/tex]
It could also be written as:
[tex]x^2+y^2=41[/tex]
which is also represented by:
[tex](x-0)^2+(y-0)^2=(\sqrt{41})^2[/tex]
This means that the circle is centered at (0,0).
3)
[tex]x^2+y^2+x+y-41=0[/tex]
It could be written in standard form by:
[tex](x+\dfrac{1}{2})^2+(y+\dfrac{1}{2})^2=(\sqrt{\dfrac{83}{2}})^2[/tex]
Hence, the circle is centered at [tex](-\dfrac{1}{2},-\dfrac{1}{2})[/tex]
Hence, option: 3 is incorrect.
4)
[tex]x^2+y^2+x-y=41[/tex]
In standard form it could be written by:
[tex](x+\dfrac{1}{2})^2+(y-\dfrac{1}{2})^2=(\sqrt{\dfrac{83}{2})^2[/tex]
Hence, the circle is centered at:
[tex](\dfrac{-1}{2},\dfrac{1}{2})[/tex]
Related Questions
What are the counting numbers in base 6
Answers
In the base 6 number system, we would only use numerals from 0 to 5. The idea of base 6 is just like the normal base 10 system, however instead of using the numerals from 0 to 9, we use numerals from 0 to 5. And instead of having a ones digit, a tens digit, a hundreds digit and so on, we use a ones digit, a sixes digit, a thirty-sixes digit, and so on. Therefore in base 6, the number 321 means 1 one plus 2 sixes plus 3 thirty-sixes, or 121. So to count until 15 for example, we would need:
Base 6 Base 10
1 1
2 2
3 3
4 4
5 5
10 (1 six plus 0 ones) 6
11 (1 six plus 1 one) 7
12 (1 six plus 2 ones) 8
13 9
14 10
15 11
20 (2 sixes plus 0 ones) 12
21 (2 sixes plus 1 one) 13
22 14
23 15
Final answer:
The counting numbers in base 6 are represented using the digits 0 to 5, where each digit position represents a power of six. The sequence starts at 0, followed by 1, 2, 3, 4, 5, and then continues with 10 (which is 6 in decimal), 11 (7 in decimal), etc.
Explanation:
The counting numbers in base 6, also known as base-6 or hexadecimal numbers, consist of the digits 0, 1, 2, 3, 4, and 5. Just like in the decimal system (base 10) where the digits go from 0 to 9, in base 6 we only use the digits 0 to 5 for each place value, and each place is six times greater than the place to its right. After reaching 5, the next number in the sequence would be represented as 10 (base 6), which is equal to 6 in base 10. The sequence continues with 11 (base 6 equals 7 in base 10), 12 (base 6 equals 8 in base 10), and so on.
The concept of base systems is an important aspect of number theory in mathematics. In everyday life, we use the base 10 numbering system, mainly because humans have ten fingers. However, in computing and other scientific fields, different base systems like base 2 (binary) or base 16 (hexadecimal) are often used.
A certain species of tree grows an average of 4.2 cm per week. write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.
Answers
Average growth rate = 4.2 cm/week.
So, common difference d = 4.2
The height of the tree a0 = 200 centimeters.
The height of the tree after end of the first week a₁ = 200 + 4.2 = 200 + 4.2(1)
The height of the tree after end of the second week a₂ = 200 + 4.2 + 4.2 = 200 + 4.2(2).
The height of the tree after end of the third week a3 = 200 + 4.2 + 4.2 + 4.2 = 200 + 4.2(3).
The height of the tree after the end of the nth week an = 200 + 4.2(n).
The equation is a_n = 200 + 4.2(n).
A boat takes 4 hours to go 20 miles upstream.It can go 32 miles downstream in same time.Find the rate of the current and the rate of the boat in still water.
Answers
now, if the boat has a speed of say "b", and the current has a speed of say "c", when the boat is going upstream, is not really going "b" fast, is going " b - c " fast, because the current is eroding speed from it, going upwards.
And when the boat is going downstream, is not going "b" fast either, because the current is now adding to speed to it, so is really going " b + c " fast.
