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Aleonysh [2.5K]
3 years ago
9

I need the answer to this question ASAP please help me out. Thank You.

Mathematics
1 answer:
yuradex [85]3 years ago
7 0

Answer:

37 degrees

Step-by-step explanation:

Vertical angles are congruent --> equal measures

m<1 = m<2

3x+7 = 7x - 33

4x = 40

x = 10

7*10 - 33 = 70-33 = 37 degrees

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Convert the equation:
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(x+1)²/6 - (y+3)²/12 = 1

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The standard form of writing the equation of an hyperbola is expressed as;

(x-h)²/a² - (y-b)²/b² = 1 where (h,k) is the centre of the hyperbola.

Given the equation:

6x²-3y²+12x-18y-3 = 0

We are to convert it to the standard form of writing the equation of a hyperbola.

Collecting the like terms will give;

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Divide through by 3

(2x²+4x)-(y²+6y)-1 = 0

Completing the square of the equation in parenthesis and adding the constants to the other side of the equation:

(2x²+4x)-(y²+6y+(6/2)²)-1 = 0+(6/2)²

(2x²+4x)-(y²+6y+9)-1 = 9

2x²+4x -{(y+3)²} = 9+1

2x²+4x - (y+3)² = 10

Divide through by 2

x²+2x -(y+3)²/2 = 5

(x²+2x+(2/2)²)-(y+3)²/2 = 5+(2/2)²

(x²+2x+1) - (y+3)²/2 = 5+1

(x+1)²-(y+3)²/2 = 6

Divide through by 6

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The resulting equation is the required standard form of a hyperbola with centre at (-1, -3)

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