🧮 algebra

1. **Stating the problem:** We need to determine the numerical values of $a$, $b$, and $c$ for the function $g(x)$ and find the coordinates of point $D$. 2. **General form and form

1. The problem is to solve the linear equation $$-2.5x - 4.8 = 7.7$$. 2. The goal is to isolate $x$ on one side of the equation.

1. **State the problem:** Solve the linear equation $-2.5x - 4.8 = 7.7$ for $x$. 2. **Isolate the variable term:** Add $4.8$ to both sides to move the constant term.

1. **State the problem:** We need to find the prime number $d$ such that the quadratic equation $$x^2 - 6x + d = 0$$ has two integer solutions. 2. **Recall the quadratic formula:**

1. **State the problem:** We need to find the prime number $d$ such that the quadratic equation $x^2 - 6x + d = 0$ has two integer solutions. 2. **Recall the quadratic formula:** T

1. The problem asks us to determine which points $(x,y)$ could be solutions to a given system of inequalities. 2. A system of inequalities consists of multiple inequalities that th

1. **State the problem:** We are given two linear equations: $$3x - 4y = 8$$

1. **Probleemstelling:** We bekijken lineaire verbanden en formules uit verschillende contexten zoals lijnen, gewichten, kosten en percentages. 2. **Belangrijke formules en regels:

1. **State the problem:** Find the equation of the line passing through points $(2,5)$ and $(5,-1)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x

1. El problema es factorizar la expresión $$a^2x^3 - 9x^3 + 1125 - 125a^2$$. 2. Primero, agrupamos términos para facilitar la factorización:

1. **Problem Statement:** Analyze the function $y=\log_2(x)$. 2. **Domain:** The logarithm is defined for positive arguments only, so $x>0$.

1. Problem: Analyze the function $y = \log_2(x)$. - Domain: $x > 0$ because the logarithm is only defined for positive numbers.

1. **State the problem:** Find the center and radius of the circle given by the equation $$x^2 + y^2 - 6x - 12y + 29 = 0$$. 2. **Formula and rules:** The general form of a circle's

1. **State the problem:** Find the center and radius of the circle given by the equation $$x^2 + y^2 - 10x + 10y + 25 = 0$$. 2. **Formula and rules:** The general form of a circle'

1. **Problem:** Divide $x^2 - 13x - 48$ by $x + 3$ using long division. 2. **Formula and rules:** For polynomial long division, divide the leading term of the dividend by the leadi

1. **Problem:** Natasha’s flat screen television was originally purchased for 300. The value decreases by 7% each year. Find the value after 5 years. 2. **Formula:** The value afte

1. **State the problem:** We are given a table showing the number of tickets purchased and the corresponding number of entries in a raffle drawing. We need to find the rule that re

1. **State the problem.** Alan spent $\frac{7}{10}$ of his allowance on food, then spent half of what was left on stationery, and he had $3$ left.

1. **State the problem.** Alan spent $\frac{7}{10}$ of his allowance on food, then spent half of what was left on stationery, and he had $3$ left.

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 by reciprocal:**

1. **State the problem:** We have three types of fruits represented by variables: red apple ($A$), bunch of bananas ($B$), and coconut half ($C$). We are given two equations: - Cen