🧮 algebra

1. The problem is to solve for $x$ given the equation $x^2 - 4 = 0$ and the condition $x = 5$. 2. The equation to solve is a quadratic equation: $$x^2 - 4 = 0$$

1. **State the problem:** Andrew bought a square piece of curtain material with an area of $5\frac{1}{16}$ meters squared. We need to find the length of one side of the square. 2.

1. Planteamos el problema: realizar la suma o resta de los polinomios dados. 2. Para restar o sumar polinomios, sumamos o restamos los coeficientes de los términos semejantes (mism

1. **State the problem:** Jay's cookie recipe requires 3 cups of chocolate chips for every 4 cups of flour. He wants to make a smaller batch using only 1 cup of flour. We need to f

1. **State the problem:** Multiply and divide the given integers using the Rules-Based Method. 2. **Rules for multiplication and division of integers:**

1. The problem is to find the function $g(x)$ in the form $a|x - h| + k$ that matches the described graph. 2. The graph is a V-shaped absolute value function with vertex at the ori

1. **State the problem:** We are given two functions: $$f(x) = 3x^4$$

1. Problema: Realizar la división de los siguientes monomios. 2. Regla general para dividir monomios: \( \frac{a^m}{a^n} = a^{m-n} \) y dividir coeficientes numéricos normalmente.

1. Problema: Multiplicar los monomios dados. 2. Regla: Para multiplicar monomios, multiplicamos los coeficientes y sumamos los exponentes de las mismas bases.

1. **State the problem:** We have the quadratic equation $$k + 9 = (6 - x)(2x + 1)$$ and need to find:

1. Problema: Calcular el valor numérico de las expresiones algebraicas dadas para los valores indicados. 2. Fórmulas y reglas importantes:

1. **State the problem:** We need to find the value of $\cos(OPA)$ given by the formula $$\cos(OPA) = \frac{x^2 - 8x + 40}{\sqrt{(x^2 - 16x + 80)(x^2 + 100)}}$$

1. The problem asks to find the value of opa when $x=8$. 2. However, the function or expression for opa in terms of $x$ is not provided.

1. **State the problem:** Solve the equation $3(3+f) = -15$ for $f$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses.

1. **State the problem:** Solve the equation $2(2+m)=16$ for $m$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses.

1. The problem is to simplify or understand the expression $\sqrt{x^2 + 100}$.\n\n2. The square root function $\sqrt{\cdot}$ returns the non-negative value whose square is the argu

1. The problem asks us to determine if the graph represents the inequality $x \leq 1.5$. 2. The graph shows a number line from -2 to 2 with a solid dot at 1, indicating that 1 is i

1. **State the problem:** We are given an area expression $81x^2$ cm$^2$ and a length of 3 cm, and we want to find the missing length of the rectangle. 2. **Formula used:** The are

1. نبدأ بكتابة المسألة: $4 + ت \div ت$ 2. القاعدة الأساسية في الحساب هي أن عملية القسمة والضرب تُنفذ قبل الجمع والطرح، لذلك نبدأ بالقسمة.

1. The problem asks to determine if the graph correctly represents the inequality $k > 4$. 2. The inequality $k > 4$ means all values strictly greater than 4, so the graph should s

1. **State the problem:** Solve the expressions for question 8 and question 9. 2. **Question 8:** Calculate $$\frac{5}{6} - \frac{3}{4} + \frac{5}{9}$$.