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
Step 1: Fill in the correct relationship sign for -9 and -3 (from question 5.2.1). On a number line, -9 is to the left of -3, meaning -9 is smaller than -3. -9 < -3 Step 2: Calculate the expressions (from question 5.3). 5.3.1 Calculate (-7) + (+5). (-7) + (+5) = -7 + 5 = -2 (-7) + (+5) = -2 5.3.2 Calculate (+8) - (-4). Subtracting a negative number is equivalent to adding its positive counterpart. (+8) - (-4) = 8 + 4 = 12 (+8) - (-4) = 12 5.3.3 Calculate (-5) + (-6) + (+14) + (-2). Combine the negative numbers first: -5 - 6 - 2 = -13 Then add the positive number: -13 + 14 = 1 (-5) + (-6) + (+14) + (-2) = 1 Step 3: Calculate the difference in temperature (from question 5.4). The temperature inside the freezer is -18^. The temperature outside is 16^. To find the difference, subtract the lower temperature from the higher temperature. Difference = 16^ - (-18^) Difference = 16^ + 18^ = 34^ The difference in temperature is 34^. Step 4: Complete the number pattern and describe it (from question 6.1). The given pattern is 5; 9; 13; 17; \_ ; \_ . Find the common difference between consecutive terms: 9 - 5 = 4 13 - 9 = 4 17 - 13 = 4 The pattern increases by 4 each time. The next two terms are: 17 + 4 = 21 21 + 4 = 25 The completed pattern is 5; 9; 13; 17; 21; 25. PATTERN IN WORDS: The pattern starts at 5 and increases by 4 for each subsequent term. Step 5: Complete the matchstick pattern table and find the rule (from question 6.2). The number of matchsticks for patterns 1, 2, 3 are 4, 7, 10. Find the common difference: 7 - 4 = 3 10 - 7 = 3 The number of matchsticks increases by 3 for each subsequent pattern. The rule for the number of matchsticks (M) in terms of the pattern number (n) is M = 3n + c. Using n=1, M=4: 4 = 3(1) + c 4 = 3 + c c = 1. So the rule is M = 3n + 1. Now, complete the table for n=5 and n=10: For n=5: M = 3(5) + 1 = 15 + 1 = 16. For n=10: M = 3(10) + 1 = 30 + 1 = 31. The completed table is: | Pattern (n) | 1 | 2 | 3 | 5 | 10 | | :---------- | :-: | :-: | :-: | :-: | :--: | | Matchsticks | 4 | 7 | 10 | 16 | 31 | Rule: M = 3n + 1 Step 6: Use the given rule to determine the missing values in the table (from question 7.1). The rule is y = 4x - 3. For x=0: y = 4(0) - 3 = 0 - 3 = -3. For x=1: y = 4(1) - 3 = 4 - 3 = 1. For x=2: y = 4(2) - 3 = 8 - 3 = 5. For x=3: y = 4(3) - 3 = 12 - 3 = 9. For x=4: y = 4(4) - 3 = 16 - 3 = 13. For x=10: y = 4(10) - 3 = 40 - 3 = 37. The completed table is: | x | 0 | 1 | 2 | 3 | 4 | 10 | | :-: | :-: | :-: | :-: | :-: | :-: | :--: | | y | -3 | 1 | 5 | 9 | 13 | 37 | Step 7: Determine the values of A, B, and C from the input-output diagram (from question 7.2). The operations are: first multiply by 5, then subtract 2. For input 3: 3 × 5 = 15 15 - 2 = 13 So, A = 13. For input 6: 6 × 5 = 30 30 - 2 = 28 So, B = 28. For input 11: 11 × 5 = 55 55 - 2 = 53 So, C = 53. Drop the next question.