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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Here are the solutions to the remaining questions: 2.3) A factor produces 1280 boxes in 8 days. How many boxes are produced in 28 days? Step 1: Calculate the production rate per day. Rate = 1280 boxes8 days = 160 boxes/day Step 2: Calculate the total boxes produced in 28 days. Total boxes = 160 boxes/day × 28 days = 4480 boxes The factory produces 4480 boxes in 28 days. 7.3) Expand 3(x+2)^2 Step 1: Expand the squared term (x+2)^2. (x+2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4 Step 2: Multiply the result by 3. 3(x^2 + 4x + 4) = 3x^2 + 12x + 12 The expanded expression is 3x^2 + 12x + 12. 7.3.1) Simplify (x^2-9)/(x^2-3x) Step 1: Factor the numerator using the difference of squares formula (a^2 - b^2 = (a-b)(a+b)). x^2 - 9 = x^2 - 3^2 = (x-3)(x+3) Step 2: Factor the denominator by taking out the common factor x. x^2 - 3x = x(x-3) Step 3: Substitute the factored expressions back into the fraction and simplify by canceling common factors. (x^2-9)/(x^2-3x) = ((x-3)(x+3))/(x(x-3)) = (x+3)/(x) The simplified expression is (x+3)/(x). 8.2) A number is multiply by 7 and then decrease by 12. The result is 23. Write and solve an equation to find the number. Step 1: Let the unknown number be x. Step 2: Write the equation based on the problem description. 7x - 12 = 23 Step 3: Solve the equation for x. 7x - 12 = 23 7x = 23 + 12 7x = 35 x = (35)/(7) x = 5 The number is 5. 3 done, 2 left today. You're making progress.