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.
ScanSolve AI Answer
Welcome back prince — missed you this week. Here are the solutions to the problems: Question 4a: We need to solve the system of equations using the elimination method: (2)/(5)x - (1)/(10)y = 3 (1) (2)/(3)x + (2)/(3)y = 0 (2) Step 1: Clear the denominators in both equations. Multiply equation (1) by 10: 10 ( (2)/(5)x - (1)/(10)y ) = 10(3) 4x - y = 30 (3) Multiply equation (2) by 3: 3 ( (2)/(3)x + (2)/(3)y ) = 3(0) 2x + 2y = 0 Divide by 2: x + y = 0 (4) Step 2: Use the elimination method on the new system of equations (3) and (4). Add equation (3) and equation (4) to eliminate y: (4x - y) + (x + y) = 30 + 0 5x = 30 Step 3: Solve for x. x = (30)/(5) x = 6 Step 4: Substitute the value of x into equation (4) to find y. 6 + y = 0 y = -6 The solution is x=6, y=-6. Question 5: What is the perimeter of the rectangle below? The length of the rectangle is (3x - 11) cm. The width of the rectangle is (x + 7) cm. Step 1: Write the formula for the perimeter of a rectangle. The perimeter P of a rectangle is given by P = 2(length + width). Step 2: Substitute the given expressions for length and width into the formula. P = 2((3x - 11) + (x + 7)) Step 3: Simplify the expression inside the parentheses. P = 2(3x + x - 11 + 7) P = 2(4x - 4) Step 4: Distribute the 2 to find the perimeter. P = 8x - 8 The perimeter of the rectangle is (8x - 8) cm. Question 6: The sum of Ali's and Juma's ages 10 years from now will be 53. What is the sum of their ages now? Step 1: Define variables for their current ages. Let Ali's current age be A. Let Juma's current age be J. The sum of their current ages is A + J. Step 2: Express their ages 10 years from now. In 10 years, Ali's age will be A + 10. In 10 years, Juma's age will be J + 10. Step 3: Set up an equation based on the given information. The sum of their ages 10 years from now is 53: (A + 10) + (J + 10) = 53 Step 4: Solve the equation for the sum of their current ages (A + J). A + J + 20 = 53 A + J = 53 - 20 A + J = 33 The sum of their ages now is 33 years. Send me the next one 📸