🧮 algebra

1. **State the problem:** Evaluate the expression $bc + 12.3$ when $a = 10$, $b = 9$, and $c = 4$. 2. **Identify the formula:** The expression is $bc + 12.3$.

1. **State the problem:** Evaluate the expression $a + 9c$ when $a = 10$, $b = 9$, and $c = 4$. 2. **Formula and explanation:** The expression is $a + 9c$. This means we take the v

1. **State the problem:** Evaluate the expression $a^2 - 18$ when $a = 10$, $b = 9$, and $c = 4$. Note that $b$ and $c$ are not used in this expression. 2. **Formula used:** The ex

1. **State the problem:** Solve the equation $-4.9y = 79.87$ for $y$. 2. **Formula and rules:** To isolate $y$, divide both sides of the equation by the coefficient of $y$, which i

1. Stating the problems: Evaluate the expression $$c^2 + 6$$ when $$a=10$$, $$b=9$$, and $$c=4$$.

1. **State the problem:** Solve the system of equations using Gaussian elimination: $$\begin{cases} 2x - y + 3z = 15 \\ x + 2y - 2z = -12 \\ 2x - 3y - 4z = 2 \end{cases}$$

1. **Problem Statement:** Define two functions $f: \mathbb{N} \to \mathbb{N}$ where \(\mathbb{N}\) is the set of natural numbers. (a) Find a function that is one-to-one (injective)

1. The problem is to understand the difference between an onto function and a one-to-one function. 2. A function $f: A \to B$ is called **onto** (surjective) if for every element $

1. **Problem Statement:** Define a function $f: \mathbb{N} \to \mathbb{N}$ that is one-to-one but not onto. 2. **Formula and Explanation:** Consider the function

1. Statement of the problem: Factor $x^2$. 2. Formula and important rules: For a positive integer $n$ we have $$x^n = x \cdot x \cdots \cdot x$$.

1. Problem (a): A businessman sold a refrigerator for 2745 making a profit of 15% on the cost price. We need to find the cost price (CP). 2. Formula: Profit% = \frac{Profit}{Cost P

1. **Problem 1:** A teacher's salary was 3300 after a 10% increase. Find the salary if the increase was 20% instead. 2. **Formula:** New Salary = Original Salary \times (1 + Increa

1. Problem 1: A teacher's salary was 3300 after a 10% increase. Find the salary if the increase was 20% instead. 2. Formula: New Salary = Original Salary \times (1 + Increase Rate)

1. **State the problem:** Solve the system of equations using Gaussian elimination: $$\begin{cases} 2x - y + 3z = 15 \\ x + 2y - 2z = -12 \\ 2x - 3y - 4z = 2 \end{cases}$$

1. **State the problem:** Solve the equation $$4\left(\frac{x}{6} + 5\right) = 2x + 10$$ for $x$. 2. **Use the distributive property:** Multiply 4 by each term inside the parenthes

1. Let's understand how signs change in algebraic expressions. 2. When you multiply or divide by a negative number, the sign of the term changes: a positive becomes negative, and a

1. The problem asks to identify the values of $x$ and $y$ for questions numbered 19, 20, and 21. 2. Since no specific equations or contexts are provided for these questions, we can

1. **Problem Statement:** We need to find the time when the temperature first reached 67°F based on the given temperature vs. time graph. 2. **Understanding the Graph:** The temper

1. **Problem Statement:** We are given a graph showing the inches of snow on the ground over time during a snowstorm. The snow falls at a constant rate for some hours, then stops,

1. **Problem Statement:** We need to find after how many minutes Indigo was 3 blocks from her house based on the given distance-time graph. 2. **Understanding the Graph:** The grap

1. **Problem Statement:** We need to match the correct graph to the story of a plumber charging a fixed fee plus a fixed amount per hour. 2. **Understanding the problem:** The tota