Check Point Exercises 1. 2 2 8 6( 3) 8 6(13 3) + − =+ − x 2 8 6(10) 8 6(100) 8 600 608 = + = + = + = 2. a. Since 2014 is 14 years after 2000, substitute 14 for x. 2 2 4 330 3310 4(14) 330(14) 3310 8714 Tx x =+ + =+ + = The average cost of tuition and fees at public U.S. colleges for the school year ending in 2014 was $8714. b. The formula underestimates the actual answer by $179. 3. The elements common to {3, 4, 5, 6, 7} and {3, 7, 8, 9} are 3 and 7. {3, 4,5,6,7} {3,7,8,9} {3,7} ∩ = 4. The union is the set containing all the elements of either set. {3,4,5,6,7} {3,7,8,9} {3,4,5,6,7,8,9} ∪ = 5. 9, 1.3, 0, 0.3, , 9, 10 2   π   − −   a. Natural numbers: 9 because 9 3 = b. Whole numbers: 0, 9 c. Integers: −9, 0, 9 d. Rational numbers: − − 9, 1.3, 0, 0.3, 9 e. Irrational numbers: , 10 2 π f. Real numbers: 9, 1.3, 0, 0.3, , 9, 10 2 π − − 6. a. 1 2 − Because 2 1.4, ≈ the number inside the absolute value bars is negative. The absolute value of x when x < 0> = 0, . Thus, 1 x x x x = = 7. − − =− = 4 (5) 9 9 The distance between –4 and 5 is 9. 8. 2 2 7(4 3 ) 2(5 ) x x xx ++ + 2 2 2 2 2 7(4 3 ) 2(5 ) 28 21 10 2 38 23 x x xx x xxx x x = ++ + = ++ + = + 9. 6 4[7 ( 2)] + −−x 6 4[7 2)] 6 4[9 ] 6 36 4 42 4 x x x x