Example Question - solve
Here are examples of questions we've helped users solve.
Finding the Value of an Expression
<p>First, calculate the multiplication: 16 × 5 = 80.</p> <p>Next, simplify the fraction: q/10.</p> <p>Now, the equation becomes: 80 × (q/10) = 8q.</p> <p>Therefore, the solution is 8q.</p>
Solving a Mathematical Expression
<p>First, simplify the expression inside the parentheses:</p> <p>\(+\frac{7}{3} = \frac{7}{3}\)</p> <p>Now substitute this back into the expression:</p> <p>24 \left( \frac{7}{3} \right) - (-1)</p> <p>which simplifies to:</p> <p>24 \cdot \frac{7}{3} + 1 = 24 \cdot \frac{7}{3} + \frac{3}{3}</p> <p>= \frac{168}{3} + \frac{3}{3} = \frac{171}{3}</p> <p>= 57.</p>
Finding the Value of n
<p>Given \( (x^n)^3 = \frac{x^{18}}{x^{-6}} \), we can start by simplifying the right side:</p> <p>First, rewrite \( x^{-6} \) as \( \frac{1}{x^6} \), so we have:</p> <p>\( \frac{x^{18}}{x^{-6}} = x^{18} \cdot x^{6} = x^{18 + 6} = x^{24} \)</p> <p>Now we have:</p> <p> \( (x^n)^3 = x^{24} \)</p> <p>Using the property of exponents, we get:</p> <p> \( x^{3n} = x^{24} \)</p> <p>Since the bases are the same, set the exponents equal:</p> <p> \( 3n = 24 \)</p> <p>Now, solving for \( n \):</p> <p> \( n = \frac{24}{3} = 8 \)</p> <p>Thus, the value of \( n \) is \( 8 \).</p>
Solving a Fraction Equation
<p>La ecuación mostrada en la imagen es:</p> <p>\[ \frac{x}{15} = \frac{3}{4} \]</p> <p>Para resolver la ecuación, podemos despejar \( x \) multiplicando ambos lados de la ecuación por 15.</p> <p>\[ x = \frac{3}{4} \times 15 \]</p> <p>Reducimos la fracción multiplicando el numerador por 15.</p> <p>\[ x = 3 \times \frac{15}{4} \]</p> <p>\[ x = \frac{45}{4} \]</p> <p>Si se prefiere, se puede dejar la respuesta como una fracción impropia o convertirla a un número mixto.</p> <p>\[ x = 11 \frac{1}{4} \]</p>
Logarithmic Equation Problem
\[ \text{原方程式為：} \log_7(7^{2y} - 18) = y + 1 \] \[ \text{假設} \log_7(7^{2y} - 18) = a \text{，則} 7^a = 7^{2y} - 18 \] \[ \text{原方程式可寫作：} 7^{y + 1} = 7^{2y} - 18 \] \[ \text{注意到} 7^{y+1} = 7^y \cdot 7 \text{，帶回方程式中：} \] \[ 7^y \cdot 7 = 7^{2y} - 18 \] \[ \text{令} x = 7^y \text{，則上式轉變為：} \] \[ 7x = x^2 - 18 \] \[ \text{此為一元二次方程，整理得：} \] \[ x^2 - 7x - 18 = 0 \] \[ \text{解此一元二次方程得：} \] \[ (x - 9)(x + 2) = 0 \] \[ x = 9 \text{ 或 } x = -2 \] \[ \text{因為} 7^y \text{總是正數，所以} x \neq -2 \] \[ \text{所以} x = 9 \text{即} 7^y = 9 \text{，將其轉為對數形式得：} \] \[ y = \log_7 9 \] \[ \text{所以答案是 C. } \log_7 9 \]
Solving a Linear Equation Step by Step
Por supuesto, resolvamos la ecuación paso a paso: La ecuación es 2(3x - 2) = 2. Primero, distribuimos el 2 que está fuera del paréntesis a cada uno de los términos dentro del paréntesis: 2 * 3x - 2 * 2 = 6x - 4. Ahora tenemos la ecuación 6x - 4 = 2. El siguiente paso es sumar 4 a ambos lados de la ecuación para deshacernos del -4 del lado izquierdo: 6x - 4 + 4 = 2 + 4 6x = 6. Ahora dividimos ambos lados de la ecuación entre 6 para despejar x: 6x / 6 = 6 / 6 x = 1. La solución es x = 1.
Understanding and Handling a Polynomial Expression
The image shows a mathematical expression which reads: \( 64y^{10} + 17y^5 + 11 \) To "solve" this expression could mean different things depending on the context, since this is just a polynomial expression. If you're looking to simplify it, it's already in simplified form, as there are no like terms to combine. If you're trying to factor it or set it equal to something and solve for \( y \), more information or a specific instruction is needed. With the information given, there is not much else to do with the expression as it stands. If you were to set this expression equal to 0, you would be looking for the roots of the polynomial equation \( 64y^{10} + 17y^5 + 11 = 0 \), but that would generally require numerical methods or more advanced algebra to solve, as it doesn't have obvious factors that would allow for easy factoring. Please provide more specific instructions if you're looking to do something else with this expression.
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