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xxTIMURxx [149]
2 years ago
5

Select the correct answer. which hyperbola has both foci lying in the same quadrant? a. b. c. d.

Mathematics
1 answer:
faltersainse [42]2 years ago
7 0

The hyperbola having both foci lying in the same quadrant is <u>(y - 16)²/9² - (x + 1)²/12² = 1</u>, making the <u>4th option</u> a right choice.

For the hyperbola with an equation of the form (x - h)²/a² - (y - k)²/b² = 1, the foci in on the points (h + c, k) and (h - c, k), where c = √(a² + b²).

For the hyperbola with an equation of the form (y - k)²/a² - (x - h)²/b² = 1, the foci in on the points (h, k + c) and (h, k - c), where c = √(a² + b²).

<u>Among the options</u>:

(a) (x - 24)²/24² - (y -1)²/7² = 1.

The equation is of the form (x - h)²/a² - (y - k)²/b².

h = 24, k = 1, a = 24, b = 7.

c = √(a² + b²) = √(24² + 7²) = √(576 + 49) = √625 = 25.

Thus, foci are at the points (h + c, k), (h - c, k) = (24 + 25, 1), (24 - 25, 1) = (49, 1), and (-1, 1), which are in different quadrants.

(b) (y - 12)²/5² - (x - 6)²/12² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = 6, k = 12, a = 5, b = 12.

c = √(a² + b²) = √(5² + 12²) = √(25 + 144) = √169 = 13.

Thus, foci are at the points (h, k + c), (h, k - c) = (6, 12 + 13), (6, 12 - 13) = (6, 25), and (6, -1), which are in different quadrants.

(c) (y - 16)²/15² - (x - 2)²/8² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = 2, k = 16, a = 15, b = 8.

c = √(a² + b²) = √(15² + 8²) = √(225 + 64) = √289 = 17.

Thus, foci are at the points (h, k + c), (h, k - c) = (2, 16 + 17), (2, 16 - 17) = (2, 33), and (2, -1), which are in different quadrants.

(d) (y - 16)²/9² - (x + 1)²/12² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = -1, k = 16, a = 9, b = 12.

c = √(a² + b²) = √(9² + 12²) = √(81 + 144) = √225 = 15.

Thus, foci are at the points (h, k + c), (h, k - c) = (-1, 16 + 15), (-1, 16 - 15) = (-1, 31), and (-1, 1), which are in the same quadrants (QUADRANT II).

Thus, the hyperbola having both foci lying in the same quadrant is <u>(y - 16)²/9² - (x + 1)²/12² = 1</u>, making the <u>4th option</u> a right choice.

Learn more about the foci of a hyperbola at

brainly.com/question/9384729

#SPJ4

For the options, refer the image.

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This statement describes a range of Micah's salary.

The range is a number that describes the distance from the beginning of something to the end of something.

In this scenario the beginning would be the beginning salary, in the end salary would be where you stop at end at after adding $876.

$1793(starting) + $876 = $2669

The maximum amount of money that Micah could earn would be $2669.
8 0
4 years ago
Need help with number 3
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Alice has two bags of marbles: Bag A contains 8 red and 3 blue marbles, and Bag B contains 5 red and 7 blue marbles. She randoml
Thepotemich [5.8K]

It might help to draw out a probability tree. Check out the diagram below. The first two branches at the top represent bags A and B. The probability of picking either bag is 1/2 assuming each bag is equally likely to be picked.

If we go with bag A, then the probability of getting blue is 3/11 since there are 3 blue out of 8+3 = 11 total. The probability of getting bag A and a blue marble is (1/2)*(3/11) = 3/22 which I've marked in the diagram as well.

If we go with bag B, then the probability of getting blue is 7/12 since there are 7 blue out of 5+7 = 12 total. The probability of getting bag B and blue is (1/2)*(7/12) = 7/24

Add up the results found getting

P(blue) = P(blue & bag A) + P(blue & bag B)

P(blue) = 3/22 + 7/24

P(blue) = 36/264 + 77/264

P(blue) = 113/264

This is shown in the diagram as well.

--------------------------------------------------

Recall that conditional probability in general is defined as follows

P(A given B) = P(A and B)/P(B)

In this problem, we'll have

P(bag B given blue) = P(bag B and blue)/P(blue)

Therefore, we can say...

P(bag B given blue) = P(bag B and blue)/P(blue)

P(bag B given blue) = (7/24)/(113/264)

P(bag B given blue) = (7/24)*(264/113)

P(bag B given blue) = (7*264)/(24*113)

P(bag B given blue) = (7*24*11)/(24*113)

P(bag B given blue) = (7*11)/(113)

P(bag B given blue) = 77/113

In short, the probability of getting bag B, given the marble is blue, is 77/113.

8 0
3 years ago
Plz I need help this is due at 7:10 and I wasn’t paying attention in class.
just olya [345]

Answer:

253cm²

Step-by-step explanation:

Area of the trapezoid = 1/2(b1+b2)*h

Given

h = 22cm

b1 = 10.5cm

b2 = 12.5cm

Substitute

Area of the trapezoid = 1/2(10.5+12.5)*22

Area of the trapezoid = 1/2(23)*22

Area of the trapezoid =11*23

Area of the trapezoid = 253cm²

Hence the area of the trapezoid is 253cm²

6 0
3 years ago
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