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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step-by-step explanation:

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)