Answers
The equation of the hyperbola with a given origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at (±[tex]\sqrt{98}[/tex], 0) is [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].
Given, that a hyperbola centred at the origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at (±[tex]\sqrt{98}[/tex], 0)
What is hyperbola?In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The formula for a hyperbola centred at the origin is [tex]\frac{x^2}{a^2} -\frac{y^2}{b^2 } =1[/tex]
The vertices are located at (±a, 0), so we have that the value of a is [tex]\sqrt{61}[/tex].
The foci are located at (±c, 0), where [tex]c^2 = a^2 + b^2[/tex].
So if we have that [tex]c = \sqrt{98}[/tex], we can find the value of b:
[tex]98 = 61 + b^2[/tex]
⇒ [tex]b^2 = 37[/tex]
⇒ [tex]b = \sqrt{37}[/tex]
So, the formula for this hyperbola is [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].
Therefore, the equation of the hyperbola with a given origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at (±[tex]\sqrt{98}[/tex], 0) is [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].
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Related Questions
Tahir purchase to toys for his children he buyS spider-man and barbie doll for rs. 3,000 and rs. 5,000 respectively if a discount of 20% is offered on all toys find amount of discount in the sale price for each toy
Answers
For the spider man the discount is of rs600, for the doll the discount is of rs1,000.
How to find the amount of discount for each toy?We know that the price of the spider-man is rs3,000, and we apply a discount of the 20%.
So the amount of discount for that toy is the 20% of rs3,000, which gives:
(20%/100%)*rs3,000 = rs600
So the amount discounted for the spider-man is rs600.
For the case of the doll, we know that its cost is rs5,000, the amount discounted is:
(20%/100%)*rs5,000 = rs1,000
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Look at the diagram. Which of the following is another name ∠2?
∠CDB
∠BCD
∠DCB
∠DBC
Answers
The other name for angle 2 is ∠DBC
The correct option is (D)
What is Angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
We know that while naming the angle we have to consider the point where the angle is made should be at center.
Hence, the angle 2 can also be written as ∠DCB.
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Jacob traveled 171 miles in 3.8 hours. He wants to know how many miles he traveled in one hour, so he set up this problem:
171 divided by 3.8
Jacob started by multiplying the divisor and the dividend by 10. This is the new problem:
1710 divided by 38
Use long division to find the quotient.
0.45
4.5
45
450
Answers
The answer is 45
------------------------------------------------------------
The ratio of Michaels's points on an English test to Paloma's points on the same test is 12:11. The ratio of Michaels's points on the English test on the same test was 4:3. the 3 students score a total of 224 points on the same test. What is the difference between Palomas and Antons' points on the English test? Try to explain fully, if possible. Thank you SO MUCH!
Answers
The difference between Palomas and Antons' points on the English test is of 14 points.
What is Ratio ?When two numbers can be written in the form as p:q , they are said to be in Ratio.
It is given that
The ratio of Michaels point to Paloma point is 12 :11
The ratio of Michaels point to Anton's Point is 4:3
Let Paloma's point be x
then Michaels point will be 12x/11
and Anton's points will be
(12x/11 ) / Anton's points = 4 /3
Anton's points = 9x/11
It is given that the sum of the points of the three students is 224
so
x + (12x/11)+ (9x/11) = 224
32x /11 = 224
x = 77
Paloma's points = 77
Anton's Points = 9x/11 = 63
The difference between Palomas and Antons' points on the English test
=77 -63
= 14 points.
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What makes the set of intergers different from the set of whole numbers
Answers
Answer:
integers include negative numbers, whole numbers are only 0 and positive numbers.
Step-by-step explanation:
whole numbers are very similar to integers as they do not have a decimal place although whole numbers are from 0, 1, 2, 3.... and so on whereas integers include negative numbers as well. So all whole numbers are integers but not all integers are whole numbers.
