This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To determine which Roman numerals are meaningless, we need to apply the rules for forming Roman numerals: • Only I, X, C, M can be repeated, up to three times. V, L, D cannot be repeated. • A smaller numeral can only precede a larger numeral if it is I (before V or X), X (before L or C), or C (before D or M). • V, L, D cannot be subtracted from any numeral. Let's examine each option: a) XLIV XL means 50 - 10 = 40. IV means 5 - 1 = 4. XLIV means 40 + 4 = 44. This is a valid Roman numeral. b) VL V means 5, L means 50. This attempts to represent 50 - 5 = 45. However, V cannot be subtracted from L. Only I can precede V or X for subtraction. This is a meaningless Roman numeral. c) XXI XX means 10 + 10 = 20. I means 1. XXI means 20 + 1 = 21. This is a valid Roman numeral. d) XCI XC means 100 - 10 = 90. I means 1. XCI means 90 + 1 = 91. This is a valid Roman numeral. e) IC I means 1, C means 100. This attempts to represent 100 - 1 = 99. However, I can only be subtracted from V or X. It cannot be subtracted from C. The correct way to write 99 is XCIX. This is a meaningless Roman numeral. f) LII L means 50. II means 1 + 1 = 2. LII means 50 + 2 = 52. This is a valid Roman numeral. g) LIV L means 50. IV means 5 - 1 = 4. LIV means 50 + 4 = 54. This is a valid Roman numeral. h) XIX X means 10. IX means 10 - 1 = 9. XIX means 10 + 9 = 19. This is a valid Roman numeral. i) III III means 1 + 1 + 1 = 3. This is a valid Roman numeral. j) VII V means 5. II means 1 + 1 = 2. VII means 5 + 2 = 7. This is a valid Roman numeral. The meaningless Roman numerals are: b) VL e) IC Drop the next question.