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Example Question - equation

Here are examples of questions we've helped users solve.

Finding Equations and Simplifications

a. To find the equation of a line that passes through points A(3, 4) and B(0, -2), use the slope formula: m = (y2 - y1) / (x2 - x1) = (-2 - 4) / (0 - 3) = -6 / -3 = 2. Using point-slope form: y - y1 = m(x - x1), we get: y - 4 = 2(x - 3). Rearranging gives: y = 2x - 6 + 4 = 2x - 2. b. The sum of 7244 + 809871 + 19 is: 7244 + 809871 + 19 = 817134. c. For simplification of 16^x * 2^4 * y^2z: 16 = 2^4, so 16^x = (2^4)^x = 2^(4x). Thus, 16^x * 2^4 * y^2z = 2^(4x + 4) * y^2 * z. d. The truth set of 8 - m = 6 is: 8 - m = 6 ⇒ m = 2. On the number line, the truth set is {2}.

Finding the Value of a Variable

To solve for $ q $, start with the equation: $ 16 \times 5 \times \frac{q}{10} = \text{{value}} $ First, simplify the left side: $ 16 \times 5 = 80 $, hence: $ 80 \times \frac{q}{10} = \text{{value}} $ Next, multiply $ 80 $ by $ \frac{1}{10} $: $ 8q = \text{{value}} $ Finally, solve for $ q $: $ q = \frac{\text{{value}}}{8} $

Finding the Value of a Variable

To solve for $ q $, start with the equation: $ \frac{3}{8} \times 4 \times q = \text{blank} $ First, calculate $ \frac{3}{8} \times 4 $: $ \frac{3 \times 4}{8} = \frac{12}{8} = \frac{3}{2} $ Now substitute this into the equation: $ \frac{3}{2} \times q = \text{blank} $ Solving for $ q $: $ q = \frac{\text{blank}}{\frac{3}{2}} = \text{blank} \times \frac{2}{3} $

Finding the Value of a Variable in an Equation

Given the equation $ x^{2m} = \frac{(x^3)^8}{x^6} $. First, simplify the right side: $ \frac{(x^3)^8}{x^6} = \frac{x^{24}}{x^6} = x^{24-6} = x^{18} $. Now, equate the exponents: So, $ 2m = 18 $. To find $ m $, divide both sides by 2: Therefore, $ m = \frac{18}{2} = 9 $.

Finding the Value of an Exponent

Given the equation: $$9^{2m - 5} \times 9^3 = 9^{m + 1}$$ Combine the left-hand side using the property of exponents: $$9^{(2m - 5) + 3} = 9^{m + 1}$$ This simplifies to: $$9^{2m - 2} = 9^{m + 1}$$ Since the bases are the same, set the exponents equal: $$2m - 2 = m + 1$$ Isolate $ m $: $$2m - m = 1 + 2$$ $$m = 3$$

Solving an Equation

Starting with the equation: r - 76 = 54 Add 76 to both sides: r = 54 + 76 r = 130 The solution is r = 130.

Matrix Equation Solution

Let A = \begin{pmatrix} 0 & 1 \\ y & 5 \end{pmatrix}, B = \begin{pmatrix} 4 & -1 \\ 6 & x \end{pmatrix}, C = \begin{pmatrix} 4 & 0 \\ x & 7 \end{pmatrix}. Then, we have: A + B = C. Thus, we can write: \begin{pmatrix} 0 + 4 & 1 - 1 \\ y + 6 & 5 + x \end{pmatrix} = \begin{pmatrix} 4 & 0 \\ x & 7 \end{pmatrix}. From this, we can derive the equations: 0 + 4 = 4, 1 - 1 = 0, y + 6 = x, 5 + x = 7. Solve the last equation for x: x = 7 - 5 = 2. Then substitute x back into the third equation: y + 6 = 2. y = 2 - 6 = -4. The values of y and x are: x = 2, y = -4.

Determine the value of a variable

Multiplique ambos lados de la ecuación por 6 para eliminar los denominadores: 6 \left( \frac{x - 1}{2} + \frac{x - 2}{3} \right) = x 3(x - 1) + 2(x - 2) = x 3x - 3 + 2x - 4 = x 5x - 7 = x 5x - x = 7 4x = 7 x = \frac{7}{4}

Finding the Value of a Variable

Empezamos con la ecuación: $\frac{x}{5} + \frac{x}{3} + \frac{x}{15} = 9$ El común denominador de los denominadores 5, 3 y 15 es 15. Multiplicamos toda la ecuación por 15: $15 \left(\frac{x}{5}\right) + 15 \left(\frac{x}{3}\right) + 15 \left(\frac{x}{15}\right) = 15 \cdot 9$ Esto nos da: $3x + 5x + x = 135$ Sumamos los términos similares: $9x = 135$ Ahora dividimos ambos lados por 9: $x = \frac{135}{9}$ Por lo tanto, $x = 15$.

Solving an Equation with Division and Parentheses

First, simplify the expression inside the parentheses: 2 + 2 = 4 Now the equation looks like this: 8 ÷ 2 × 4 Next, perform the division and multiplication from left to right: 8 ÷ 2 = 4 Then multiply: 4 × 4 = 16 Thus, the final answer is: 16

Algebraic Equation Simplification

\[ 5x - (-8) + (-9) = 9x - (-7 + 1) \] \[ 5x + 8 - 9 = 9x - (7 - 1) \] \[ 5x - 1 = 9x - 6 \] \[ 5x - 9x = -6 + 1 \] \[ -4x = -5 \] \[ x = \frac{-5}{-4} \] \[ x = \frac{5}{4} \]

Basic Algebraic Equation Problem

Seja $ x $ o número desconhecido. A equação baseada no problema é: \[ \frac{x - 4}{3} = 2 \] Multiplicar ambos os lados da equação por 3 para isolar o termo $ x - 4 $: \[ x - 4 = 3 \cdot 2 \] $ x - 4 = 6 $ Adicionar 4 a ambos os lados para resolver $ x $: \[ x = 6 + 4 \] $ x = 10 $ Portanto, o número é 10.

