Here are two stories: A family buys 6 tickets to a show. They also each spend $3 on a snack. They spend $24 on the show.

Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends, and then adds 6 more ounces for each.
Here are two equations:

3(x+6)=24
6(x+3)=24

1. What does x represent in each equation?

2. Find the solution to each equation.

3. Explain or show your reasoning.

4. What does each solution tell you about its situation?

Triangle xyz, with vertices x(-2, 0), y(-2, -1), and z(-5, -2), undergoes a transformation to form triangle x? y? z? , with vertices x? (4, -2), y? (4, -3), and z? (1, -4). the type of transformation that triangle xyz undergoes is a . triangle x? y? z? then undergoes a transformation to form triangle x? y? z? , with vertices x? (4, 2), y? (4, 3), and z? (1, 4). the type of transformation that triangle x? y? z? undergoes is a .

Solve these problems: 1.what is the perimeter of an equilateral triangle with sides measuring 6cm? 2. a regular pentagon has sides measuring 3.2 cm. what is its perimeter? 3. a regular decagon has sides of 3.5mm . what is it’s perimeter? 4. a regular octagon has a perimeter of 64cm. what is the length of one of the sides? 5. a regular hexagon has a perimeter of 72mm . what is the length of one of the sides? 6. what is the perimeter of a rhombus with sides measuring 11m?

David and alton are training for a race. they spend 35 minutes stretching and then go on a 5 mile practice run. david runs at a pace of 7 min/mile. alton runs at a pace of 8 min/mile. write an equation for each runner that shows the total length of their workout. then solve each equation showing your work