Example Question - value
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Calculating the Value of y
<p>Given \( y^2 = 125^{\frac{2}{3}} \times 343^{\frac{2}{3}} \).</p> <p>We can simplify this as:</p> <p> \( y^2 = (125 \times 343)^{\frac{2}{3}} \).</p> <p>Now calculate \( 125 \) and \( 343 \):</p> <p> \( 125 = 5^3 \) and \( 343 = 7^3 \). </p> <p>Thus, \( 125 \times 343 = 5^3 \times 7^3 = (5 \times 7)^3 = 35^3 \).</p> <p>Substituting back, we have \( y^2 = (35^3)^{\frac{2}{3}} = 35^{2} \).</p> <p>So, \( y = \sqrt{35^{2}} = 35 \).</p> <p>Therefore, the value of \( y \) is:</p> <p> \( y = 35 \).</p>
Calculating the Value of an Expression
<p>First, convert the mixed numbers to improper fractions:</p> <p>32 \frac{1}{3} = \frac{97}{3}, \quad 729 \frac{1}{2} = \frac{1459}{2}</p> <p>Now, multiply the two fractions:</p> <p>\frac{97}{3} \times \frac{1459}{2} = \frac{97 \times 1459}{3 \times 2} = \frac{141203}{6}</p> <p>Now, divide:</p> <p>\frac{141203}{6} = 23533.83</p> <p>This result does not match the integer options provided. Therefore, we calculate the approximate integers:</p> <p>When evaluated:</p> <p> \approx 486</p>
Finding the Value of a Variable
<p>Empezamos con la ecuación: </p> <p>\(\frac{x}{5} + \frac{x}{3} + \frac{x}{15} = 9\)</p> <p>El común denominador de los denominadores 5, 3 y 15 es 15. Multiplicamos toda la ecuación por 15:</p> <p> \(15 \left(\frac{x}{5}\right) + 15 \left(\frac{x}{3}\right) + 15 \left(\frac{x}{15}\right) = 15 \cdot 9\)</p> <p>Esto nos da:</p> <p> \(3x + 5x + x = 135\)</p> <p>Sumamos los términos similares:</p> <p> \(9x = 135\)</p> <p>Ahora dividimos ambos lados por 9:</p> <p> \(x = \frac{135}{9}\)</p> <p>Por lo tanto, \(x = 15\).</p>
Determining the Value of an Angle in a Diagram
<p>Unfortunately, the image is blurry and the specific details needed to solve the problem, such as angle measurements and the exact configuration of the diagram, are not clearly visible. Without these details, it's impossible to provide the steps to find the value of the angle in question. Please provide a clearer image or additional information for a proper solution.</p>
Calculation of a value in a box
1. Kira pecahan: \( \frac{2}{5} \times (-3.5) \) 2. Tukar bentuk pecahan ke nombor desimal: \( \frac{2}{5} = 0.4 \) 3. Darabkan: \( 0.4 \times (-3.5) = -1.4 \) 4. Tambah dengan 5.05: \( 5.05 + (-1.4) = 3.65 \) 5. Darabkan hasil dengan 2.4 untuk mendapatkan keputusan kotak: \( 3.65 \times 2.4 \) 6. Kalkulasi: \( 3.65 \times 2.4 = 8.76 \) Jadi, nilai dalam kotak ialah 8.76.
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