🧮 algebra

1. **Problem statement:** We have four functions: $$f_1(x) = x^2 - 2,$$

1. The problem is to understand why the variable $x$ in part a is given the value 8.5 instead of the variable $a$. 2. Usually, in algebra or problem-solving, variables like $a$ and

1. **State the problem:** We need to find the average revenue of a shop over four months with revenues ₵18,500, ₵20,000, ₵21,500, and ₵24,000. 2. **Formula for average:** The avera

1. **State the problem:** Find the values of $x$ that are not allowed in the expression $\frac{x+4}{x^2-16}$. 2. **Understand the rule:** The denominator of a fraction cannot be ze

1. The problem is to express the number 1 in a way that is suitable for a 4-mark question, likely requiring detailed explanation or multiple steps. 2. We start by stating the probl

1. The problem asks for the minimum integer $n$ such that $|f(\alpha)| \leq 10^{-6}$, where $\alpha$ is the root at point B and $x_{n+1}$ is the iteration step. 2. Typically, this

1. **State the problem:** Express the quadratic expression $4x^2 - 12x + 13$ in the form $(2x + a)^2 + b$, where $a$ and $b$ are constants. 2. **Recall the formula:** To write a qu

1. **State the problem:** Find the domain of the function $$f(x) = \frac{2}{x^{2} - 64}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real number

1. **Problem Statement:** Determine the equation of the graph described, which is a "V" shaped absolute value function with vertex at $(4,1)$. 2. **Recall the general form of an ab

1. The problem is to write an expression or equation in a clean, simplified form. 2. To clean or simplify an expression, combine like terms, factor where possible, and write it in

1. **State the problem:** Solve the equation $$a + \frac{2}{6} - \frac{1}{a} + 2 = \frac{1}{6}$$ for $a$. 2. **Simplify constants:** Note that $\frac{2}{6} = \frac{1}{3}$, so rewri

1. Problem: Simplify the product \( \frac{5y^3}{32x} \cdot \frac{-4}{15x^2 y^3} \). Step 1: Multiply numerators and denominators:

1. **Problem:** Simplify $\frac{5y^3}{32x} \times \frac{-4}{15x^2 y^3}$. 2. **Formula:** Multiply numerators and denominators, then simplify common factors.

1. The problem involves simplifying and understanding the expressions arranged in a pyramid shape. 2. Let's analyze each expression step-by-step.

1. **Problem Statement:** (a) Given $a = b^x$, $b = c^y$, and $c = a^z$, prove that $xyz = 1$.

1. **Problem:** Given $a = b^x$, $b = c^y$, and $c = a^z$, prove that $xyz = 1$. 2. **Step 1:** Express $a$ in terms of $a$ using the given equations.

1. **State the problem:** Solve the equation $$\frac{y+2}{y-1} - \frac{4-y}{2y} = \frac{7}{3}$$ for $y$. 2. **Identify the common denominator:** The denominators are $y-1$, $2y$, a

1. **State the problem:** We are given five linear equations and asked to find specific points or coordinates related to each line, such as where the line intersects $y=5$, the $x$

1. The problem is to solve for $D$. 2. Since no equation or context is given, we assume $D$ is a variable to be isolated or found.

1. **State the problem:** Solve the equation $$|x^2 - 2x - 16| = 8$$ and verify solutions graphically. 2. **Recall the definition of absolute value:** For any expression $A$, $$|A|

1. **State the problem:** Kwame spends fractions of his monthly salary on food, rent, and sweets, and after these expenses, he has 90 left. We need to find his total salary, and ho