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
1) Sandra's age is given by the expression 80 - 40 ÷ 10 × 4. To find her age, follow the order of operations (PEMDAS/BODMAS): Division and Multiplication before Subtraction. Step 1: Perform the division. 40 ÷ 10 = 4 Step 2: Perform the multiplication. 4 × 4 = 16 Step 3: Perform the subtraction. 80 - 16 = 64 Sandra's age is 64 years old. 2) Given the equations: 1. m^2 + n^2 = 200 2. m + n = 200 Step 1: Square the second equation. (m + n)^2 = (200)^2 m^2 + 2mn + n^2 = 40000 Step 2: Substitute the first equation (m^2 + n^2 = 200) into the expanded equation from Step 1. (m^2 + n^2) + 2mn = 40000 200 + 2mn = 40000 Step 3: Solve for mn. 2mn = 40000 - 200 2mn = 39800 mn = (39800)/(2) mn = 19900 Step 4: Consider a quadratic equation whose roots are m and n. This equation is typically written as x^2 - (m+n)x + mn = 0. Substitute the values m+n=200 and mn=19900: x^2 - 200x + 19900 = 0 Step 5: Determine if there are real solutions for x (and thus for m and n) by checking the discriminant ( = b^2 - 4ac). Here, a=1, b=-200, c=19900. = (-200)^2 - 4(1)(19900) = 40000 - 79600 = -39600 Since the discriminant is negative ( < 0), there are no real solutions for x. This means there are no real numbers m and n that can satisfy both given equations simultaneously. Therefore, the ratio (n)/(m) cannot be determined as a real number. The problem has no real solution. Last free one today — make it count tomorrow, or type /upgrade for unlimited.