80 girls and boys have planned for a movie. they are in a ratio of 6 girls to 2 boys . how many girls are there?

Let g represent the amount of girls at the movie and b represent the amount of boys, and t represent the total amount of kids at the movie. t = g + b the equation the represents the situation, so 8 = 6 + 2 represents that if there is a total of 8 kids, there are 6 girls and 2 boys. Because the ratio is 6:2, the amount of girls to the total amount of kids is 6:8 (which is the same is 3/4) and the amount of boys to the total amount of kids is 2:8 (which is the same is 1/4). Therefore, the equation that represents the situation is t = 3/4t + 1/4t, meaning that g = 3/4t and b = 1/4t. If there is a total of 80 kids, replace t with 80 and solve for g (number of girls at the movie): 

g = 3/4t

g = 3/4(80)

g = 60

There are 60 girls at the movie.

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4