Which equation is equivalent to the following? 2x^2 - 12x + 2y^2 + 20y - 28 = 0

1) 2(x-3)^2 +2( y+5)^2=44
2) 2(x-3)^2+2(y+5)^2=60
3) 2(x-3)^2+2(y+5)^2=62
4) 2(x-3)^2+2(y+5)^2=96

Therefore, the equivalent expression is: 2*(x - 3)² + 2*(y + 5)² = 96. Number 4)

Step-by-step explanation:

In order to find the equivalent expression, lets first factor the common term, which is "2":

2*(x² - 6*x + y² + 10 *y - 14) = 0

If we look closely to the terms that have "x" and "y", they both have a square structure, therefore we can complete the squares by manipulating the indepent term. Let's first check the term with "x" and "y":

x² - 6*x + c² = x² - 2*3*x + c² = (x - c)²

y² + 10*y + d² = y² + 2*5*y + d²= (y + d)²

In order to complete the squares, c must be equal to 3 and d must be equal to 5. We can arrange that, by summing and subtracting these numbers squared, we have:

2*(x² - 6*x + 3² + y² + 10 *y +5² - 14 - 3² - 5²) = 0

2*(x² - 6*x + 3²) + 2*(y² + 10*y + 5²) -28 - 18 - 50 = 0

2*(x - 3)² + 2*(y + 5)² = 96

Therefore, the equivalent expression is: 2*(x - 3)² + 2*(y + 5)² = 96

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

597

step-by-step explanation: