Solve for the radius of a circle, find the value of k, determine the values for which a rational expression is undefined, and solve an exponential equation.

Hey dinmulitawkalu — ready when you are. 41. Step 1: The formula for the length of a chord c in a circle with radius r and central angle is c = 2r (()/(2)). Given c = 12 cm and = 150^. 12 = 2r ((150^)/(2)) 12 = 2r (75^) Step 2: Solve for r. r = (12)/(2 (75^)) r = (6)/((75^)) Step 3: Calculate the value. Using (75^) ≈ 0.9659: r = (6)/(0.9659) r ≈ 6.2118 cm Rounding to one decimal place, r ≈ 6.2 cm. The final answer is D. 6.2 cm. 42. Step 1: Substitute the point (3, 1) into the equation y = x^2 - 5x + k. Here, x=3 and y=1. 1 = (3)^2 - 5(3) + k Step 2: Simplify the equation. 1 = 9 - 15 + k 1 = -6 + k Step 3: Solve for k. k = 1 + 6 k = 7 The final answer is C. 7. 43. Step 1: A rational expression is undefined when its denominator is equal to zero. Set the denominator to zero. 3x^2 - 12 = 0 Step 2: Solve for x. 3x^2 = 12 x^2 = (12)/(3) x^2 = 4 x = ±sqrt(4) x = ± 2 So, the values for which the expression is not defined are x = 2 and x = -2. The final answer is B. x = -2, 2. 44. Step 1: Rewrite the equation 4^x = (1)/(1024). Express 1024 as a power of 4. 4^5 = 1024 Step 2: Substitute this into the equation. 4^x = (1)/(4^5) Step 3: Use the property of exponents a^-n = (1)/(a^n). 4^x = 4^-5 Step 4: Since the bases are the same, equate the exponents. x = -5 The final answer is D. -5. Send me the next one 📸