What are the solutions to questions 4, 5, and 6?

Hey anngachuiri0, good to see you again. Here are the solutions to the questions you sent: 4. Express 72 as a product of its prime factors using a factor tree. (3 marks) Step 1: Start with 72 and find two factors. 72 = 2 × 36 Step 2: Continue factoring until all branches end in prime numbers. 36 = 2 × 18 18 = 2 × 9 9 = 3 × 3 Step 3: Collect all the prime factors. 72 = 2 × 2 × 2 × 3 × 3 72 = 2^3 × 3^2 The prime factors of 72 are 2 × 2 × 2 × 3 × 3. The product of its prime factors is 2^3 × 3^2. 5. The cube below was used to hold milk. What is the volume of the cube? (3 marks) Step 1: Identify the side length of the cube from the image. The side length of the cube is 20 cm. Step 2: Use the formula for the volume of a cube. The volume V of a cube with side length s is V = s^3. Step 3: Substitute the side length into the formula and calculate. V = (20 cm)^3 V = 20 cm × 20 cm × 20 cm V = 8000 cm^3 The volume of the cube is 8000 cm^3. 6. Salome had 6 oranges, Moraa had 18 of them while Jeremy had 12 oranges. What is the L.C.M of the numbers? (3 marks) Step 1: List the numbers given. The numbers are 6, 18, and 12. Step 2: Find the prime factorization of each number. 6 = 2 × 3 18 = 2 × 3 × 3 = 2 × 3^2 12 = 2 × 2 × 3 = 2^2 × 3 Step 3: To find the L.C.M, take the highest power of each prime factor present in any of the numbers. The prime factors are 2 and 3. The highest power of 2 is 2^2 (from 12). The highest power of 3 is 3^2 (from 18). Step 4: Multiply these highest powers together. L.C.M = 2^2 × 3^2 L.C.M = 4 × 9 L.C.M = 36 The L.C.M of 6, 18, and 12 is 36. 10. Simplify the expression 5x + 20 + 8x + 10. Step 1: Group like terms together. 5x + 8x + 20 + 10 Step 2: Combine the x terms. 5x + 8x = 13x Step 3: Combine the constant terms. 20 + 10 = 30 Step 4: Write the simplified expression. 13x + 30 The simplified expression is 13x + 30. Send me the next one 📸