The time it took one way, is the same time it took back, 4 hours each way.
thus
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{t}\\ &------&------&------\\ Upstream&20&b-c&4\\ Downstream&32&b+c&4 \end{array} \\\\\\ \begin{cases} 20=4(b-c)\implies \frac{20}{4}=b-c\implies 5+c=\boxed{b}\\ 32=4(b+c)\implies \frac{32}{4}=b+c\implies 8=b+c\\ --------------------\\ 8=\left(\boxed{5+c} \right)+c \end{cases} \\\\\\ 8=5+2c\implies 3=2c\implies \cfrac{3}{2}=c\implies 1\frac{1}{2}=c[/tex]
what's the speed of the boat? well, 5 + c = b.
A = h/2 * (a + b ); for h
Answers
h/2=A/(a+b)
h=2A/(a+b)
ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?
Answers
40*40 = 1600
9* 9 = 81
so a^2 = b^2 + c^2
1681 = 1600 + 81
1681 = 1681 ...it's right triangle
CA = 41 = Hypo.
cosC = Adj / Hypo
cosC = BC / CA = 40/41
answer
cosC = 40/41
Answer:
The correct answer is
C 40/41
Step-by-step explanation:
a culture started with 6,000 bacteria. After 4 hours, it grew to 6,600 bacteria. Predict how many bacteria will be present after 10 hours. round your answer to the nearest whole number.
Answers
P = 6,600
A = 6,000
t = 4
k = ?
6600 = 6000e^(4k)
6600/6000 = e^(4k)
1.1 = e^(4k)
Take the natural log of both sides.
ln 1.1 = 4k ln e (remember that ln e = 1)
ln 1.1 = 4k
(ln 1.1) / 4 = k
k = 0.0238
Bacteria after 10 hours.
P = 6000e^(0.0238*10)
= 6000e^0.238
= 7612
Therefore, the bacteria will grow to 7612 after 10 hours.
how do write an equation to represent a real world situation?
Answers
In a circle of radius 25 inches, a central angle of 35 degrees will intersect the circle forming an arc of length ____
Answers
arc length = (central angle/360) x 2 x PI x r
= (35/360) x 2 x 3.14 x 25
=15.2638
round answer as needed, you don't say how to round it.
Which of the following is a polynomial with roots negative square root of 5, square root of 5, and −3?
x^3 − 2x^2 − 3x + 6
x^3 + 2x^2 − 3x − 6
x^3 − 3x^2 − 5x + 15
x^3 + 3x^2 − 5x − 15
Answers
If using spss, what is the exact likelihood of obtaining a t-test value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true
Answers
Supposing that the null hypothesis is true, the precise possibility of obtaining a t-test value at least as extreme or as ear to the one that was actually observed was 0.1%. This value can be found in the “Independent Samples t-test” table in the SPSS output, where the exact p value is reported as 0.001. If the null hypothesis is assumed to be true, then statistically noteworthy result should be highly improbable. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis.
To add, used for non-batched and logical batched statistical analysis, SPSS Statistics was a software package for that specific purpose.
If there are 400 cubic centimeters of a chemical in 1 liter of solution, how many cubic centimeters of water must be added to dilute it to a 25% solution?
Answers
[tex]\bf \begin{array}{lccclll} &\stackrel{cm^3}{amount}&\stackrel{\textit{\% of chemical}}{concentration}&\stackrel{total~amount}{concentration}\\ &------&------&------\\ solution&1000&0.4&400\\ water&x&0&0x\\ ------&------&------&------\\ mixture&y&0.25&0.25y \end{array}[/tex]
so.. whatever "x" and "y" are, we know that 1000 + x = y.
and that 400 + 0x = 0.25y.
thus then
[tex]\bf \begin{cases} 1000+x=\boxed{y}\\ 400+0x=0.25y\\ 400=0.25y\\ ----------\\ 400=0.25\left( \boxed{1000+x} \right) \end{cases} \\\\\\ 400=250+0.25x\implies 150=0.25x\implies \cfrac{150}{0.25}=x\implies 600=x[/tex]
Which if the following is the smallest value 0.79, 2.40, 3.00007, 0.424, or 100?
Answers
hope this helps
The smallest value is 0.424
-----------------------------------------------------------------------------
You might think that 0.79 is the smallest one but it also has 0 which is not written. 0.790 is bigger than 0.424
I hope that helps!
A pilot can travel 540 miles with the wind in the same amount of time as 380 miles against the wind. Find the speed of the wind if the pilots speed in still air is 230 miles per hour.
