Find the standard form of the equation of the hyperbola x2 − 4y2 − 2x + 16y − 31 = 0. place the signs and values in the correct places in the standard form of the equation. - + 1 2 4 5

Given equation:

Making it into groups of x and y terms.

( x^2-2x ) + (-4y^2 +16y ) -31 =0

Adding 31 on both sides.

( x^2-2x ) + (-4y^2 +16y ) =31.

Factoring of -4 from second group.

( x^2-2x ) -4 (y^2 - 4y ) = 31.

Completing the squares

(x^2 -2x +1) - 4(y^2 -4y +4)

We added 1 in first parenthesis and -4*4 = -16 in second parenthesis.

Adding 1 and -16 on right side too, we get

(x^2 -2x +1) - 4(y^2 -4y +4)  = 31+1 -16

Making perfect squares

(x-1)^2 - 4(y-2)^2 = 16.

Dividing both sides by 16, we get

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we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .

need more info

step-by-step explanation: