Question

I need a little help finishing an assignment. I've already done half.

Danielle is playing the newest app on her phone, Algebra City Defense. Earlier in the game, you and Danielle helped the Mathonauts defend the city against a giant, three-headed monster. After defeating the monster, the game advances to Level Two! You and Danielle must help the Mathonauts blast off to their Interstellar Headquarters.

1. Before blast-off, the Mathonauts must set the trajectory of their ship. Create a linear equation with a positive slope to be your original trajectory.
-y=5x+1

2. After blast-off,

Answer 1

sensors have picked up an incoming meteor. The Mathonauts frantically start preparing for impact. If the linear equation of the meteor’s path is known, describe to the captain how to solve where your equation from question 1 and the meteor’s path will cross. Explain any possible methods used in discovering a solution.
- Substitution method. You solve for x or y in one equation, then you plug in your answer to the other equation to recieve the next value for either x or y.

3. Having survived the meteor impact, thanks to some last-minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path.
-You substitute your original trajectory (y=5x+1) into the equation that the Interstellar Headquarters is based on (y2+x2=40,000). You will now have 2(5x+1)+x2=40,000 and you solve for x. After that, you will have x=3333.12 for your answer. Now take 333.12 to your original equation. The equation is y=5(3333.12)+1 and will solve for y. The value will be y=16666.85. You now know the ship’s path will cross the Interstellar Headquarters’ at the coordinate (3333.12, 16666.85).

4. While docked, the captain wants to resupply the ship’s missiles and ray-guns. You will need to explain to the captain what information you must know and how that can be used to determine the number of missiles and ray-guns to fill the ship and use all the batteries.
⦁ The ship can hold only 15 weapons total and only has 45 batteries.
⦁ The missiles and ray-guns each require different amounts of batteries to operate.
-The captian would have to inform me how much batteries both the missiles and the ray guns need to operate. After that I can use the information to plan how many of each I will load.

Answer 2

I need help with this part
Before departing the Interstellar Headquarters, the ship’s navigator begins to plan the next trip. She uses a map with their current trajectory already graphed on it. There is also a table that has coordinate points of a satellite that the Mathonauts must intercept. Explain to the navigator how she can use the graph and table to find where they will intercept the satellite. Assume the path of the satellite is linear. Use the coordinates to create an equation representing the path of the satellite. Explain the process and show how to find the point of intersection algebraically.

graph of linear function, y equals 2 x minus 5
x y
1 0
2 1
3 2
The navigator has to program the ship’s computer so that it will be prepared to intercept the satellite. To program it, the satelite’s path is set equal to the ship’s. The programmed equation is –4x – 2 = –x + 3. Explain to the navigator how the programmed equation can be graphed to find the point of intersection. Use complete sentences.
Now the Mathonauts are ready to blast off and save the day once again, thanks to your help!