🧮 algebra

1. **State the problem:** We have a building valued at $261000$ and its value increases by $4.5\%$. We need to find the new value after the increase. 2. **Formula used:** To find t

1. Let's start with a more complex example of multiplication of algebraic fractions. Given: $$\frac{3x^2 - 6x}{4x} \times \frac{8x^3}{12x^2 - 18x}$$

1. Let's start with an example of multiplication of algebraic fractions. Given: $$\frac{2x}{3} \times \frac{4}{5x}$$

1. **State the problem:** We are given the function $$g(x) = x^2 + 11x$$ and want to analyze its properties such as vertex and x-intercepts. 2. **Formula and rules:** This is a qua

1. **State the problem:** Factor the quadratic function $$g(x) = x^2 + 6x + 8$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers tha

1. **State the problem:** We need to find the solution to the system of equations: $$y = -2x + 7$$

1. **State the problem:** Solve the system of equations: $$7x - y = 7$$

1. The problem asks: "What is the y?" but it is incomplete as it does not specify a function, equation, or context to determine $y$. 2. To find $y$, we need an equation or expressi

1. **State the problem:** Simplify or understand the expression $$1.8y + 0.72$$. 2. **Identify terms:** The expression consists of two terms: $$1.8y$$ (a term with variable $$y$$)

1. **Stating the problem:** Solve the quadratic equation $$x^{2}-6x-6=0$$ using the sum-product method. 2. **Sum-product method formula:** For a quadratic equation $$x^{2}+bx+c=0$$

1. **State the problem:**\n\nFactorise the expression $$\frac{4x - 3 + 2(3 - x)}{2x^2 - x - 6}$$.\n\n2. **Simplify the numerator:**\n\nExpand the term $2(3 - x)$:\n$$4x - 3 + 2(3 -

1. **State the problem:** Simplify the given algebraic fractions. 2. **Part (a): Simplify** $$\frac{15a^3b^2c}{65(ab^2)^2}$$

1. **State the problem:** We need to find the y-intercept and x-intercept of the line given by the equation $$7x - y = 7$$. 2. **Recall the definitions:**

1. **State the problem:** Find the y-intercept and x-intercept of the line given by the equation $$7x - y = 7$$. 2. **Recall the definitions:**

1. **State the problem:** We need to calculate the sum of the fractions $\frac{-1}{5}$ and $\frac{7}{4}$. 2. **Find a common denominator:** The denominators are $5$ and $4$. The le

1. **State the problem:** Calculate the value of $$\frac{7}{4} - \left(-\frac{1}{2}\right)$$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positi

1. Planteamos el problema: Resolver la ecuación $$8 - \frac{1}{t} - \frac{7}{t^2} = 0$$ y encontrar el conjunto solución. 2. Para resolver, multiplicamos toda la ecuación por $$t^2

1. **State the problem:** We need to find the equation of a line that passes through the point $(2,2)$ and is perpendicular to the line $x = -1$. 2. **Understand the given line:**

1. Planteamos el problema: Queremos encontrar el nivel de producción $x$ para diferentes situaciones: ganancia de $5000$, pérdida de $1475$ y punto de equilibrio.

1. Planteamos el problema: Resolver la ecuación $$10 - \frac{1}{t} - \frac{9}{t^2} = 0$$ y encontrar el conjunto solución. 2. Para resolver, multiplicamos toda la ecuación por $$t^

1. **State the problem:** We need to solve the system of inequalities: $$m > 9$$