Answers
540/(230+w)=380/(230-w)
540(230-w)=380(230+w)
124200-540w=87400+380w
124200-920w=87400
-920w=-36800
w=40
So the wind speed is 40 miles per hour.
Peter decides to mix grades of gasoline in his truck. He puts in 11 gallons of regular and 7 gallons of premium for a total cost of $76.99. If premium gasoline costs $0.25 more per gallon than regular, what was the price of each grade of gasoline?
Answers
p = r + 0.25
11r + 7(r + 0.25) = 76.99
11r + 7r + 1.75 = 76.99
18r = 76.99 - 1.75
18r = 75.24
r = 75.24/18
r = 4.18 <=== regular : $ 4.18 per gallon
p = r + 0.25
p = 4.18 + 0.25
p = 4.43 <=== premium : $ 4.43 per gallon
Final answer:
Peter bought regular and premium gasoline at $4.18 and $4.43 per gallon respectively, after solving a system of equations based on the total gallons and cost.
Explanation:
We are given a problem where Peter mixes two grades of gasoline—regular and premium—with premium costing $0.25 more than regular. To solve this, we can set up a system of equations representing the cost of each type of gasoline and the total cost.
Let the cost per gallon of regular gasoline be r, and thus premium will be r + $0.25 as it is $0.25 more expensive. Peter buys 11 gallons of regular and 7 gallons of premium, spending a total of $76.99. So, we have two equations:
11r + 7(r + $0.25) = $76.99r = regualar gasoline price per gallonSimplifying the first equation:
11r + 7r + $1.75 = $76.99
18r + $1.75 = $76.99
18r = $76.99 - $1.75
18r = $75.24
r = $75.24 / 18
r = $4.18
So the regular gasoline price per gallon is $4.18 and the premium gasoline price per gallon is $4.18 + $0.25 = $4.43.
Text me the answer please
Answers
This is because there are 8 equal parts and 4 is just one of those 8 parts.
so
we want to hit the 4
there are 1 of those numbers on the spinner
and 8 numbers total
1 desired outcome
8 total possible outcomes
1/8 is the probablitiy
?=8
An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground? (s= 16t^2)
Answers
s=16t^2
where
s=distance in feet travelled (downwards) since airborne with zero vertical velocity and zero air-resistance
t=time in seconds after release
Here we're given
s=144 feet
=>
s=144=16t^2
=>
t^2=144/16=9
so
t=3
Ans. after 3 seconds, the object hits the ground 144 ft. below.
Answer:
After 3 seconds the object hit the ground.
Step-by-step explanation:
An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground.
Given that displacement, s = 16t²
To reach ground displacement should be 144 feet.
That is
s = 16t² = 144
t² = 9
t = 3 seconds.
After 3 seconds the object hit the ground.
Can someone please solve this ASAP?
Answers
surface area = 5ab +5bh
a = 4
b=7
h=18
5*4*7 = 140
5*7*18 = 630
630+140 = 770 square meters
A road crew spread 1 1/3 tons of gravel evenly over 8 feet of road.how many tons of gravel did they spread on each foot of road?
Answers
How do I answer this question?
Answers
a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, how many miles from earth is the star?
Answers
3.4 * 5.87х10^12 miles
In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]
How can the number of miles be calculated?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that star=3.4 light years from earth
1 light years= [tex]5.87*10x^{12} miles[/tex]
The number of miles from earth is
[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]
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Two pairs of shoes and four pairs of socks cost $131, and three pairs of shoes and five pairs of socks cost $190. Find the cost of a pair of socks.
Answers
x = socks
3( 2s + 4x = 131) ------> 6s + 12x = 393
-2( 3s + 5x = 190) ------>-6s - 10x = -380
(2x = 13)/ 2
x = 6.5
A pair of socks is equal to $6. 50
Hope this helps :)
Please give brainliest
A $28,000 car loan is used to purchase a new car. The loan is for 6 years and has a 5.75% APR. Use the amortization formula to determine the amount of the monthly payments.
Answers
[tex]\bf \qquad \begin{cases} P= \begin{array}{llll} \textit{original amount}\\ \end{array}\to & \begin{array}{llll} 28,000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 5.75\%\to \frac{5.75}{100}\to &0.0575\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &6 \end{cases} \\\\\\ pymt=28000\left[ \cfrac{\frac{0.0575}{12}}{1-\left( 1+ \frac{0.0575}{12}\right)^{-12\cdot 6}} \right][/tex]
Can segments with lengths of 36, 48, and 60 form a triangle? If so, would the triangle be acute, right, or obtuse?
