Category: Mathematics

Simplify the following expression: \[ \sqrt{\frac{9x^2}{y^3}} \] Solution Step-by-Step Simplification: Separate the square root of a fraction: The square root of a fraction can be written as the square root of the numerator divided by the square root of the denominator: \[ \sqrt{\frac{9x^2}{y^3}} = \frac{\sqrt{9x^2}}{\sqrt{y^3}} \] Simplify the numerator: The square root of \(9x^2\) can […]

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Given the following system of linear equations, solve for \(x\) and \(y\): \[ \left\{ \begin{array}{l} 5x + 3y = -4 \\ x – 3y = 10 \end{array} \right. \] Solution We can solve this system using substitution or elimination. Here, we will use the substitution method. Step 1: Solve one equation for one variable Let’s […]

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Given the system of linear equations, solve for \(x\) and \(y\): \[ \left\{ \begin{array}{l} 5x + 3y = -4 \\ x – 3y = 10 \end{array} \right. \] Solution We will use the elimination method to solve this system. Step 1: Align the system of equations The equations are already in standard form, so we […]

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Solve the following quadratic equation using the AC-method: \[ 7x^2 – 2x – 5 = 0 \] Solution Step 1: Identify the values of \(a\), \(b\), and \(c\) The quadratic equation is in the form , where: Step 2: Multiply a and c Now, multiply the coefficients \(a\) and \(c\): \[ a \times c = 7 […]

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