4 Find three integers of which the sum is -9. (Hint: Use two positive integers and one negative integer)

Here are the solutions to the questions. Question 3.4 Step 1: Choose two positive integers. Let's choose 1 and 2. Step 2: Find the third integer such that the sum is -9. Let the three integers be a, b, c. We have a=1 and b=2. a + b + c = -9 1 + 2 + c = -9 3 + c = -9 Step 3: Solve for c. c = -9 - 3 c = -12 So, the three integers are 1, 2, and -12. The final answer for 3.4 is 1, 2, -12 (other combinations are possible). Question 3.5 Step 1: Define the initial amount of money. Let M be the total amount of money Mr. Jacobs had in his wallet initially. Step 2: Calculate the total fraction of money spent. He spent (1)/(2) on sweets and (1)/(3) on soft drinks. Total fraction spent = (1)/(2) + (1)/(3). To add these fractions, find a common denominator, which is 6. (1)/(2) + (1)/(3) = (3)/(6) + (2)/(6) = (5)/(6) Step 3: Calculate the fraction of money remaining. The fraction of money remaining is 1 - total fraction spent. 1 - (5)/(6) = (6)/(6) - (5)/(6) = (1)/(6) Step 4: Use the remaining amount to find the initial money. We are told that R25 is remaining, which represents (1)/(6) of the initial money. (1)/(6) M = 25 Step 5: Solve for M. Multiply both sides by 6: M = 25 × 6 M = 150 The final answer for 3.5 is R150. Question 4.1.1 The pattern grows by adding a new row of squares at the top in each subsequent stage. The number of squares in the new row is equal to the stage number. The total number of squares in each stage is the sum of consecutive integers from 1 up to the stage number. Question 4.1.2 Step 1: Determine the number of squares in each stage. Stage 1: 1 square Stage 2: 1 + 2 = 3 squares Stage 3: 1 + 2 + 3 = 6 squares This is a sequence of triangular numbers, where the number of squares in stage n is given by the formula T_n = (n(n+1))/(2). Step 2: Calculate the number of squares for the 40th stage. Substitute n = 40 into the formula: T_40 = (40(40+1))/(2) T_40 = (40 × 41)/(2) T_40 = 20 × 41 T_40 = 820 The final answer for 4.1.2 is 820 squares. Send me the next one 📸