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.
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You're on a roll — here are the solutions with full steps for the problems in the image: 1.1 Step 1: Multiply the two given numbers. 28694 × 428 Step 2: Perform the multiplication. 28694 × 428 = 12280352 The product is 12280352. 1.2 Step 1: Divide the first number by the second number. 187296 ÷ 4 Step 2: Perform the division. 187296 ÷ 4 = 46824 The quotient is 46824. 1.3 Step 1: Divide the first number by the second number. 46514 ÷ 17 Step 2: Perform the division. 46514 ÷ 17 = 2736.1176... Step 3: Express the quotient, noting it's not an exact division. The quotient is approximately 2736.12. 1.4 Step 1: According to the order of operations (multiplication before subtraction), perform the multiplication first. 563 × 18 = 10134 Step 2: Perform the subtraction using the result from Step 1. 10134 - 4 = 10130 The result is 10130. 1.5 Step 1: Determine the total number of parts in the ratio. Total parts = 3 + 4 = 7 Step 2: Calculate the value of one part by dividing the total amount by the total number of parts. Value of one part = R3507 = R50 Step 3: Calculate Kenzie's share by multiplying her ratio part by the value of one part. Kenzie's share = 3 × R50 = R150 Step 4: Calculate Connor's share by multiplying his ratio part by the value of one part. Connor's share = 4 × R50 = R200 Kenzie gets R150 and Connor gets R200. 1.6 Step 1: Identify the given speed and time, and recall the formula for distance. Given: Speed = 60 km/hour, Time = 8 hours. Formula: Distance = Speed × Time. Step 2: Substitute the given values into the formula and calculate the distance. Distance = 60 km/hour × 8 hours = 480 km We can travel 480 km. 1.7 Step 1: Identify the given distance and time, and recall the formula for speed. Given: Distance = 480 km, Time = 4 hours. Formula: Speed = Distance ÷ Time. Step 2: Substitute the given values into the formula and calculate the speed. Speed = 480 km4 hours = 120 km/hour We are driving at a speed of 120 km/hour. 1.8 Step 1: Start the factor tree by finding two factors of 24. c 24 \\ / \ \\ 2 \ \ \ 12 Step 2: Continue breaking down composite factors until all branches end in prime numbers. c 24 \\ / \ \\ 2 \ \ \ 12 \\ \ \ \ / \ \\ \ \ \ 2 \ \ \ 6 \\ \ \ \ \ \ \ / \ \\ \ \ \ \ \ \ 2 \ \ \ 3 Step 3: Write the prime factorization using exponents for repeated prime factors. 24 = 2 × 2 × 2 × 3 = 2^3 × 3 The prime factorization of 24 is 2^3 × 3. What's next?