🧮 algebra

1. **State the problem:** We need to calculate the value of the expression $$-15 \times 2^{\frac{4}{5}}$$ and express the answer in its simplest form. 2. **Recall the rules:** The

1. The problem is to calculate $3 \frac{2}{3} \div \frac{5}{6}$ and express the answer as a simplified fraction. 2. First, convert the mixed number $3 \frac{2}{3}$ to an improper f

1. **State the problem:** Simplify the expression $\frac{8r}{10rw}$. 2. **Recall the formula and rules:** When simplifying fractions, divide numerator and denominator by their grea

1. **Problem Statement:** Given that point $P(a,b)$ is the midpoint of a line segment between the x-axis and y-axis, show that the equation of the line is $$\frac{x}{a} + \frac{y}{

1. **State the problem:** Simplify the expression $$- \frac{1}{4} \times \left( \frac{5}{8} + \frac{7}{8} \right) \div 2 \frac{2}{5} + \frac{5}{6}$$ using BIDMAS (Brackets, Indices

1. **State the problem:** Evaluate the expression \[ \left(-\frac{1}{4}\right) \times \left(\frac{5}{8} + 1 \frac{7}{8}\right) \div 2 \frac{2}{5} + \frac{5}{6} \] using BIDMAS (Bra

1. **State the problem:** We need to find the value of $\frac{5}{12} - \frac{1}{9}$. 2. **Formula and rules:** To subtract fractions, they must have a common denominator. The commo

1. **State the problem:** Find the equation of the line passing through the point $(0, 2)$ making an angle $\frac{2\pi}{3}$ with the positive x-axis. 2. **Formula and rules:** The

1. The problem is to analyze the quadratic function $$y = -3(x - 1)^2 + 12$$ and understand its graph. 2. This is a quadratic function in vertex form: $$y = a(x - h)^2 + k$$ where

1. Énonçons le problème : Résoudre l'équation $ (2x + 1)^2 - 5 = 0 $.\n\n2. Utilisons la formule de résolution : Pour une équation de la forme $a^2 - b = 0$, on peut écrire $a^2 =

1. Let's start with a basic substitution problem: Solve the system of equations using substitution. Given:

1. Let's start with a simple algebra problem suitable for Year 7 students. 2. Problem: Solve for $x$ in the equation $$2x + 5 = 15$$.

1. The problem is to analyze the equation $y = -x + 1$. 2. This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. **State the problem:** Fully factorise the expression $$18x^2 + 12xy - 24x$$. 2. **Identify the greatest common factor (GCF):** Look at the coefficients 18, 12, and -24. The GCF

1. **State the problem:** Simplify the expression $$\frac{3a^3}{12a^9}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n

1. **State the problem:** Fully factorise the quadratic expression $t^2 + 7t - 18$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers th

1. The problem is to verify the logarithmic identity: $$\ln(xy) = \ln x - \ln y$$. 2. Recall the logarithm product rule: $$\ln(ab) = \ln a + \ln b$$ for positive $a$ and $b$.

1. **Problem Statement:** Graph the equation $3y + 15x = 30$ and find its slope and intercepts. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $y

1. The problem is to find the distance traveled in 5 hours given that 60 km is traveled in 2 hours, assuming inverse proportionality. 2. In inverse proportionality, when one quanti

1. **State the problem:** We need to add the fractions $\frac{298}{40}$ and $\frac{76}{32}$. 2. **Find a common denominator:** The denominators are 40 and 32. The least common deno

1. **State the problem:** We need to divide the polynomial $3x^2 - 18x - 46$ by the binomial $3x + 5$. 2. **Formula and method:** Polynomial division is similar to long division wi