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
Here are the solutions to the problems from the image. Problem 1 (Evaluation): ii) Evaluate the expression based on the student's markings: The expression is given as (8(x)7)(x)(3/5). Based on the numbers 2 and 12 written below the expression, and the (x) symbols likely representing multiplication, the expression is interpreted as: (8 × 7)/(2 × 12) × (3)/(5) Step 1: Multiply the numbers in the numerator and denominator of the first fraction. (56)/(24) × (3)/(5) Step 2: Simplify the first fraction. (56)/(24) = (7 × 8)/(3 × 8) = (7)/(3) Step 3: Multiply the simplified fractions. (7)/(3) × (3)/(5) Step 4: Cancel out the common factor of 3. 7 × 33 × 5 = (7)/(5) Step 5: Convert the fraction to a decimal. (7)/(5) = 1.4 The evaluated expression is 1.4. Problem 2 (Equations): a) Solve for P and K from the equations: 3(X) P = 6 K(X)K = 4 Step 1: Interpret (X) as multiplication. The equations become: 3P = 6 K × K = 4 K^2 = 4 Step 2: Solve for P. 3P = 6 P = (6)/(3) P = 2 Step 3: Solve for K. K^2 = 4 K = ± sqrt(4) K = ± 2 The values are P=2 and K=2 or K=-2. (The student's work shows K=2, implying a positive value). b) Solve for P from the equation: 3( )6 = P This equation is ambiguous due to the empty parenthesis. Assuming it represents multiplication, the equation is: 3 × 6 = P Step 1: Multiply the numbers. P = 18 The value of P is 18. Drop the next question.