🧮 algebra

1. **State the problem:** We are given the polynomial function $p(a) = a^3 - 5$ and asked to find $p(x - 4)$. 2. **Formula used:** To find $p(x - 4)$, substitute $a$ with $(x - 4)$

1. **State the problem:** Given the ratios $x:y = 0.5 : \frac{1}{2}$ and $z:y = 0.6 : 1$, find the combined ratio $x:y:z$ and the ratio $x:z$. 2. **Simplify the ratio $x:y$:**

1. **State the problem:** Simplify the expression $b)\ (m - 2) + 2a(2 - m)$ and verify the factorization. 2. **Rewrite the expression:** The original expression is

1. **State the problem:** Dominique can spend up to 20 dollars on drinks for the dance squad. A bottle of water costs 0.80 and a sports drink costs 1.25. We need to write inequalit

1. The problem is to solve algebraic expressions without using vectors, focusing on simple and easy methods. 2. We will use basic algebraic operations such as addition, subtraction

1. The problem asks which transformation corresponds to the graph of the function $y = x^2 + 4$ compared to the base function $y = x^2$. 2. The base function $y = x^2$ is a parabol

1. The problem asks how the graph of the quadratic function $y = (x - 3)^2$ moves compared to the parent function $y = x^2$. 2. The general form for a horizontal shift of a quadrat

1. The problem asks us to find the vertex of the parabola given two points: (0, 13) and (3, 4). 2. The vertex of a parabola is the point where it reaches its minimum or maximum val

1. The problem states that a parabola has a vertex at $(-3, 2)$ and asks for the axis of symmetry. 2. The axis of symmetry of a parabola is a vertical line that passes through the

1. The problem asks us to find which quadratic equation has a vertex at $(-3,4)$. 2. Recall the vertex form of a quadratic equation is $$y = a(x-h)^2 + k$$ where $(h,k)$ is the ver

1. **Problem statement:** a. Define what 1 unit of water consumed means.

1. **State the problem:** Expand the expression $$(2x+5)(3x+6)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Expand the expression $$(2x-4)(x+3)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials): $$(a+b)(c+d) = ac + ad + bc

1. **Task 1: Interpret the graph** (i) The domain of a graph is the set of all possible input values (x-values) for which the graph is defined. The range is the set of all possible

1. The problem is to solve the assignment question, but since no specific math problem was provided, I will explain how to approach typical algebra assignments. 2. Generally, algeb

1. Since you asked to show only the working out, I will provide the detailed steps for a generic algebraic problem as an example. 2. Suppose we want to solve the quadratic equation

1. Let's start by understanding what you want to simplify. Simplifying usually means making an expression or problem easier to work with or understand. 2. If you have a specific ma

1. **State the problem:** Simplify the expression $$\sqrt{2}^2 + 5(2)$$. 2. **Recall the rules:**

1. **Task 1: Interpret the graph** (i) The domain of a graph is the set of all possible input values (x-values) for which the graph is defined. The range is the set of all possible

1. **State the problem:** Simplify the expression $4 + 5 \times 3 \times 4 \times 5 \div 2 \times 100$. 2. **Recall the order of operations (PEMDAS/BODMAS):**

1. **Task 1: Interpret the Domain and Range Graph** 1. The problem asks to identify the domain and range of the graph, and determine if it represents a function and a one-to-one fu