🧮 algebra

1. **State the problem:** Factorise the quadratic expression $x^2 + 18x + 17$. 2. **Recall the formula:** To factorise a quadratic $ax^2 + bx + c$, we look for two numbers that mul

1. **Problem Statement:** We are given the function $$y = x(x - 4) - 5$$ which simplifies to $$y = x^2 - 4x - 5$$.

1. The problem is to determine if a function is surjective (onto). 2. A function $f: A \to B$ is surjective if for every element $b$ in the codomain $B$, there exists at least one

1. The problem is to determine if a function $f$ is injective (one-to-one). 2. A function $f$ is injective if and only if for every $x_1$ and $x_2$ in the domain, whenever $f(x_1)

1. **Problem 1: Find the value of 5c given the mapping:** Given the mapping:

1. **State the problem:** A man takes 60 minutes less than his apprentice to paint a room. Together, they take 72 minutes to paint the room. We need to find the time the apprentice

1. **State the problem:** Given the mapping from $x$ to $y$ values: $$\begin{array}{c|cccccc}

1. **State the problem:** A man takes 60 minutes less than his apprentice to paint a room. Together, they take 72 minutes to paint the room. We need to find the time the apprentice

1. **State the problem:** Solve the system of equations using the method of substitution: $$x - 2y = 3$$

1. **State the problem:** Solve the system of equations using substitution: $$x + 2y = 3$$

1. The problem is to multiply expressions using the distributive law, which states that for any numbers $a$, $b$, and $c$, we have $a(b+c) = ab + ac$. 2. This law allows us to mult

1. **State the problem:** Multiply the two polynomials $ (2x^2+4) $ and $ (x^2-3x+1) $. 2. **Recall the distributive property:** To multiply two polynomials, multiply each term in

1. The problem is to understand how to get the expression $5 \times 10^{8} q^{2}$. 2. This expression is a product of three parts: the number 5, the power of ten $10^{8}$, and the

1. **Problem Statement:** We are asked to provide 3 examples of rational functions: a monomial, a binomial, and a trinomial.

1. **Stating the problem:** Solve the monomial equation $ax^n = b$ for $x$. 2. **Formula and rules:** To solve a monomial equation, isolate $x^n$ by dividing both sides by $a$ (ass

1. The problem is to solve the equation given by the user (though no explicit equation was provided, we assume a general solving task). 2. To solve an algebraic equation, we use th

1. The problem is to provide 3 examples of monomials. 2. A monomial is an algebraic expression consisting of only one term, which is a product of numbers and variables with non-neg

1. The problem is to find the square root of a number greater than 150. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **Problem statement:** (a) Determine between which two consecutive integers the given irrational numbers lie.

1. The problem is to find the expression for $N^2 \times 2$ given $N(x) = 2 - 2x$. 2. First, understand that $N^2$ means $N(x)$ squared, or $(2 - 2x)^2$.

1. **State the problem:** We are given the equation $$x^2 - y^2 = 2$$ and asked to analyze it. 2. **Identify the type of curve:** This is a hyperbola because it can be rewritten in