You are traveling to an island that is accessible only by boat. You plan to take a steamboat there and a yacht back. The steamboat makes the trip in 5 hours. The yacht makes the trip in 2.5 hours. The yacht is 20 knots faster than the steamboat. For each boat, the trip time multiplied by the speed equals the distance traveled. You know both boats will travel the same distance. How fast is each boat traveling in knots (nautical miles per hour)?

1. Write an expression for the distance going to the island. Let x be the speed of the boat you are taking to the island. Distance is equal to speed times time.

2. Write an expression for the speed of the boat coming back from the island in terms of the other boat's speed. Let x be the speed of the boat you are taking to the island.

3. Write an expression for the distance returning from the island. Use the expression for speed you found in question 4. Remember that distance is equal to speed times time.

4. Each ship travels the same distance. Set the distances equal to each other to get the equation for the speed of the ship you are taking to the island.

5. Solve the equation from question 6 for x. What does this tell you? (5 points: 1 point for showing your work, 3 points for solving for x, 1 point for explaining the answer)

6. How fast does the second boat travel? Show your work.

Aadc is formed by reflecting aabc across line segment ac, as shown in the figure. if the length of ac is 4 units, the area of aadc is square units.

Pls math have no ideamultiply and simppify. 2x^2y^3z^2 • 4xy^4x^2

Question 1 (3 points) saved what is the solution for the following system of equations? use any method to solve. y = -x +4 y = x - 2 question 1 options: ( 4 , -2) (2, 1) (3, 1) (3, -2) question 2 (3 points) saved the solution to a system of equations is where the lines intersect. question 2 options: true false question 3 (3 points) which ordered pair is the best estimate for the solution of the system of equations? the graph of the system of equations : y = 3/2x +6 and y=1/4x - 2 question 3 options: (-6, -3) (-6.5, -3.5) (-7, -4) (-7, -3.5) question 4 (3 points) what is the solution for the following system of equations? use any method to solve. 2x + 8y = 4 x = -3y + 5 question 4 options: x = 14, y= -3 x = 2, y = -3 x = -3, y = -3 x = 12, y = 5 question 5 (3 points) solve the following system using any method. 8a - 4b = 20 5a - 8b = 62 question 5 options: a = 5, b = -4 a = 8, b = 4 a = -5, b = -8 a = -2, b = -9 question 6 (3 points) breana is selling tickets to a choral performance. on the first day of ticket sales, she sold 3 senior citizen tickets and 1 child ticket for a total of $38. breana took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. what is the price of a senior citizen ticket? question 6 options: question 7 (3 points) a farmer has 5 times as many cows as pigs. the farmer only has cows and pigs, and he has 168 animals. how many cows does he have? question 7 options: 140 cows 120 cows 50 cows 28 cows question 8 (3 points) how many solutions does the system have? question 8 options: zero one infinitely many question 9 (3 points) what is the solution to the system of equations? graph of x+2y = 6 and y = x question 9 options: (1 , -2) (2, 2) (3, 5) (-2, 2)