Rewrite 2x^2 + 2y^2 -8x +10y + 2 = 0 in standard form. find the center and radius of the circle. show all of your work for full credit.

(x-2)^2 + (y + 5/2)^2=(√37/2)^2

Step-by-step explanation:

divide the given equation by 2

x^2 + y^2 - 4x + 5y +1 = 0

complete the square x^2 - 4x + 4 + y^2 +5y + 25/4 = -1 + 4 + 25/4

(x - 2)^2 + (y + 5/2)^2 = 37/4

r^2 = 37/4  so √37/4 = √37/2  (2 is not in the radical sign)

final equation is (x - 2)^2 + (y + 5/2)^2 = (√37/2)^2

center(2, - 5/2) radius is √37/2

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.