HELP
Can someone help me with number 26 plss
Answers
Answer:
(-2,-9)
(-1,8)
(0,-5)
(1,0)
(2,7)
Step-by-step explanation:
Combine the radicals 4√7 + 3√28
Answers
Answer:
10√7
Step-by-step explanation:
you can simplify the second radical and break it up into
√4 * √7 which then simplifies to 2√7 which you then multiply by 3. 4√7 + 3(2√7) which becomes 4√7 + 6√7 and then you just add the numbers Infront to get 10√7
Fully simply 15x^4y^4(−5x^3y^5)
Answers
Answer:
[tex]-75x^{7}y^{9}[/tex]
Step-by-step explanation:
This is the last question PLSSSSS HELP
Answers
Answer:
D
Step-by-step explanation:
The volume of a cylinder is pi * r^2 * h
A) V = 3.14 * (0.7/2)^2 * 6.2 = 2.4 m^2
B) V = 3.14 * (0.9/2)^2 * 3.4 = 2.2 m^2
C) V = 3.14 * (1.2/2)^2 * 6.8 = 7.7 m^2
D) V = 3.14 * (1.4/2)^2 * 6.2 = 9.5 m^2
If x is increased by 25% then, by what % is x² increased
Answers
By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.
How to determine the percentage increase rate
In this case we have a linear variable x, whose increase is described by the following expression:
y = x · (1 + r/100) (1)
Where r is the increase rate.
If we square (1), then we find that:
y² = x² · (1 + r/100)² = (1 + r'/100) (2)
Where r' is the equivalent increase rate.
(1 + r/50 + r²/10000) = (1 + r'/100)
r'/100 = r/50 + r²/10000
r' = r/2 + r²/100
If we know that r = 25, then the equivalent increase rate is:
r' = 25/2 + 25²/100
r' = 18.75
By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.
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The square below represents one whole.
Express the shaded area as a fraction, a
decimal, and a percent of the whole.
Fraction:
Decimal:
Percent:
%
Answers
Answer:
fraction:4/10 or 2/5
decimal: 0.4
percent: 40%
Step-by-step explanation:
The rectangle is divided into 10 parts, this is a total number that goes on the bottom of a fraction. 4 parts are shaded, that number goes on the top of the fraction.
4/10 is shown in the image. But 4/10 can be reduced. You should always simplify a fraction when it is possible.
4/10 = 2/5
As for the decimal, 4/10 spoken, "four tenths" tells you the decimal 0.4 (we all say "point four", but this is properly called "four-tenths" also) You can divide, because a fraction bar is a division symbol:
4÷10 OR 2÷5 and you will get the decimal 0.4
To change the decimal to a percent, multiply by 100.
0.4 × 100 is 40
0.4 is 40%
fraction:: 4/10 or 2/5 (simplified)
decimal: 0.04
percentage: 4%
The number of boys who signed up to play winter basketball is 175 percent of what it was last year. if 320 boys played winter basketball last year, how many signed up to play this year?
Answers
The number of boys signed up to play basketball this year is 560.
Given that, the number of boys who played basketball last year = 320.
We need to find the number of boys signed up to play basketball this year.
What is a percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Now, the number of boys signed up to play basketball this year = 175 per cent of what it was last year.
So, the number of boys signed up to play basketball this year = 175% of 320
[tex]=\frac{175}{10} \times 320=1.75 \times 320=560[/tex]
Therefore, the number of boys signed up to play basketball this year is 560.
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When the greatest common divisor and least common multiple of two integers are multiplied, the product is 180. How many different values could be the greatest common divisor of the two integers
Answers
The different values that could be be the greatest common divisor of the two integers are; 1, 2, 3, 4, 6
How to find the greatest common divisor?
Let the numbers be a, b. Thus, the product of the GCD(a, b) and the LCM(a, b) will be ab.
Now, for us to get something to be a factor of the GCD we need to make it be a factor of both a, b. Thus, its' square must be a factor of 180.
Therefore, the only numbers whose square is a factor of 1800 are 1, 2, 3, 4, 6 and as such they are the only GCDs possible.
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PLEASE HELP
How many integers are there on the number line between $2\sqrt{10}$ and $10\sqrt{2}$?
Answers
Answer:
8
Step-by-step explanation:
To one decimal place:
[tex]2 \sqrt{10} = 6.3[/tex]
[tex]10 \sqrt{2} = 14.1[/tex]
So there are eight integers between 2√10 and 10√2: 7, 8, 9, 10, 11, 12, 13, and 14.
