🧮 algebra

1. **State the problem:** Solve the linear equation $2y - x = 4$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by per

1. **State the problem:** Simplify or understand the expression $4\sqrt{x}$. 2. **Recall the definition:** The square root function $\sqrt{x}$ represents the principal (non-negativ

1. The problem states that Juan and Ivy have the same number of spring rolls for dinner, with each container holding $r$ spring rolls. 2. From the description, Juan has 4 container

1. Zadání problému: Vyřešte rovnici $$2x + 3 = 7$$. 2. Použitá formule a pravidla: Cílem je izolovat proměnnou $x$ na jedné straně rovnice. To znamená, že musíme odstranit konstant

1. **Stating the problem:** We are given the numbers 24 and 48 and asked to find their ratio to 0 and 8 respectively, which means we want to find the ratio $\frac{24}{0}$ and $\fra

1. **Problem statement:** Evaluate $\log_6 54 + \log_6 2 - \log_6 3$. 2. **Formula used:** The logarithm properties we use are:

1. Work out: a) $(-4) + (-13)$ - When adding two negative numbers, add their absolute values and keep the negative sign.

1. **State the problem:** Factor the expression $$27x^3 - 125$$. 2. **Recognize the form:** This is a difference of cubes since $$27x^3 = (3x)^3$$ and $$125 = 5^3$$.

1. **State the problem:** Factor the expression $$27x^3 - 125$$. 2. **Recognize the form:** This is a difference of cubes since $$27x^3 = (3x)^3$$ and $$125 = 5^3$$.

1. **State the problem:** We need to sketch the graph of the equation $$y+2=-3(x+2)$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y=mx+b$$ w

1. The problem is to understand and use the point-slope form of a linear equation. 2. The point-slope form formula is:

1. **State the problem:** Find the sum of the series $$\sum_{n=1}^\infty \left( \frac{3}{n(n+1)} + \frac{1}{2^n} \right).$$ 2. **Split the series:** The series is the sum of two se

1. The problem asks us to determine which value of $a$ makes the given relation a function. 2. A relation is a function if every input (first element of each ordered pair) correspo

1. The problem asks us to determine which point does not lie on the graph of the line given by the equation $$y = -2x + 7$$. 2. To check if a point $ (x, y) $ lies on the graph, su

1. **State the problem:** Sandra deposited 2500 in a savings account that earns compound interest annually. After 4 years, the amount is 2937.91. We need to find the annual interes

1. **State the problem:** We have an original line given by the equation $y = x + 1$ and its transformed image line $y = x + 2$. We need to find the transforming vector that moves

1. **Stating the problem:** We have an original line given by the equation $y = x + 1$ and its transformed image line $y = x + 2$. We need to find the transforming vector that move

1. **State the problem:** Solve the linear equation $13y + 4 = 5y - 3$ for $y$. 2. **Write down the equation:**

1. **State the problem:** Multiply mixed numbers and fractions, and find the missing numerator in the fractions represented by squares. 2. **Recall the formula:** To multiply mixed

1. **State the problem:** We are given the first three terms in descending powers of $x$ in the expansion of $$\left( 2x^{2} - \frac{1}{4x} \right)^n$$ as $$256x^{16} + ax^{13} + b

1. **State the problem:** We need to find integers $n$, $a$, $b$, and $c$ such that the first three terms in descending powers of $x$ in the expansion of $$\left(2x^{2} - \frac{1}{