Answers
Here we have 36+48=84 > 60, so the three segments form a triangle.
Since the ratio of the sides are 36 : 48 : 60 form the ratio of 3:4:5, which is exactly the ratio of a right triangle, we conclude that the triangle is a right triangle.
Segments with lengths of 36,48 and 60 can form a triangle. By employing the Pythagorean Theorem, we find that this is a right triangle as the lengths adhere to the theorem.
Explanation:The question asks if segments with lengths of 36, 48, and 60 can form a triangle, and if so, the type of the triangle. Yes, these segments can form a triangle. To classify the triangle as obtuse, right or acute, we use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c^2 = a^2 + b^2. Substituting our values: 60^2 equals to 36^2+48^2 (3600 = 1296+2304). Since both sides of the equation are equal, we get the conclusion that this is a right triangle.
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Ignoring color, what kind of symmetry does the pinwheel have? A. rotational symmetry B. line symmetry C. both rotational and line symmetry D. neither
Answers
What is the inverse of the function below? F(x) = x - 6
Answers
F(x)=x-6
Inverse function:
x = F(x)+6
To show that there are different mathematical objects just use e.g F(y)
F(y)=y+6
Answer:
f(x)=x+6
Step-by-step explanation:
its the exact opposite of the answer, so if it was x-6 then the inverse would be x+6
Raphael paid 636 for camera during a 60% off sale with the cameras regular price
Answers
If the price is 60% lower than usual, Raphael is paying only (100% - 60%), or 40%, for the camera.
Thus, 0.40x = $636. Divide both sides of this eq'n by 0.40 to find the original price of the camera.
x = $636/0.40 = ?
G study find the exact value of each of the remaining trigonometric functions cos theta=4/5 270< theta
Answers
Sin = -3/5
Tan = -3/4
Given that cos theta is 4/5 within the 270 to 360-degree range, sin(theta) is -3/5, tan(theta) is -3/4, sec(theta) is 5/4, csc(theta) is -5/3, and cot(theta) is -4/3.
Explanation:The question indicates that we are dealing with trigonometry and specifically asks for the remaining trigonometric functions given that cos theta = 4/5 and theta is in the range of 270o to 360o.
This implies that theta is in the fourth quadrant where cosine is positive, and the other trigonometric functions can have different signs.
Since we have the cosine of theta, we can use the Pythagorean identity to find the sine of theta. The identity states that in2(theta) + cos2(theta) = 1.
Plugging in the given cosine value, we have:
sin2(theta) + (4/5)2 = 1
sin2(theta) = 1 - 16/25
sin2(theta) = 9/25
sin(theta) = ±√(9/25) = ±3/5
However, since theta is in the fourth quadrant, the sine is negative, and therefore we find:
sin(theta) = -3/5
For the tangent of theta, we use the definition tan(theta) = sin(theta)/cos(theta), which yields:
tan(theta) = (-3/5) / (4/5) = -3/4
The values of the other three trigonometric functions (secant, cosecant, and cotangent) are the reciprocals of the three we just calculated:
sec(theta) = 1/cos(theta) = 5/4
csc(theta) = 1/sin(theta) = -5/3
cot(theta) = 1/tan(theta) = -4/3
A bag contains 40 marbles, 4 of which are blue, 10 are red, 25 are green, and 1 is purple. Shawna takes a marble out of the bag, records the color, and returns it to the bag. How many green marbles should she expect after 400 trials? (5 points)
Answers
Since she returns the marble every time, the probability of drawing a green marble remains constant, which is 25/40.
What is the area of a parallelogram with a base of 20 inches and an altitude of 8 inches?
Answers
The area of a parallelogram with a base of 20inches and an altitude of 8 inches is 160 inches square.
What is a parallelogram in math?
A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles identical). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is referred to as a rectangle.
Conclusion: The opposite sides are equal in length and the opposite angles are identical in degree. To find the area, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.
A = base * altitude
A = 20 * 8
A = 160 inches square.
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Find the value of ab
Answers
(1/12)*(1/6)= (1/72)
Final answer: 1/72