Evaluate the expression inside the square root.

Welcome back Dalena — missed you this week. Step 1: Evaluate the expression inside the square root. To combine the fractions, find a common denominator, which is 12. (1)/(12) - (1)/(3) + (1)/(2) = (1)/(12) - (1 × 4)/(3 × 4) + (1 × 6)/(2 × 6) = (1)/(12) - (4)/(12) + (6)/(12) = (1 - 4 + 6)/(12) = (3)/(12) Simplify the fraction: (3)/(12) = (1)/(4) Step 2: Take the square root of the simplified fraction. sqrt((1)/(4)) = sqrt(1)sqrt(4) = (1)/(2) The evaluated expression is (1)/(2). Step 1: Calculate the new hourly rate. The original rate is Ksh. 210 per hour. The rate changed in the ratio 8:7, meaning the new rate is (8)/(7) times the old rate. New rate = Ksh. 210 × (8)/(7) New rate = Ksh. (210 ÷ 7) × 8 New rate = Ksh. 30 × 8 New rate = Ksh. 240 per hour Step 2: Convert the total working hours to an improper fraction. 10(1)/(2) hours = (2 × 10 + 1)/(2) hours = (21)/(2) hours Step 3: Calculate the total earnings. Total earnings = New rate × Total hours Total earnings = Ksh. 240 × (21)/(2) Total earnings = Ksh. (240 ÷ 2) × 21 Total earnings = Ksh. 120 × 21 Total earnings = Ksh. 2520 Baraka would earn Ksh. 2520. Step 1: Express all bases as powers of 2. The given equation is 4^3x × 8 = ((1)/(32))^2x-1. We know that 4 = 2^2, 8 = 2^3, and 32 = 2^5. Therefore, (1)/(32) = 2^-5. Substitute these into the equation: (2^2)^3x × 2^3 = (2^-5)^2x-1 Step 2: Apply the power rule (a^m)^n = a^mn. 2^2 × 3x × 2^3 = 2^-5 × (2x-1) 2^6x × 2^3 = 2^-10x + 5 Step 3: Apply the product rule a^m × a^n = a^m+n on the left side. 2^6x+3 = 2^-10x + 5 Step 4: Since the bases are equal, equate the exponents. 6x + 3 = -10x + 5 Step 5: Solve the linear equation for x. Add 10x to both sides: 6x + 10x + 3 = 5 16x + 3 = 5 Subtract 3 from both sides: 16x = 5 - 3 16x = 2 Divide by 16: x = (2)/(16) x = (1)/(8) The solution is x = (1)/(8). Send me the next one 📸