🧮 algebra

1. **State the problem:** We are given the quadratic function $$y = -x^2 - 6x - 10$$ and want to analyze its properties such as shape, vertex, and intercepts. 2. **Formula and rule

1. **State the problem:** We need to analyze and solve the quadratic function $$y = -x^2 - 6x - 10$$. 2. **Formula and rules:** The quadratic function is in the form $$y = ax^2 + b

1. **State the problem:** Solve the quadratic equation $$2x^2 - 7x + 3 = 0$$ by factorisation. 2. **Recall the factorisation method:** For a quadratic equation $$ax^2 + bx + c = 0$

1. State the problem: Simplify each expression. 2. The three expressions to simplify are: a) $ (5x^2)^3 $.

1. **Problem:** Simplify the expression $a (5x^2)^3$. 2. **Formula:** Use the power of a product rule: $(ab)^n = a^n b^n$ and the power of a power rule: $(x^m)^n = x^{mn}$.

1. Let's first clarify the concept you are referring to, as it wasn't specified in your message. 2. Common algebraic concepts like solving linear equations, quadratic equations, or

1. **Stating the problem:** Mr. Elia has 201900 Tanzania shillings and wants to buy groceries with discounts of 5%, 10%, and 15%. We need to find how much he will pay after each di

1. The problem is to verify the expression $8 \times 8 = 5 + 3$ eights and simplify it. 2. The expression $8 \times 8$ means multiplying 8 by 8.

1. **State the problem:** We need to find the value of $y$ when $x=\frac{4}{5}$ in the formula $$y = \frac{4}{x} + \sqrt{x} + 0.2 - 5x.$$\n\n2. **Write down the formula:** $$y = \f

1. The problem is to find the formula for a given mathematical relationship or function. 2. A formula is an equation that expresses a relationship between variables.

1. **State the problem:** Factor the expression $$2x^2 - 72y^2$$. 2. **Identify the common factor:** Both terms have a common factor of 2.

1. **State the problem:** We are given the function $c(t) = 28 + 4 \sin\left(\frac{\pi}{2} t\right)$ and we want to understand its behavior. 2. **Formula and explanation:** This is

1. The problem asks to find $f(-4)$ for the function $f(x) = -2x + 5$ and then to find the value of $p$ given $f(x) = px - 8$ and $f(4) = 20$. 2. For the first part, substitute $x

1. Masalah ini meminta kita menentukan banyak batang korek api yang diperlukan untuk membuat pola segitiga ke-7. 2. Dari pola yang diberikan, kita lihat jumlah batang korek api unt

1. **Problem Statement:** Convert the polar coordinate point (3, 45°) to rectangular coordinates and plot it. 2. **Formula:** To convert from polar to rectangular coordinates, use:

1. Arithmetic Sequence (AS): An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.

1. Let's start by stating the problem: We need to find the domain, range, and zeros of a function. However, the specific function is not provided, so I'll explain the general appro

1. **State the problem:** We are given the quadratic function $y = x^2 - 6x + 10$ and the equation $1 = x - 3$. We want to analyze the function and solve for $x$ in the equation. 2

1. Let's start with Arithmetic Sequences (AS). An arithmetic sequence is a list of numbers with a constant difference between consecutive terms. 2. The formula for the $n$th term o

1. Let's start with Arithmetic Sequence (AS). An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference, called the commo

1. The problem is to graph the function $y = a^x$ where $a > 0$ and $a \neq 1$. 2. The general form of an exponential function is $y = a^x$, where $a$ is the base and $x$ is the ex