🧮 algebra

1. **State the problem:** We need to solve the simultaneous equations graphically: $$y = x^2 - x - x - 6$$

1. State the problem: Solve the quadratic equation $ax^2 + bx + c = 0$. 2. Formula used: The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ which gives the roots o

1. **State the problem:** Solve the equation $2(306x^2 - 400) = 33$ for $x$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses:

1. **Problem statement:** Given points $P(-4, -1)$, $Q(6, 3)$, $R(6, b)$, and $S(-4, -3)$, we need to: a) Determine the gradient (slope) of line segment $PQ$.

1. **State the problem:** We need to solve the simultaneous equations graphically: $$y = x^2 - x - x - 6$$

1. **State the problem:** We are given that 5 miles equals 8 kilometres and a line graph represents this conversion. Points on the line are (0, m) and (5, n). We need to find the v

1. The problem states that £1 = €1.55 and the graph shows a straight line relating pounds (£) to euros (€). 2. The points on the graph are (0, a) and (1, b). Here, the x-axis repre

1. The problem involves understanding the linear relationship between pounds (£) and euros (€) given the exchange rate £1 = €1.55. 2. We are given two points on the graph: (0, a) a

1. **State the problem:** We need to find the relationship between the mass of sugar (in kg) and its cost (in pence) given that sugar costs 80p for every 2 kg. 2. **Identify the fo

1. **State the problem:** We have a recipe that requires 8 grams of butter for every 1 gram of flour.

1. **State the problem:** Solve the equation $$\frac{3}{5} + \frac{2}{b} = 1$$ for $b$. 2. **Isolate the term with $b$:** Subtract $\frac{3}{5}$ from both sides:

1. **State the problem:** We are given the linear function $y = 3x - 5$ and a table of values for $x$ and $y$. Some $y$ values are missing, and we need to find them using the funct

1. **State the problem:** We are given the linear function $y = 2x + 5$ and a table of values for $x$ and $y$. We need to find the missing $y$ values for $x = -2, -1, 0$ and unders

1. **State the problem:** We are given the linear equation $y = 2x + 1$ and a table of $x$ and $y$ values with some missing $y$ values labeled as $A$ and $B$. 2. **Goal:** Find the

1. **State the problem:** We are given the linear function $y = 5x$ and a table with $x$ values $-1, 0, 1, 2$. We need to find the corresponding $y$ values labeled as $A, B, C, D$.

1. **State the problem:** We are given the linear function $y = x + 3$ and a partial table of values. We need to complete the table and draw the graph on a Cartesian coordinate sys

1. **State the problem:** Simplify the expression $$\frac{\sqrt{7} + 2}{3} - \frac{2}{\sqrt{7}}.$$\n\n2. **Rewrite the expression:** To combine the terms, find a common denominator

1. **Stating the problem:** Simplify the given expressions involving roots and rational exponents. 2. **Important rules:**

1. **State the problem:** Find the greatest common factor (GCF) of each given set of numbers. 2. **Recall the definition:** The GCF of a set of numbers is the largest positive inte

1. Let's restate the problem: We want to understand why the maximum value cannot be 80 when considering the root values 180, 200, 80, 95, and 100. 2. The root values likely represe

1. **Problème :** Une entreprise investit 5 000 dans une technologie qui prend de la valeur à un taux de 12% par an. 2. **Formule utilisée :** La valeur future d'un investissement