🧮 algebra

1. **State the problem:** Find the slope of the line passing through the points $(-9, -10)$ and $(7, 7)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_

1. **Problem statement:** Der Wildbestand eines Naturparks nimmt exponentiell ab und sinkt innerhalb von 5 Jahren um 4%. Im Jahr 2010 wurden 1780 Tiere gezählt.

1. **Problem statement:** (a) Fully factorise $a^2 + 2ab + b^2 - 49$.

1. **State the problem:** We need to graph the inequality $y > \frac{1}{2}x - 6$. 2. **Understand the boundary line:** The boundary line is given by the equation $y = \frac{1}{2}x

1. **Stel het probleem vast:** We moeten de ongelijkheid $$-4 \cdot (-x - \frac{5}{4}) > x + 8$$ grafisch oplossen en de oplossingsverzameling aanvullen. 2. **Schrijf de ongelijkhe

1. The problem involves two fractions being added and then the third fraction multiplied by the result of that addition. 2. Let's denote the first two fractions as $\frac{a}{b}$ an

1. **Stating the problem:** Solve the equation $$\sqrt[10]{\frac{x^2 + \frac{x}{y}}{}} = \sqrt[10]{\left(x + \frac{1}{x^2}\right)^5} \cdot \sqrt{x}$$ given in exercise 123, page 69

1. The problem involves understanding and comparing different functions: a linear function $y = ax + b$, a reciprocal function $y = \frac{1}{x}$, and a quadratic function described

1. **State the problem:** Solve the logarithmic equation $$\log_6(-4x) - \log_6 7 = \log_6 54$$ for $x$. 2. **Recall the logarithm subtraction rule:** $$\log_b A - \log_b B = \log_

1. **State the problem:** Solve the equation $$\frac{2x - 1}{3} - \frac{3x + 1}{5} = 1$$. 2. **Identify the formula and rules:** To solve equations with fractions, find a common de

1. Stating the problem: Simplify the expression $$\frac{3x - 4}{5} + \frac{5x - 2}{5}$$. 2. Since both terms have the same denominator 5, we can combine the numerators over the com

1. El problema consiste en unir enunciados para completar frases sobre funciones y sus puntos de corte con los ejes. 2. Primero, recordemos que una función es una relación entre do

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}.$$\n\n2. **Use the given equalities:** We know $a - b = 2$ and

1. **State the problem:** Simplify the expression $$\frac{-14.2 m^2}{2m}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing terms with the same base, s

1. **State the problem:** Find the slope $m$ of the line passing through the points $(11,14)$ and $(-18,3)$. 2. **Recall the slope formula:**

1. **State the problem:** Simplify the expression $$\frac{3y}{y^2 + 3y - 10} - \frac{5}{2y + 10}$$ and check if it equals $$\frac{5y - 5}{y^2 + 3y - 10}$$. 2. **Factor the denomina

1. The problem is to write a given expression or function as $f(x)$, which means expressing it as a function of $x$. 2. The general form of a function is $f(x) = \text{expression i

1. The problem asks to find the average rate of change of the function $f(x) = 7$ on the interval $[6, 8]$. 2. The formula for the average rate of change of a function $f$ on the i

1. **State the problem:** We need to find the missing values A, B, C, and D in the tables for the simultaneous equations: $$y + 9x = 0$$

1. **State the problem:** Simplify the expression $$\frac{3}{5} - \frac{2x - 1}{10} + \frac{3x - 2}{4}$$. 2. **Find a common denominator:** The denominators are 5, 10, and 4. The l

1. **State the problem:** We have two equations based on Alfie's and Lyra's operations with numbers $c$ and $d$: