🧮 algebra

1. **State the problem:** Solve the quadratic equation $$5y^2 + 4y + 17 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ay^2 + by + c = 0$

1. **State the problem:** We have data for mass $y$ (grams) at time $t$ (minutes) and want to check if $y = at^n$ fits the data. 2. **Show the formula and transform it:** Starting

1. **State the problem:** Hana thinks of a fraction equivalent to $\frac{5}{9}$ where the numerator is greater than 18 and the denominator is less than 40. 2. **Recall the rule for

1. **Problem Statement:** Order each set of numbers from least to greatest and fill in the blanks with the correct terms. 2. **Ordering Numbers:** To order numbers, convert all to

1. **مشكلة:** تحديد عدد جذور المعادلة التربيعية من خلال تمثيلها البياني. 2. **معلومات أساسية:** عدد جذور المعادلة التربيعية يساوي عدد نقاط تقاطع منحنى الدالة التربيعية مع محور السي

1. **State the problem:** Solve the equation $c t + ||x - y|| = 2 3 klx - lout$ for the variable of interest. 2. **Understand the notation:** Here, $||x - y||$ denotes the norm (or

1. **State the problem:** Solve the equation $$(x + y)^{10} = y + x$$ given the constraint $$0 \leq x + y \leq 10$$.

1. **State the problem:** Use the distributive property to remove the parentheses in the expression $9(3 + v)$. 2. **Recall the distributive property formula:** For any numbers $a$

1. **Stating the problem:** We are given a quadratic function $$y=2.5(x-5)^2+0.5$$ and a linear equation $$\frac{5}{22}x + \frac{1}{33}y = 1$$. We also have a right triangle EFB wi

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