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
Hey Nmk, good to see you again. Here are the solutions for problems 1-8: 1) Given formula: y = x + 8. Make x the subject. Step 1: Subtract 8 from both sides of the equation. y - 8 = x + 8 - 8 y - 8 = x Step 2: Rewrite with x on the left side. x = y - 8 The subject is x = y - 8. 2) Given formula: y = x - 3. Make x the subject. Step 1: Add 3 to both sides of the equation. y + 3 = x - 3 + 3 y + 3 = x Step 2: Rewrite with x on the left side. x = y + 3 The subject is x = y + 3. 3) Given formula: b = a + c. Make a and c the subject. a) Make a the subject: Step 1: Subtract c from both sides of the equation. b - c = a + c - c b - c = a Step 2: Rewrite with a on the left side. a = b - c The subject is a = b - c. b) Make c the subject: Step 1: Subtract a from both sides of the equation. b - a = a + c - a b - a = c Step 2: Rewrite with c on the left side. c = b - a The subject is c = b - a. 4) Given formula: y = 3x. Make x the subject. Step 1: Divide both sides of the equation by 3. (y)/(3) = (3x)/(3) (y)/(3) = x Step 2: Rewrite with x on the left side. x = (y)/(3) The subject is x = (y)/(3). 5) Given formula: y = (x)/(4). Make x the subject. Step 1: Multiply both sides of the equation by 4. y × 4 = (x)/(4) × 4 4y = x Step 2: Rewrite with x on the left side. x = 4y The subject is x = 4y. 6) Given formula: b = ac. Make a and c the subject. a) Make a the subject: Step 1: Divide both sides of the equation by c. (b)/(c) = (ac)/(c) (b)/(c) = a Step 2: Rewrite with a on the left side. a = (b)/(c) The subject is a = (b)/(c). b) Make c the subject: Step 1: Divide both sides of the equation by a. (b)/(a) = (ac)/(a) (b)/(a) = c Step 2: Rewrite with c on the left side. c = (b)/(a) The subject is c = (b)/(a). 7) Given formula: n = 5ax. Make a and x the subject. a) Make a the subject: Step 1: Divide both sides of the equation by 5x. (n)/(5x) = (5ax)/(5x) (n)/(5x) = a Step 2: Rewrite with a on the left side. a = (n)/(5x) The subject is a = (n)/(5x). b) Make x the subject: Step 1: Divide both sides of the equation by 5a. (n)/(5a) = (5ax)/(5a) (n)/(5a) = x Step 2: Rewrite with x on the left side. x = (n)/(5a) The subject is x = (n)/(5a). 8) Given formula: (x)/(y) = 9. Make x the subject. Step 1: Multiply both sides of the equation by y. (x)/(y) × y = 9 × y x = 9y The subject is x = 9y. Send me the next one 📸