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* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1. Sam used the rules of solving equations to find the solution was x = -7. Write at least 2 different problems that might possibly have been the question asked by the teacher that led Sam to the correct answer. Prove your problems are valid responses by solving each equation. 2. Juan and five buddies attended the Captain America: Civil War premier at Keystone Cinemas. They spent $97 total. They had purchased 5 bags of popcorn and 6 tickets. What could be the prices of the tickets and popcorn in order to reach the $97 total? 3. Look at the table below. Write a rule for the multiplication rule of integers from what you can see in the table? 5 x -3 = -15 -5 x -3 = 15 5 x -2 = -10 -5 x -2 = 10 5 x -1 = -5 -5 x -1 = 5 5x0 =0 -5 x 0 = 0 5x1 =5 -5 x 1 = -5 5 x 2 = 10 -5 x 2 = -10 5 x 3 =15 -5 x 3 =-15 5. Describe the pattern you see in the list of numbers below: 13, 26, 39, 52, 65 4. If the pattern shown in the table continues, what amount will have been raised by Week 5? Scholarship Funds Week 0 1 2 3 ? Amount 0 0 2 4 6 (thousands $) 7. Look at the original expression of 8 + 4 ∙ 2 + 6 ÷ 3. Below are three expressions that have the same numbers but the parentheses are in different places. Determine which ones have the same answer as the original expression and explain why they have the same answer. a) 8 + (4 ∙ 2) + 6 ÷ 3 b) (8 + 4) ∙ 2 + 6 ÷ 3 c) 8 + 4 ∙ 2 + (6 ÷ 3) 8. Which equation represents the table shown? Hours Money ($) 15 127.50 25 212.50 35 297.50 9. Gemma said, “I found a way to decide if the difference is positive or a negative when I subtract integers.” What way do you think Gemma found? 10. Find two integers that when subtracted have a negative number as the difference. How can you come up with more integer pairs that fit the description? 11. Create an equation that has solution of x = 5. Use more than one operation. 12. Write two rational expressions whose product is 1. 13. Create a geometry problem using multiplication of rational expressions to find an expression for the area of a triangle. Then solve that problem. 14. Use a property other than a product of powers to write an expression that is equivalent to 16x8. 15. Use a whole number other than 1 and a fraction to get a product less than 1. 16. Add 458 and 397 in two different ways. How are the ways you added them alike? How are they different? 17. How can you solve this equation in more than one way? 4(𝑥 + 3) − 6 −8=7 3 18. Tobin subtracted two integers. His difference was -12. Find 3 pairs of numbers that he could have subtracted. 19. Divide 8/9 by 2/3 using two different methods. How are the methods you used to divide them alike? How are they different? 20. The area of a rectangle is x2 – x – 2, find a length and width. 6. Find 2 fractions whose quotient is 2 2/3. a. y = 8.5x c. y = 15x b. y = 8.5x + 12.50 d. y = 15x + 12.50