🧮 algebra

1. **State the problem:** We have the system of equations: $$2x - 3y = 4$$

1. **State the problem:** We have two pools with initial amounts of water and different rates of filling. We want to find after how many minutes the two pools will have the same am

1. **Problem 1:** Identify the graph represented by the linear relation $y = \frac{1}{2}x + 2$. 2. The equation is in slope-intercept form $y = mx + b$, where $m$ is the slope and

1. **State the problem:** We need to expand and simplify the expression $$(2x-1)(x^2+4x+7)$$ and write it in the form $$ax^3 + bx^2 + cx + d$$. Then find the value of $$b+c$$. 2. *

1. **State the problem:** Solve the quadratic equation $$x^2 - 4x - 12 = 0$$ by factoring. 2. **Recall the factoring method:** To solve by factoring, we express the quadratic in th

1. Problem: Find the zeroes, domain, range, axis of symmetry, and vertex for the quadratic function $y = x^2 - 9$. 2. Formula and rules:

1. **State the problem:** Solve the equation $$\frac{x^2}{3x - 1} + 2 = \frac{2(x - 3)}{3x - 1}$$ for $x$. 2. **Identify the common denominator:** The denominators on both sides ar

1. **State the problem:** Solve the quadratic equation $$x^2 + 14x + 48 = 0$$ for $x$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the so

1. **State the problem:** We are given a function $y = f(x)$ represented by points $(-3, 2), (-2, 4), (-1, 2)$ forming a "tent" shape. We need to find the transformed function $h(x

1. **State the problem:** Simplify the expression $$(\alpha - \beta)^2 + 4(\alpha - \beta) + 4$$. 2. **Recall the formula:** The expression resembles a perfect square trinomial of

1. **State the problem:** Find the highest common factor (HCF) of 70 and 385 using their prime factor trees. 2. **Prime factorization:**

1. **State the problem:** We are given a rectangle with sides AG and NL. The length of side AG is $x^2$ and the length of side NL is $3x - 4$. Since opposite sides of a rectangle a

1. **Problem Statement:** We have several sequences and factorization problems to solve.

1. **Problem Statement:** We have a sequence of patterns made of matchsticks forming triangles. The first pattern has 3 matchsticks, the second 5, the third 7, and so on. We need t

1. The problem is to solve the inequality $\log x \leq -10$. 2. Recall that $\log x$ usually means the logarithm base 10, so the inequality is $\log_{10} x \leq -10$.

1. **State the problem:** Factor the expression $6a - 9$ by extraction. 2. **Formula and rule:** To factor by extraction, find the greatest common factor (GCF) of all terms and fac

1. **State the problem:** We need to solve the system of equations: $$x + y = 69$$

1. The problem is to evaluate the expression $e^{-\infty^2}$. 2. Recall that $\infty$ represents an infinitely large number, and squaring it, $\infty^2$, is still infinitely large.

1. **State the problem:** Solve the system of equations: $$X + Y = 0$$

1. **Problem Statement:** Solve the simultaneous equations from Q1 part a): $$4x + 6y = 16$$

1. **Problem Statement:** Find the number of pupils taking 10 to 30 minutes to travel to school on Monday, given that on Tuesday the number was 25% less than on Monday.