🧮 algebra

1. **State the problem:** Make $x$ the subject of the equation $$y = \frac{5 - 2x}{x + 3}$$. 2. **Formula and rules:** To make $x$ the subject, we need to isolate $x$ on one side o

1. **State the problem:** Solve the simultaneous equations: $$4x - 5y = 20$$

1. **State the problem:** Calculate the value of $$A = \sqrt{\frac{5 \cdot 4^{n-1}}{2^{2n-2} + 4^{n-2}}}$$

1. **State the problem:** We have a function $L(T)$ representing the pages left to read after $T$ hours, where the book has 150 pages and Ray reads at 25 pages per hour. 2. **Formu

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. **State the problem:** We are given a graph representing the number of pages left to read ($L$) over time ($T$) with domain $0 \leq T \leq 6$ and range $0 \leq L \leq 150$. We w

1. **State the problem:** Find the equation of the line passing through the points (-5, -5), (-2, -2), (3, 3), and (7, 7). 2. **Formula used:** The equation of a line in slope-inte

1. **Problemi:** Sa për qind e 25 është 5? 2. **Formula:** Për të gjetur përqindjen, përdorim formulën:

1. Problemi: Gjej 16% të 25 dhe kontrollo nëse është 5. Formula për përqindjet është: $$\text{Përqindja} = \frac{p}{100} \times \text{vlera}$$ ku $p$ është përqindja.

1. Solve the equation $2x + 3 = 11$. 2. Start by isolating $x$ on one side.

1. **State the problem:** Solve the equation $9x - 12x + 4 = 0$ for $x$. 2. **Combine like terms:** The terms $9x$ and $-12x$ are like terms and can be combined.

1. **State the problem:** We are given two functions:

1. **State the problem:** Solve the equation $$\frac{30}{90} = \frac{3x}{50}$$ for $x$. 2. **Use the cross-multiplication formula:** For two fractions equal to each other, $$\frac{

1. **State the problem:** Solve for $x$ in the proportion $\frac{5}{25} = \frac{x}{12}$.\n\n2. **Formula and rule:** In a proportion $\frac{a}{b} = \frac{c}{d}$, we can find the un

1. **State the problem:** Solve the equation $$\frac{x}{15} = \frac{8}{20}$$ for $x$. 2. **Formula and rules:** To solve for $x$ in a proportion, we use cross multiplication: $$a/b

1. **State the problem:** Solve the equation $$\frac{6}{x+6} = \frac{4}{7}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, we use cross-multiplication:

1. **State the problem:** Solve the equation $$\frac{6}{x} + 6 = \frac{4}{7}$$ for $x$. 2. **Isolate the fraction term:** Subtract 6 from both sides:

1. **State the problem:** Solve the equation $\frac{15}{27} = \frac{2x}{x+26}$ for $x$. 2. **Write the equation:**

1. **State the problem:** Simplify the expression $$\sqrt{(3y^2)^2} \cdot \left(\sqrt{3y^2}\right)^2$$. 2. **Recall the properties of square roots and exponents:**

1. **State the problem:** Simplify the expression $$23 - \frac{3}{4} (\sqrt{150a})^{2} \cdot 8a \sqrt{242a^{2}}$$. 2. **Recall important rules:**

1. **Stating the problem:** We are given the equation $$\sqrt{x^2 + y^2} = 1$$ which represents a graph. 2. **Understanding the formula:** The expression $$\sqrt{x^2 + y^2}$$ repre