Example Question - variables
Here are examples of questions we've helped users solve.
Matrix Equation Solving
<p>Given the equation:</p> <p>\(\begin{pmatrix} 0 & 1 \\ y & 5 \end{pmatrix} + \begin{pmatrix} 4 & -1 \\ 6 & x \end{pmatrix} = \begin{pmatrix} 4 & 0 \\ x & 7 \end{pmatrix}\)</p> <p>We can separate this into two equations by comparing corresponding elements:</p> <p>1. \(0 + 4 = 4\)</p> <p>2. \(1 - 1 = 0\)</p> <p>3. \(y + 6 = x\)</p> <p>4. \(5 + x = 7\)</p> <p>From equation 1 and 2, we directly confirm that both hold true. Now, solving for \(x\) from equation 4:</p> <p>From \(5 + x = 7\)</p> <p>\(x = 7 - 5\)</p> <p>Thus, \(x = 2\).</p> <p>Now substitute \(x\) into equation 3:</p> <p>\(y + 6 = 2\)</p> <p>Thus, \(y = 2 - 6\)</p> <p>So, \(y = -4\).</p> <p>Final values: \(x = 2, y = -4\).</p>
Finding the Value of x
<p>Comencemos por simplificar la ecuación dada:</p> <p>2 - \{4 - (x - 1)\} = 7 - 3x</p> <p>Primero, expandimos y simplificamos el lado izquierdo:</p> <p>2 - 4 + x - 1 = 7 - 3x</p> <p>Esto se convierte en:</p> <p>x - 3 = 7 - 3x</p> <p>Añadimos 3x a ambos lados:</p> <p>x + 3x - 3 = 7</p> <p>4x - 3 = 7</p> <p>Añadimos 3 a ambos lados:</p> <p>4x = 10</p> <p>Dividimos ambos lados por 4:</p> <p>x = \frac{10}{4}</p> <p>x = \frac{5}{2}</p> <p>Así que el valor de x es:</p> <p>x = \frac{5}{2}</p>
Algebraic Expression with Three Variables
<p>No se proporciona una pregunta específica junto con la expresión algebraica "x + y + z". Sin información adicional o un problema específico para resolver que involucre esta expresión, no se puede proporcionar una solución matemática. Por favor, proporcione más detalles o una pregunta específica relacionada con esta expresión para proceder con una solución.</p>
Algebraic Equation Simplification
<p>\[ 5x - (-8) + (-9) = 9x - (-7 + 1) \]</p> <p>\[ 5x + 8 - 9 = 9x - (7 - 1) \]</p> <p>\[ 5x - 1 = 9x - 6 \]</p> <p>\[ 5x - 9x = -6 + 1 \]</p> <p>\[ -4x = -5 \]</p> <p>\[ x = \frac{-5}{-4} \]</p> <p>\[ x = \frac{5}{4} \]</p>
Solving Algebraic Equations
<p>Для решения уравнений вида \(\frac{x}{a} = b\) и \(\frac{m}{n} = c\), где \(x, m, n, a, b, c\) - числа, нужно выполнить следующие шаги:</p> <p>а) \(\frac{x}{9} = 13\)</p> <p>Шаг 1: Умножьте обе части уравнения на 9.</p> <p>\(x = 13 \times 9\)</p> <p>\(x = 117\)</p> <p>б) \(\frac{132}{k} = 11\)</p> <p>Шаг 1: Умножьте обе части уравнения на \(k\).</p> <p>132 = 11k</p> <p>Шаг 2: Разделите обе части уравнения на 11.</p> <p>\(k = \frac{132}{11}\)</p> <p>\(k = 12\)</p> <p>в) \(\frac{m}{12} = 28\)</p> <p>Шаг 1: Умножьте обе части уравнения на 12.</p> <p>\(m = 28 \times 12\)</p> <p>\(m = 336\)</p> <p>г) \(\frac{528}{n} = 66\)</p> <p>Шаг 1: Умножьте обе части уравнения на \(n\).</p> <p>528 = 66n</p> <p>Шаг 2: Разделите обе части уравнения на 66.</p> <p>\(n = \frac{528}{66}\)</p> <p>\(n = 8\)</p>
Simplifying an Algebraic Expression
<p>\[\frac{x - 7 - 2 \cdot (-2)}{3}\]</p> <p>\[\frac{x - 7 + 4}{3}\]</p> <p>\[\frac{x - 3}{3}\]</p> <p>\[= \frac{x}{3} - 1\]</p>
Solving a Simple Algebraic Expression
<p>Para resolver la expresión algebraica dada, simplemente se sigue la ley de los exponentes que indica cómo manejar la multiplicación de términos con la misma base.</p> <p>\[ a^{1/4} \cdot a = a^{1/4 + 1} = a^{1/4 + 4/4} = a^{5/4} \]</p>
Polynomial Equation Analysis
<p>Bạn chưa cung cấp đầy đủ thông tin hoặc câu hỏi cụ thể cần giải quyết liên quan đến các phương trình đa thức B và D trong hình ảnh vì vậy tôi không thể đưa ra lời giải cụ thể. Nếu bạn cần tìm đạo hàm, tích phân, hoặc giải bất kỳ bài toán cụ thể nào liên quan đến B hoặc D, vui lòng cung cấp thông tin chi tiết hơn.</p>
Algebraic Expressions
1. 8p 2. ab 3. b^2 4. 6x + 6
Simplifying Expression with Variables
На картинке представлено выражение: \(8p - 4g + 4p - g\) Чтобы решить это выражение, мы должны объединить подобные слагаемые. Подобные слагаемые — это те слагаемые, которые содержат одинаковые переменные в одинаковой степени. В данном случае, \(8p\) и \(4p\) являются подобными слагаемыми, так же как \(-4g\) и \(-g\). Сложим подобные слагаемые: \(8p + 4p = 12p\), \(-4g - g = -5g\). Теперь объединим их вместе: \(12p - 5g\). Это и есть упрощенный ответ выражения с картинки.
