🧮 algebra

1. **Problem:** Represent "6 more than four times the number n" as an algebraic expression. 2. **Formula and Explanation:** "Four times the number n" means multiplying n by 4, whic

1. **Problem:** Write an algebraic expression for "Seven more than a number divided by six". 2. **Understanding the problem:** We need to express the phrase "Seven more than a numb

1. **Stating the problem:** We are given two lists: Midterms scores ($x$) and Travel times ($y$). We need to create a table with columns $x$, $y$, $xy$, $x^2$, and $y^2$.

1. **State the problem:** We are given the price ratio of three types of cars: Suzuki Swift, Ford Fiesta, and Honda Jazz as $3 : x : 4$. The total price of all three cars is 300000

1. **State the problem:** Solve the system of equations using the Gauss Elimination Method: $$\begin{cases} 2y + z = -8 \\ x - 2y - 3z = 0 \\ -x + y + 2z = 3 \end{cases}$$

1. Problem: Calculate the value of $y$ for the equation $y = 32 - 4x + x^2$ when $x = 3$. 2. Formula: Substitute the value of $x$ into the equation and simplify.

1. **State the problem:** We have three types of cars: Suzuki Swift, Ford Fiesta, and Honda Jazz. Their prices are in the ratio $3:x:4$ respectively. 2. **Given:**

1. **Problem Statement:** We have two alloys A and B with Aluminum (Al) and Nickel (Ni) in ratios 4:3 and 3:5 respectively.

1. Stating the problem: Find the unknown percentage $x$ such that $$65\% \text{ of } 180 + x\% \text{ of } 210 = 80\% \text{ of } 225.$$\n\n2. Write the equation using decimals for

1. Let's start with the basics of Arithmetic Sequences (AS) and Geometric Sequences (GS). 2. An Arithmetic Sequence is a sequence where each term increases by a constant difference

1. Let's start by defining Arithmetic Sequence (AS) and Geometric Sequence (GS). An Arithmetic Sequence is a sequence of numbers where the difference between consecutive terms is c

1. **State the problem:** We are given the equation $$2(2x - 2) = 3x - 7$$ which relates the height of a door and the length of a garland. 2. **Write the equation and expand:** Use

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