Solving a Simple Algebraic Equation

Seja $ x $ o número desconhecido. Temos a seguinte equação baseada na descrição: $ (x - 4) / 3 = 2 $ Multiplicamos ambos os lados da equação por 3 para isolar $ x - 4 $: $ x - 4 = 3 \times 2 $ $ x - 4 = 6 $ Adicionamos 4 a ambos os lados da equação para encontrar $ x $: $ x = 6 + 4 $ $ x = 10 $ Portanto, o número é 10.

Find the Original Number in a Simple Algebraic Equation

Seja $ x $ o número desconhecido. A primeira operação é multiplicar $ x $ por 2: $ 2x $. Em seguida, adiciona-se 3 ao produto: $ 2x + 3 $. A soma final é dada como 7: $ 2x + 3 = 7 $. Agora, resolve-se a equação para $ x $: Subtrai-se 3 de ambos os lados da equação: $ 2x = 7 - 3 $. $ 2x = 4 $. Divide-se ambos os lados por 2 para encontrar $ x $: $ x = \frac{4}{2} $. $ x = 2 $. O número desconhecido é 2.

Complex Number Equation Simplification

Rješavamo zadanu jednadžbu korak po korak. $3 + z - 4(1+i) \cdot \overline{z} = (z - 1)i$ Prvo ćemo distribuirati $ -4 $ kroz zagrade. $3 + z - 4(1+i) \cdot (x - yi) = (x + yi - 1)i$, gdje je $z = x + yi$ Sada množimo kompletne brojeve s konjugiranim kompleksnim brojem. $3 + x + yi - 4 \cdot (x - yi) - 4 \cdot (x - yi)i = xi - yi^2 - i$ Imajući na umu da je $i^2 = -1$, možemo uvijek zamijeniti $yi^2$ sa $-y$. $3 + x + yi - 4x + 4yi - 4xi + 4y = xi + y - i$ Sada grupiramo realne i imaginarene dijelove s obije strane jednadžbe. $(3 - 4x + 4y + x) + (y + 4yi - 4xi - i)i = (xi + y) - i$ Jednakost realnih i imaginarnih dijelova mora biti zadovoljena na obije strane jednadžbe. Za realni dio: $3 - 3x + 4y = 0$ $4y = 3x - 3$ $y = \frac{3x - 3}{4}$ Za imaginarni dio: $y - 4xi = -1$ $-4xi = -y - 1$ $xi = \frac{y + 1}{4}$ Sada kada imamo dva izraza za $y$ i $xi$, možemo ih koristiti kako bismo našli rješenje za $x$ i $y$. $x = \frac{y + 1}{4i}$ $x = \frac{\frac{3x - 3}{4} + 1}{4i}$ $x = \frac{3x - 3 + 4}{16i}$ $16xi = 3x + 1$ $x(16i - 3) = 1$ $x = \frac{1}{16i - 3}$ $x = \frac{1}{16i - 3} \cdot \frac{16i + 3}{16i + 3}$ $x = \frac{16i + 3}{256 - 9}$ $x = \frac{16i + 3}{247}$ Sada kada smo našli $x$, možemo riješiti za $y$ koristeći izraz koji smo već izveli. $y = \frac{3x - 3}{4}$ $y = \frac{3 \cdot \frac{16i + 3}{247} - 3}{4}$ $y = \frac{48i + 9 - 741}{988}$ $y = \frac{48i - 732}{988}$ $y = \frac{48i}{988} - \frac{732}{988}$ $y = \frac{6i}{123} - \frac{183}{247}$ Tako imamo rješenje za $z$: $z = x + yi$ $z = \frac{16i + 3}{247} + \left(\frac{6i}{123} - \frac{183}{247}\right)i$ $z = \frac{16i + 3}{247} + \frac{6i^2}{123} - \frac{183i}{247}$ $z = \frac{16i + 3}{247} - \frac{6}{123} - \frac{183i}{247}$ $z = \frac{3 - 6 \cdot 2}{247} + \frac{16i - 183i}{247}$ $z = \frac{3 - 12}{247} + \frac{16i - 183i}{247}$ $z = \frac{-9}{247} + \frac{-167i}{247}$ $z = -\frac{9}{247} - \frac{167i}{247}$ Dakle, rješenje za zadanu jednadžbu je: $z = -\frac{9}{247} - \frac{167i}{247}$

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Example Question - equation

Here are examples of questions we've helped users solve.

Finding Equations and Simplifications

Finding the Value of a Variable

Finding the Value of a Variable

Finding the Value of a Variable in an Equation

Finding the Value of an Exponent

Solving an Equation

Matrix Equation Solution

Determine the value of a variable

Finding the Value of a Variable

Solving an Equation with Division and Parentheses

Algebraic Equation Simplification

Basic Algebraic Equation Problem

Solving a Simple Algebraic Equation

Find the Original Number in a Simple Algebraic Equation

Complex Number Equation Simplification

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