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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Welcome back Caleb🥰 — been a while! Let's pick up where you left off. Q.1.10 To find the percentage increase in speed, we use the formula: Percentage Increase = New Speed - Original SpeedOriginal Speed × 100\% Step 1: Identify the original and new speeds. Original Speed = 18 km/h New Speed = 30 km/h Step 2: Calculate the change in speed. Change in Speed = 30 km/h - 18 km/h = 12 km/h Step 3: Calculate the percentage increase. Percentage Increase = 12 km/h18 km/h × 100\% Percentage Increase = (2)/(3) × 100\% Percentage Increase ≈ 0.6666... × 100\% Percentage Increase ≈ 66.67\% The correct option is (3). The final answer is 66.67%. Q.1.11 To determine the value of z in the expression 5(3z - 5) = 70: Step 1: Divide both sides of the equation by 5. (5(3z - 5))/(5) = (70)/(5) 3z - 5 = 14 Step 2: Add 5 to both sides of the equation. 3z - 5 + 5 = 14 + 5 3z = 19 Step 3: Divide both sides by 3. (3z)/(3) = (19)/(3) z = (19)/(3) The correct option is (4). The final answer is z = (19)/(3). Q.1.12 To determine the answer to the exponent problem (x^-4x^2)^-3: Step 1: Simplify the expression inside the parentheses using the quotient rule for exponents, (a^m)/(a^n) = a^m-n. x^-4x^2 = x^-4-2 = x^-6 Step 2: Apply the outer exponent using the power rule for exponents, (a^m)^n = a^m · n. (x^-6)^-3 = x^(-6) × (-3) = x^18 The correct option is (3). The final answer is x^18. Send me the next one 📸