🧮 algebra

1. **State the problem:** Calculate $8 + 3$. 2. **Recall the addition rule for integers:** When adding two positive integers, simply add their absolute values.

1. **State the problem:** Creed wants to find the cost of 1 kg (1000 g) of Halloween Treats when 450 g costs 3.75. 2. **Formula used:** To find the cost per gram, use the unit rate

1. The problem is to solve the proportion $$\frac{x}{78} = \frac{8}{13}$$ and find the value of $x$. 2. The formula for solving proportions is to cross multiply: $$a/b = c/d \impli

1. **State the problem:** We are given a line passing through points $(-7, -8)$ and $(1, 6)$ and asked to find the y-intercept of this line. 2. **Formula and rules:** The y-interce

1. **State the problem:** Find the gradient (slope) of the line passing through points $(-2, -5)$ and $(1, 4)$.\n\n2. **Formula for gradient:** The gradient $m$ of a line through p

1. **Problem statement:** Identify the degree, leading coefficient, and end behavior of each polynomial function. 2. **Key concepts:**

1. Problem: Bestimme zu jedem Graphen die Funktionsgleichung der drei Geraden g1, g2 und g3. 2. Allgemeine Formel für eine lineare Funktion: $$y = mx + b$$ wobei $m$ die Steigung u

1. **State the problem:** We need to find an expression that represents the total profit from selling $h$ hot dogs, $p$ pretzels, and $d$ drinks. 2. **Identify the profit per item:

1. State the problem: Simplify and factorise the expression b) $3x^2 - 11 + x^2 - 7$. 2. Formula and rules: Combine like terms by adding coefficients of the same power, e.g. $ax^n

1. **State the problem:** Jade is twice as old as Sara. If Sara is $y$ years old, find an expression for Jade's age. 2. **Understand the relationship:** "Twice as old" means Jade's

1. **State the problem:** We want to find the largest whole number $x$ such that $8 + x$ is larger than $2x$. 2. **Write the inequality:**

1. **State the problem:** Simplify the expression $$\frac{m^{x+9}}{m^3}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, s

1. **State the problem:** Solve the equation $$\frac{6}{x+2} = \frac{5x-1}{2-3x}$$ for $x$. 2. **Understand the formula and rules:** To solve an equation with fractions, we can cro

1. **State the problem:** We are given a cubic function $$f(x) = x^3 - 14x^2 + 61x - 84$$ and told that one factor is $$(x - 7)$$. We need to find all zeros of the function. 2. **U

1. The problem is to simplify the expression $\frac{4}{ }$, but the denominator is missing. 2. A fraction requires both a numerator and a denominator to be defined.

1. **State the problem:** Solve the quadratic equation $$x^2 + x - 6 = 0$$ using the graph of the function $$y = x^2 + x - 6$$. 2. **Formula and rules:** The solutions to $$x^2 + x

1. **Stating the problem:** We are given a sequence defined by the formula $H_n = 2400n + 67600$.

1. **State the problem:** We have two salary progressions: Helen's salary is constant at $70000$ each year, and Jane's salary starts at $70000$ and grows exponentially by $3\%$ eac

1. **State the problem:** Evaluate the expression $$\sqrt[3]{\sqrt{256} + \sqrt{81}} + \sqrt[3]{512 + \sqrt[3]{1}}$$ and simplify the answer. 2. **Recall important rules:**

1. **State the problem:** We have two decimal numbers with missing digits represented as $\square . 7 \square$ and $\square \square \square 0$. We need to fill in the blanks using

1. The problem involves evaluating the expression $7n - 1$ for a given $n$ or understanding its form. 2. The expression $7n - 1$ is a linear algebraic expression where $n$ is a var