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 2 of the recall, the manufacturer fixed 192 cars. In week 4, manufacturer fixed 184 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week at the mechanic.
f(x) = 4x + 200
f(x) = 2x + 192
f(x) = −4x + 200
f(x) = −2x + 192
Answers
Answer:
the answer is f(x)=2x+192
Answer:
The answer is F(x)=2x+192
Is 40% of 90 closer to 10 or 30?
Answers
Answer:
Closer to 30.
Step-by-step explanation:
To answer this first find 40% of 90.
90*0.4=36
0.4 is the same as 40%
Hope this helps!
If not, I am sorry.
what is Math?
who ever answer this question I shall mark him as brainiest.
Answers
Answer:
Maths is the subject which deals with numbers, calculations, areas, geometry etc
Various topics in maths are
trigonometry
geometry
airthmatic
etc
Mike wants to make meatloaf. His recipe
uses a total of 7 pounds of meat. If he uses a 3 to one ratio of beef to pork,how Mach pork will he use?
Answers
Answer:
Mark will use 1.25 pounds of pork.
Step-by-step explanation:
Let b represent the number of pounds of pork and p represent the number of pounds of beef. Since the ratio of beef to pork is 3 to 1, we have b/p = 3/1, which then becomes b = 3p. From this:
[tex]3p + p = 7[/tex]
[tex]4p = 7[/tex]
[tex]p = 1.75[/tex]
[tex]b = 3 \times 1.75 = 5.25[/tex]
pls hurry i really i need to finish
Answers
1,2
2,4
3,6
4,8
There u go hope u get it done
2
4
6
8
i hope you get it right !
A survey of 1,000 men and women asked, "Do you earn over $50,000 per year?" The table below shows the responses for males and females:
Male Female Total
Income over $50,000 475 375 850
Income below $50,000 75 75 150
Total 550 450 1,000
Based on these data, are "being female" and "earning over $50,000" independent events?
Yes, P(being female | the person earns over $50,000) = P(being female)
Yes, P(being female | the person earns over $50,000) ≠ P(being female)
No, P(being female | the person earns over $50,000) = P(being female)
No, P(being female | the person earns over $50,000) ≠ P(being female)
Answers
Based on the data, it is found that "being female" and "earning over $50,000" are not independent events. the correct answer is option D.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Two events, A and B are independent, if:
P(A [tex]\cap[/tex] B) = P(A) P(B)
In this problem, the events are:
Event A: Being female.Event B: Earning over $50,000.Out of the 1000 people, 450 are female, hence:
P(A) = [tex]\dfrac{450}{1000}[/tex] = 0.45
850 earn over $50,000, hence:
P(B) = [tex]\dfrac{850}{1000}[/tex] = 0.85
375 are women who earn over $50,000, hence:
P(A [tex]\cap[/tex] B) = [tex]\dfrac{375}{1000}[/tex] = 0.375
The multiplication of the probabilities is:
P(A [tex]\cap[/tex] B) = 0.45(0.85} = 0.3825
Therefore based on the data, it is found that "being female" and "earning over $50,000" are not independent events. the correct answer is option D.
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Mike has a large amount of chocolate spheres, each chocolate sphere having a radius of 2 inches.
Answers
The value of the expression Z² + Q² is 4321
How to evaluate the expression?The radius of the chocolate spheres is given as:
r = 2
The maximum number of chocolates that can fit in a spherical capsule is calculated as:
Max = R³/r³
Where:
R represents the radius of the sphere.
For the spherical capsule whose radius is 8 inches, we have:
Z = 8³/2³
Evaluate
Z = 64
For the spherical capsule whose radius is 5 inches, we have:
Q = 5³/2³
Evaluate
Q = 15.625
Remove decimal
Q = 15
So, we have:
Z² + Q² = 64² + 15²
Evaluate the exponent
Z² + Q² = 4096 + 225
Evaluate the sum
Z² + Q² = 4321
Hence, the value of Z² + Q² is 4321
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Which is a nonlinear relationship
Answers
Answer:
D. 4
Explanation:
Linear relationship refers to relationships which give straight lines when graphed. All the segments, except segment 4, show straight-line, linear relationships.
As section 4 is curved, it show nonlinear relationship.
The lines shown below are perpendicular. If the green line has a slope of
1/7 what is the slope of the red line?
A.7
B.1/7
C.-7
D. -1/7
Answers
Answer:
c: -7
Step-by-step explanation:
the slope of a perpendicular line is the negative reciprocal of the original line
a way to find this is to flip the numerator and the denominator of a slope and make it negative
1/7 --> 7 --> -7
that would be your slope
1. Decide if the following is a properly formed syllogism. If you are going to wrap Holly’s gift, you need wrapping paper. If you need wrapping paper, you have to go to the store. Therefore, if you go to the store, then you’re going to wrap Holly’s gift.
A) This is a syllogism.
B) This is not a syllogism.
Answers
This is not a syllogism. Hence option B is correct.
What is a syllogism?A logical structure for a formal argument that includes a major, minor, and conclusion.
This syllogism cannot be concluded without a given statement.
You'll need wrapping paper if you're going to wrap Holly's present. To get wrapping paper, you must visit a store.
Therefore, you will wrap Holly's present if you visit the store. This isn't a syllogism
Hence option B is correct.
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Answer:
This is not a syllogism
Step-by-step explanation:
I took the quiz. :)
Two rigid transformations are used to map TriangleJKL to TriangleMNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?
a reflection across the line containing LK
a reflection across the line containing JK
a rotation about point L
a rotation about point K
Answers
Triangle JKL is mapped to Triangle MNQ by two rigid transformations. Vertex L to vertex Q translation is the first. a rotation about point L is the second transformation. Option A is correct.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
Two rigid transformations are used to map Triangle JKL to Triangle MNQ. The first is a translation of vertex L to vertex Q.
The second transformation is a rotation about point L.
Hence option A is correct.
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Answer: Option 3 or C. a rotation about point L
Step-by-step explanation:
I took the quiz and got 100% correct on Edge 2022. Trust me if you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful. Good luck everyone! :)
Tariq also designs hot tubs. The diameter of the hot tub is 3 meters. What is the area of the deck that surrounds the hot tub? If necessary, round to the nearest tenth.
Answers
The area of the deck that surrounds the hot tub is 17.93 m²
What is Area?
The area is the amount of space within the perimeter of a 2D shape.
radius = 3/2 = 1.5 m
Area of deck,
=Area of square - area of circle
= side side- πr²
=5*5 - 3.14* 1.5*1.5
= 25- 7.065
= 17.93 m²
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Calculate the a) total tax rate, and b) sales tax.
Answers
The total tax rate and the sales tax will be given below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Total selling price (TSP), State tax rate (STR), City tax rate (CTR), Total tax rate (TTR) and Sales tax (ST).
The table complete table is given below.
Item TSP STR CTR TTR ST
Clothing $81.39 3% 0% 3% $2.44
Cell phone $159.95 5% 0% 5% $7.99
MP3 player $195.55 4% 2% 6% $11.73
Computer $1599.75 4.88% 1.50% 6.38% $102.06
Take-out $49.85 8.13% 2.50% 10.63% $5.29
Pickup truck $38,526.42 6.50% 1.25% 7.75% $2985.79
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4. If u = {1,2,3,....10) A = { odd numbers up to 9} B = {numbers less than 7). Write out the members of the following sets: (i) AUB (ii) An B (ii) A(prime) U B
Answers
Answer:
i. {1,2,3,4,5,6,7,9}
ii. {1,3,5}
iii. {1,2,3,4,5,6,8,10}
Step-by-step explanation:
U= {1,2,3,4,5,6,7,8,9,10}
A= {1,3,5,7,9}
B= {1,2,3,4,5,6}
A U B = {1,2,3,4,5,6,7,9}
A n B = { 1,3,5}
A (prime) U B =
A(prime)= {2,4,6,8,10}
Therefore A(prime)= {1,2,3,4,5,6,8,10}
y-2-√x-6
what is the domain of this function?
Answers
Determine the intercepts of the line.y=−2x−21
help please now
Answers
Answer:
( -10.5 , 0 ) and ( 0 , -21 )
Step-by-step explanation:
→ Determine where a line intersects
x and y intercept
→ Set x equal to 0 to find y - intercept
( 0 , -21 )
→ Set y equal to 0 to find x intercept
0 = -2x - 21
→ Add 21 to both sides
21 = -2x
→ Divide both sides by -2
-10.5 = x
