🧮 algebra

1. **Problem statement:** Suppose the ratio of the ages of two siblings is 3:5. If the older sibling is 20 years old, find the age of the younger sibling. 2. **Formula and rules:**

1. **Problem statement:** Suppose two siblings currently have ages in the ratio 3:5. Years ago, the ratio of their ages was half the ratio of their ages years from now. Find their

1. **State the problem:** Calculate Carmela's percent score given she obtained 618 marks out of 800 total marks. 2. **Formula used:** Percent Score = \(\frac{\text{Marks obtained}}

1. **Problem statement:** Suppose the ratio of the ages of two siblings is 3:5. If the sum of their ages is 40 years, find their individual ages. 2. **Formula and rules:** Let the

1. **State the problem:** Simplify the expression $1000 - [300 + 50 + (40 \times 3) + (200 \times 2)]$. 2. **Recall the order of operations:** Calculate inside the brackets first,

1. Express the partial fraction decomposition of \( \frac{3x}{(x+1)(x-2)} \). 2. The problem is to write \( \frac{3x}{(x+1)(x-2)} \) as a sum of simpler fractions of the form \( \f

1. **State the problem:** Simplify the expression $$7[3 -2 1] - \frac{1}{3} [21 6 -9]$$ where the brackets denote scalar multiplication of each element in the vector. 2. **Apply sc

1. The problem is to simplify the expression "re". 2. Since "re" is not a standard algebraic expression or equation, it appears to be just two letters together.

1. **Stating the problem:** Solve the system of linear equations for part (a): $$\begin{cases} 2x + y - 3z = 3 \\ x - y + 5z = -2 \\ 2x + 2y - z = -1 \end{cases}$$

1. Problem 1: Solve the equation $2x + 3 = 7$. 2. Use the formula for linear equations: $ax + b = c$.

1. Énoncé du problème : On considère la matrice \( A = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix} \) et on sait que \( A \) est nilpotente d'indice \( p \).

1. نبدأ بحل المعادلة الأولى من تمرين 4 (A): المعادلة هي $$\ln\left(\frac{x+2}{x+1}\right) = \ln(x+3)$$

1. **State the problem:** Solve the quadratic expression $m^2 - 10m - 11 = 0$ for $m$. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the solu

1. **State the problem:** Solve the compound inequality $$-6 \leq 2(x - 5) < 7$$. 2. **Understand the inequality:** This is a compound inequality involving a linear expression. We

1. **State the problem:** Simplify or factor the quadratic expression $m^2 - 10m + 11$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two number

1. **Problem Statement:** Identify the slope and y-intercept of the linear equation $$y = -2x + 4$$ and explain how to graph it. 2. **Formula and Rules:** The slope-intercept form

1. **State the problem:** Solve the quadratic equation $$2x^2 + 7x + 3 = 0$$ by factorization. 2. **Recall the factorization method:** For a quadratic equation $$ax^2 + bx + c = 0$

1. **State the problem:** We are given two functions: - $f(x) = 3\sqrt{x}$

1. **State the problem:** Solve the simultaneous equations: $$4c + 3d = 4$$

1. **State the problem:** Evaluate the expression $2 + 4(x - 4)^3$ when $x = 6$. 2. **Write the formula:** The expression is $2 + 4(x - 4)^3$.

1. **Evaluate** $f(-9)$ for the piecewise function: The piecewise function $f(x)$ is defined as: