🧮 algebra

1. **Problem statement:** Given the functions $f(x) = -2\left(x + \frac{2}{5}\right)$ and $g(x) = \frac{2 - 5x}{4}$, find the zeros of $f$ and $g$, their intersection point, and th

1. The problem is to match each formula to its corresponding term. 2. Here are the formulas and their meanings:

1. **Problem statement:** We have an arithmetic progression (AP) with first term $a_1=4$ and 100th term $a_{100}=64$. We need to find the sum: $$\sum_{k=1}^{99} \frac{1}{\sqrt{a_k

1. Let's solve an example involving fractions: Simplify the expression $$\frac{3}{4} + \frac{2}{5}$$. 2. To add fractions, we need a common denominator. The denominators here are 4

1. **State the problem:** Simplify the expression $3(2x+3)+14-2(4^2)$. 2. **Recall the order of operations:** First, evaluate exponents, then multiplication and division from left

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one side of the

1. **State the problem:** Solve the equation $$16 - 2t = 5t + 9$$ for the variable $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one sid

1. **State the problem:** Simplify the expression \(\frac{x^2-25}{x^2+5x} \div \frac{xy+6x-5y-30}{5x-15}\). 2. **Rewrite division as multiplication:** Dividing by a fraction is the

1. Planteamos el problema: Demostrar por inducción matemática que la solución general de la ecuación en diferencias no homogénea $$a_{n+1} - a_n = g(n), \quad n \in \mathbb{N}^*$$

1. **State the problem:** Find all values of $x$ such that $g(x) = -1$ and determine the end behavior of $g(x)$ as $x \to -\infty$. 2. **Recall the function $g(x)$:** Given by

1. **State the problem:** Simplify the expression $$\frac{x^2-25}{x^2+5x} \div \frac{xy+6x-5y-30}{5x-15}$$. 2. **Rewrite the division as multiplication by the reciprocal:**

1. **Stating the problem:** Factoring is the process of breaking down an expression into simpler expressions (factors) that, when multiplied together, give the original expression.

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$\begin{cases} 2x + y = 8 \\ 2x - y = 12 \end{cases}$$

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. Das Problem ist nicht spezifiziert, daher kann ich nur allgemeine Hinweise zum Rechnen geben. 2. Beim Lösen von Gleichungen ist es wichtig, die Grundregeln der Algebra zu beacht

1. **State the problem:** Margo borrows 700 and agrees to pay 8% annual interest after 7 months. We need to find the interest she will pay. 2. **Formula used:** The simple interest

1. **State the problem:** Harrison lent his sister 3750 to buy a house. After 4 years, she paid back 3750 plus 600 interest. We need to find the rate of interest per year. 2. **For

1. **State the problem:** We need to find the new price after applying a 20% discount to the original price of 24. 2. **Formula used:** The new price after a discount is given by:

1. **State the problem:** Rita's music store bought a guitar at a wholesale price of $600 and marked it up by 40%. We need to find: a) The markup amount.

1. **State the problem:** The first chapter of a book is 14 pages long and represents 2% of the entire book. We need to find the total number of pages in the book. 2. **Formula use

1. **State the problem:** Calculate the sales tax on a suit priced at 1644 with a sales tax rate of 2%. 2. **Formula:** Sales tax is calculated using the formula: