The equation x^2/24^2 - y^2/b^2 = 1 represents a hyperbola centered at the origin with a directrix of x = 576/26.
What is the value of b?
A. 10
B. 16
C. 20
D. 26
Answers
Answer:
a
Step-by-step explanation:
edge
The value of B is 16.
The correct option is B
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
The standard equation for a hyperbola centered at the origin is:
(x²)/(a²) - (y²)/(b²) = 1
where "a" and "b" are the lengths of the transverse and conjugate axes, respectively. To find the value of "b" for the given hyperbola equation, we need to first rewrite it in the standard form.
(x²)/(24²) - (y²)/(b²) = 1
Multiplying both sides by (24²)(b²), we get:
b²(x²) - (24²)(y²) = (24²)(b²)
Dividing both sides by (24²), we get:
b²(x²)/(24²) - y² = b²
Comparing this with the standard equation, we can see that a = 24 and b is the square root of the constant term, which is b² = 576. Therefore, b = 24.
However, the given directrix of x = 576/26 is not consistent with the equation of the hyperbola. The directrix for a hyperbola with center at the origin and transverse axis along the x-axis is given by x = a²/b. Using the value of a = 24, we can find the directrix as:
x = (24²)/b
Setting this equal to 576/26, we get:
(24²)/b = 576/26
Solving for b, we get:
b = 16
Therefore, the correct answer is (B) 16.
To learn more about the quadratic equation;
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Related Questions
Help pls :))))))))))))))
Answers
Answer:left is 7 right is 6
Step-by-step explanation:
left is 7 right is 6
Answer:
the right side is 6 and the left side is 7
Step-by-step explanation:
These triangles are similar. Since the bottom side goes from 15 to 5, that means you divide the other 2 sides by 3 also.
pls help i don’t know how to simplify lol
Answers
Answer:
the first one is 5/12 and the second one is 6/28. Hope this helps and have a nice day:)
Answer: 5/12, 3/14
Step-by-step explanation:
first problem:
first, we just reduce the numbers.
5/4 x 1/3
then, we simply multiply.
5/12
second problem:
again, we just reduce the numbers.
3/2 x 1/7
and then multiply.
3/14
Help please
The answer choices are
A) x=3/x
B)x=9/x
C)0=3/x+x
D)0=9/x+x
Answers
Answer:
A
Step-by-step explanation:
Assuming each area code is just as likely as any other, what's the probability that the area code of two back to back spam calls are 804
Answers
Complete Question:
Yanay gets a lot of spam calls. An area code is defined to be a three digit number from 200-999 inclusive. In reality, many of these area codes are not in use, but for this question we'll simplify things and assume they all are.
Assuming each area code is just as likely as any other, what's the probability that the area code of two back to back spam calls are 804?
Answer:
1/6400 or 0.0000015625
Step-by-step explanation:
Given
Area Codes = 200 to 999 (inclusive)
Required
Determine the probability that back to back calls have area code 804
[First, we need to calculate the totality of area codes]
Total Area Codes = 999 - 200 + 1
Total Area Codes = 800
The probability of each code is 1/800
So, the probability of having back to back code of 804 is:
Probability = 1/800 * 1/800
Probability = (1/800)²
Probability = 1/640000
Hence, the required probability is 1/640000 or 0.0000015625
WILL GIVE BRAINLIEST but you have to show your work
Answers
Answer:
x=-3
Step-by-step explanation:
[tex]\sqrt{x+7}-x=5\\\sqrt{x+7}=5+x\\x+7=x^2+10x+25\\x^2+9x-18=0\\(x+3)(x+6)=0\\x=-3, x=-6\\\sqrt{-3+7}-(-3)=5\\\sqrt{-6+7}-(-6)=7=5[/tex]
x=-6 is extraneous because 7 does not equal to 5
x=-3 is the answer because 5=5
An item cost $420 before tax, and the sales tax is $33.60. Find the sales tax
Answers
Answer:
8%
Step-by-step explanation:
used a calculator