Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. Let c represent the number of children they take to both shows and let a represent the number of adults they take to both shows. Write a system of inequalities to model this situation.

Let the number of children taken to the movies  = x

Let the number of adults taken to the movies  = y

Lets talk about Matinee tickets first:

so 4$ per child/adult

4x + 4y 80    (since the budget is 80$, we can spend 80$ , hence the less- than or equal-to)

4(x+y) 80

x + y 40

So, for the matinee show, the sum of number of children and adults should be less than or equal to 40

Lets talk about the Evening show:

so 6$/child and 8$/adult

6x + 8y 100

2(3x + 4y) 100

3x + 4y 50

So, for the Evening show, the sum of 3 times the number of children and 4 times the number of adults should not exceed 50

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

i would need to see the dot plot : )