🧮 algebra

1. **State the problem:** Simplify the expression $$7x^3 + \frac{4}{x^5} - \frac{3}{\sqrt[3]{5x}} + \frac{7x^2}{3} - \sqrt[3]{5}.$$ 2. **Recall important rules:**

1. **State the problem:** A grocery store had 2,418 boxes of cereal on Monday. By Friday, customers had bought 1,146 boxes. The remaining boxes were organized on 24 shelves evenly.

1. **State the problem:** We are given a line with equation $y = ax + b$. We need to find the values of $a$ (slope) and $b$ (y-intercept).

1. **Problem:** Factor the polynomial $x^2 + 11x + 28$. 2. **Formula:** To factor a quadratic $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$.

1. Stating the problem: Solve the equation $$x^4 - 30x^2 + 125 = 0$$ for $x$. 2. Recognize this is a quartic equation but can be treated as a quadratic in terms of $x^2$.

1. Stát an fhadhb: Tá líne ar dheis agus ba mhaith linn a fháil amach cén fáth gur fána dhiúltach atá inti. 2. Foirmle fána líne: Má tá dhá phointe ar líne, $ (x_1, y_1) $ agus $ (

1. **State the problem:** Find the coordinates of points A and B where the line $2x + 3y - 6 = 0$ intersects the x-axis and y-axis respectively, and then find the area of triangle

1. The problem is to solve a math problem, but since no specific problem was given, let's solve a simple algebraic equation as an example: Solve for $x$ in the equation $2x + 3 = 7

1. **State the problem:** Solve the proportion $\frac{2}{r} = \frac{12}{18}$. 2. **Formula and rule:** To solve proportions of the form $\frac{a}{b} = \frac{c}{d}$, use cross multi

1. **State the problem:** Solve the equation $$\frac{3}{4} + \frac{x}{3} = 5 - \frac{7}{12}$$ for $x$. 2. **Rewrite the equation:** Combine the constants on the right side:

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **State the problem:** Write the expression $3(2 - i) + i(5 + 2i)$ in the form $x + yi$, where $x, y \in \mathbb{R}$. 2. **Apply distributive property:**

1. **State the problem:** We have two functions:

1. **Stating the problem:** We need to find which pairs of ratios are equivalent in each question. 2. **Formula and rule:** Two ratios $a:b$ and $c:d$ are equivalent if their cross

1. **State the problem:** We want to find an equation that models the height $H$ (in cm) of a child as a function of age $A$ (in years) using the given data points: $(2, 84.5)$, $(

1. **Enunciare il problema:** Risolviamo l'equazione esponenziale $$2^x + 2^{x+1} = 2^{x-1} + 7$$. 2. **Formula e regole importanti:** Ricordiamo che per le potenze con la stessa b

1. Énonçons le problème : Calculer $\frac{3}{4}$ divisé par $\frac{5}{8}$.\n\n2. Rappelons la formule pour diviser deux fractions : \n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \

1. **Problem:** Write down the centre and radius length of the circle $$x^2 + y^2 - 6x - 2y - 15 = 0$$. If the line $$3x + 4y + c = 0$$ is a tangent to this circle, find the two va

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations to both sides of the equat

1. **State the problem:** We analyze the function's domain, range, intercepts, and asymptotes based on the graph description. 2. **Domain:** The function has a vertical asymptote n

1. **Problem Statement:** Given a graph with two decreasing diagonal lines separated by a vertical dashed red line at $x=1$, answer questions about domain, range, intercepts, and a