Gina wants to take dance classes. she compares two dance studios to determine which has the best deal for her. dance world charges a rate for each class. toe tappers charges a rate for each class plus a one-time registration fee. the system of equations shown models the total costs for taking x classes at each.

dance world: y = 15x
toe tappers: y = 25 + 12.5x

how many classes would gina need to take for the total cost to be the same at both dance studios?

10 classes.

Step-by-step explanation:

Let x be the total number of classes and y be the total charge after x classes.

The given system of equations shown models the total costs for taking x classes at each.

Dance World:

Toe Tappers:

According to the question, to find x such that  the total cost to be the same at both dance studios.

Hence, Gina need to take 10 classes for the total cost to be the same at both dance studios.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!