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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QUESTION 1 1.1. Step 1: Perform the operations from left to right. 6 - 8 + (-3) = 6 - 8 - 3 Step 2: Subtract and add. 6 - 8 - 3 = -2 - 3 = -5 The correct option is B. -5. 1.2. The question asks for the answer to (-2)(-2)(-2)(-2). Step 1: Multiply the first two terms. (-2) × (-2) = 4 Step 2: Multiply the result by the next term. 4 × (-2) = -8 Step 3: Multiply the result by the last term. -8 × (-2) = 16 However, 16 is not among the given options. It is possible there is a typo in the question and it intended to ask for (-2)(-2)(-2). Assuming this, we proceed: (-2) × (-2) × (-2) = 4 × (-2) = -8 The correct option, based on the assumption of three factors, is D. -8. 1.3. Step 1: Write the fraction and simplify the signs. (-150)/(-350) = (150)/(350) Step 2: Divide both the numerator and the denominator by their greatest common divisor. First, divide by 10. (150 ÷ 10)/(350 ÷ 10) = (15)/(35) Step 3: Divide by 5. (15 ÷ 5)/(35 ÷ 5) = (3)/(7) The correct option is C. (3)/(7). 1.4. Step 1: Divide the numerator by the denominator. (7)/(40) = 7 ÷ 40 = 0.175 The correct option is A. 0,175. 1.5. Step 1: Identify the pattern. The given sequence is 1; 1(1)/(2); 2; 2(1)/(2); ... This can be written as 1; 1.5; 2; 2.5; ... The common difference between consecutive terms is 0.5 or (1)/(2). Step 2: Calculate the next three terms. The next term after 2(1)/(2) is 2(1)/(2) + (1)/(2) = 3. The term after that is 3 + (1)/(2) = 3(1)/(2). The term after that is 3(1)/(2) + (1)/(2) = 4. The next three terms are 3; 3(1)/(2); 4. The correct option is C. 3; 3(1)/(2); 4. 1.6. Step 1: Evaluate the exponent first. 5 × (-5)^2 = 5 × (25) Step 2: Perform the multiplication. 5 × 25 = 125 The correct option is D. 125. 1.7. Step 1: Simplify each term. 3 × 2 × m - 3 × 1 × m = 6m - 3m Step 2: Combine like terms. 6m - 3m = 3m The correct option is D. 3m. 1.8. Step 1: Write the equation. (x)/(4) = 3 Step 2: Multiply both sides by 4 to solve for x. x = 3 × 4 x = 12 The correct option is A. x=12. QUESTION 2 2.1. Step 1: Perform the operation inside the parentheses. (3-3) × 1 + 2 + 2 = (0) × 1 + 2 + 2 Step 2: Perform the multiplication. 0 × 1 + 2 + 2 = 0 + 2 + 2 Step 3: Perform the additions. 0 + 2 + 2 = 4 The simplified answer is 4. 2.2. Step 1: Express the ratio as a fraction. 6:18 = (6)/(18) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 6. (6 ÷ 6)/(18 ÷ 6) = (1)/(3) Step 3: Write the simplified fraction back as a ratio. (1)/(3) = 1:3 The simplified answer is 1:3. 2.3. Step 1: Multiply the two negative numbers. Remember that a negative number multiplied by a negative number results in a positive number. (-3) × (-6) = 18 The simplified answer is 18. What's next? Send 'em! 📸