🧮 algebra

1. **State the problem:** Solve the equation $2 = 12$. 2. **Analyze the equation:** The equation $2 = 12$ is a statement that claims two numbers are equal.

1. **State the problem:** We have a line given by the equation $y = ax + b$ where $a = 0.6$ and we need to find the value of $b$. 2. **Recall the formula:** The equation of a line

1. **Stating the problem:** We need to find the cost of 20 litres of a paint mixture where white and blue paints are mixed in the ratio 3:2. 2. **Understanding the ratio:** The rat

1. **State the problem:** We are given a rational function with a vertical asymptote at $x = -2$ and a horizontal asymptote at $y = 0$. We need to write the equations of the asympt

1. **State the problem:** Solve the system of equations by substitution and graphing: $$y = 3x - 1$$

1. **State the problem:** We need to perform the operations: From the sum of $3a^2 - ab - 2b^2$ and $2a^2 + 5ab - 3b^2$, subtract $a^2 - 3ab - 4b^2$.

1. **State the problem:** Simplify the expression $$\frac{x + 6}{x^2 + 3x - 18} + \frac{1}{x - 3} + \frac{5}{2x + 12}$$. 2. **Factor denominators where possible:**

1. **State the problem:** Simplify the expression $$\frac{x^2 + 10x + 21}{2x^2 + 10x + 8} \div \frac{5x^2 - 20x - 105}{3x^2 + 15x + 12}$$

1. **Problem statement:** We are given two true statements about visitor numbers at a swimming pool and asked to verify them mathematically.

1. **State the problem:** Simplify the expression $8:2(2+2)$. 2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses first. Calculate inside the parentheses:

1. The problem asks us to write the values 21%, 6/25, 0.15, and 32/200 in ascending order. 2. To compare these values, we convert them all to decimals.

1. **State the problem:** We are given that 135% of a value equals 4185 kg, and we need to find the original value. 2. **Formula and explanation:** To find the original value when

1. **State the problem:** Solve the linear equation $2x + 6 = 12$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Subtra

1. **Problem statement:** Given the function $f(x) = \frac{x^2 - 8}{x^2 - 4}$, find the maximal domain $D$, zeros, symmetry, behavior at domain boundaries, and asymptotes. 2. **Dom

1. El problema es analizar y resolver la función $y = x^2 - 1$. 2. Esta es una función polinómica de segundo grado, también llamada función cuadrática.

1. **State the problem:** Simplify the expression $2i - 14i$. 2. **Recall the rule:** When subtracting like terms, subtract their coefficients and keep the variable the same.

1. **State the problem:** Solve the simultaneous equations: $$5x + 3y = 0$$

1. **State the problem:** Divide the expression \(\frac{q^2 + 2q}{q + 2}\) by \(q\) and write the answer in simplest form. 2. **Rewrite the division as multiplication by the recipr

1. **State the problem:** Divide the expression $$\frac{25x + 20}{5} \div (5x + 4)$$ and write the answer in simplest form. 2. **Recall the division rule for fractions:** Dividing

1. **State the problem:** We need to find the central angle measure $x^\circ$ for the Bowerman slice in a circle graph representing votes. 2. **Formula:** The central angle for a s

1. **State the problem:** Solve the equation $$\sqrt{x} + 6 = 12$$ for $x$. 2. **Formula and rules:** To solve equations involving square roots, isolate the square root term and th