Solving a System of Linear Equations using Elimination Method
El conjunto de ecuaciones proporcionado es un sistema de ecuaciones lineales. Para resolverlo, utilizaremos el método de eliminación para reducir el sistema a ecuaciones con menos variables y luego resolver esas ecuaciones. Comenzamos con el sistema original: \[ \begin{cases} x + y = 0 \\ x + 2y - 3z = -3 \\ 2x + 3y - 4z = -3 \end{cases} \] Primero, vamos a restar la primera ecuación de la segunda y la tercera para eliminar la variable \(x\): Restando la primera ecuación de la segunda: \[ (x + 2y - 3z) - (x + y) = -3 - 0 \] \[ 2y - y - 3z = -3 \] \[ y - 3z = -3 \] ... (ecuación 2') Restando el doble de la primera ecuación de la tercera: \[ (2x + 3y - 4z) - 2(x + y) = -3 - 2(0) \] \[ 2x + 3y - 4z - 2x - 2y = -3 \] \[ y - 4z = -3 \] ... (ecuación 3') Ahora tenemos un sistema simplificado con las siguientes dos ecuaciones: \[ \begin{cases} y - 3z = -3 \quad \text{(ecuación 2')} \\ y - 4z = -3 \quad \text{(ecuación 3')} \end{cases} \] Restamos la ecuación 2' de la ecuación 3': \[ (y - 4z) - (y - 3z) = -3 - (-3) \] \[ -4z + 3z = 0 \] \[ -z = 0 \] \[ z = 0 \] Una vez que tenemos \(z = 0\), podemos sustituir este valor en la ecuación 2' o 3' para encontrar el valor de \(y\): \[ y - 3(0) = -3 \] \[ y = -3 \] Ahora que conocemos los valores de \(y\) y \(z\), podemos sustituir estos valores en la primera ecuación original para encontrar \(x\): \[ x + (-3) = 0 \] \[ x = 3 \] Por ende, la solución al sistema de ecuaciones es: \[ x = 3, y = -3, z = 0 \]
Proportional Relationship Between Variables
To solve the question in the image, we need more information about the relationship between y and x. If the relationship is linear and directly proportional, then we can use a simple ratio to find the value of y when x = 2. Assuming the relationship is y = kx, where k is the constant of proportionality, we can first find k using the information we have: y = 96 when x = 4. So: 96 = k * 4 Solving for k: k = 96 / 4 k = 24 Now that we have the value of k, we can find y when x = 2: y = k * x y = 24 * 2 y = 48 Therefore, if the relationship between y and x is directly proportional, then y = 48 when x = 2. However, without additional information about the specific relationship between y and x (such as the equation of a curve, if it's not linear), we cannot definitively solve for y.
Solving a Simplification Expression with Variables and Coefficients
To solve the expression \( \frac{10x^8}{5x^4} \), you can simplify it by dividing both the coefficients (the numerical parts) and the variables separately. First, divide the coefficients: \( \frac{10}{5} = 2 \) Next, apply the laws of exponents for dividing like bases: \( x^8 / x^4 = x^{8-4} = x^4 \) Combine these two results to get the final answer: \( 2x^4 \)
Algebraic Expression Simplification
The question in the image shows an algebraic expression: \( \frac{325 ys + 3ns}{100 ks} \) It seems like the intention is to simplify the expression, but there's no common factor between the numerator and denominator that can be canceled out. If 'ys', 'ns', and 'ks' are variables, then it is already in its simplest form, and without additional context or relationships between these variables, no further simplification can be made. If there is a specific way these variables relate or if there's a specific operation you'd like to perform on this expression please provide that information, and I can help you further. Otherwise, if 'ys', 'ns', and 'ks' represent different units or terms beyond basic algebraic variables, you would need to apply the appropriate rules for those particular units or terms.
Solving Matrix Equation for Variables
The image shows a matrix equation that we need to solve to find the values of p and q. The matrix equation is given as: ``` [ 4/p p ] [ 7(q) 11(p) ] [-1/q -p ] = [ -3 13 ] ``` To solve for p and q, we need to equate elements in the corresponding positions from the given two matrices. That will give us a system of equations as follows: 1. (4/p) * 7(q) + p * (-3) = 11(p) 2. (-1/q) * 7(q) + (-p) * (-3) = 13 Let's solve these equations. For the first equation: (4q/p) * 7 + p * (-3) = 11p 28q/p - 3p = 11p 28q = 14p^2 q = (14p^2)/28 q = p^2/2 (1) For the second equation: ((-7) + 3p) = 13 3p - 7 = 13 3p = 20 p = 20/3 Now we can substitute the value of p into equation (1) to find q: q = (20/3)^2/2 q = 400/9 * 1/2 q = 400/18 q = 200/9 q = 22.222... Therefore, the values of p and q are: p = 20/3 q = 200/9 However, note that the way both equations are constructed implies that there is an element of matrix multiplication involved, which is not correctly represented in the image. Normally, when multiplying two matrices, the elements are multiplied and then added together according to matrix multiplication rules. The image seems to imply direct multiplication which would defy the matrix multiplication rules. But based on the provided equations and assuming they are correctly representing a matrix product, the above solution for p and q is correct.
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