Answer: Option B
The given equation is 1.5x = 0.04y.We need to find the value of (y-x)(y+x).
To solve the question, we can follow these steps:
Step 1: Solve for x in terms of y from the given equation.1.5x = 0.04yx = (0.04y)/1.5x = (4/150)yx = (2/75)y
Step 2: Substitute the value of x in terms of y into (y-x)(y+x).(y-x)(y+x) = [y - (2/75)y][y + (2/75)y](y-x)(y+x) = [(73/75)y][(77/75)y](y-x)(y+x) = (73/75)*(77/75)*y^2(y-x)(y+x) = (5629/5625)*y^2
Step 3: Simplify the expression.(y-x)(y+x) = (5629/5625)y^2(y-x)(y+x) = (73/75)(77/75)y^2(y-x)(y+x) = (73/77)(75/73)*(77/75)*y^2(y-x)(y+x) = (73/77)*y^2
Therefore, the value of (y-x)(y+x) is (73/77)*y^2.
Option B, 73/77, is the correct answer.
Some relevant definitions and formulas used in the solution are:

• Equation: An equation is a statement that two expressions are equal. It is represented using the symbol "=".
• Solving an equation: Solving an equation involves finding the value of the variable that makes the equation true.
• Quadratic equation: A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
• Quadratic formula: The quadratic formula is used to solve quadratic equations. It is given by x = (-b ± sqrt(b^2 - 4ac))/(2a).
• Simplifying an expression: Simplifying an expression involves writing the expression in a simpler form without changing its value. This may involve factoring, combining like terms, or using other algebraic techniques.

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