🧮 algebra

1. **State the problem:** We want to find the cost of 24 stainless steel golden Christmas baubles if 6 baubles cost 29. 2. **Identify the formula:** This is a direct proportion pro

1. **State the problem:** Simplify the expression $$\frac{-x^4 + 3x^3 + 5x^2 + x + 4}{-x + 3x + 2}$$. 2. **Simplify the denominator:** Combine like terms in the denominator:

1. **State the problem:** Solve the equation $$-3\{4+2(-3x+6)\}=-2(5x-8)$$ for $x$. 2. **Apply the distributive property inside the braces:**

1. The problem is to analyze the line given by the equation $5x + 4y = 8$ and understand its graph. 2. The standard form of a line is $Ax + By = C$. Here, $A=5$, $B=4$, and $C=8$.

1. **State the problem:** We want to express the series $-1 + \frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \cdots + \frac{1}{100}$ in sigma notation. 2. **Identify the pattern:** The

1. **State the problem:** Simplify the expression $$\frac{3a - 1}{18a} + \frac{4a + 2}{9a}$$. 2. **Identify the common denominator:** The denominators are $$18a$$ and $$9a$$. The l

1. **State the problem:** We are given a point $(4, -5)$ and a linear equation $2x - 5y = -10$. We want to check if the point lies on the line represented by the equation. 2. **For

1. **State the problem:** Find the equation of the line passing through the point $(-1, -7)$ and satisfying the equation $3x + 12y = -6$. 2. **Rewrite the given line equation in sl

1. Planteamos el sistema de ecuaciones: $$6X - 10Y = 12$$

1. **State the problem:** Determine if the point $(-2, -2)$ lies on the line given by the equation $$y = -\frac{1}{3}x + 9$$. 2. **Recall the formula:** The equation of the line is

1. **Problem statement:** We have a rectangular lawn with width $3x$ metres and area $15x^2 + 45x$ square metres. We want to find:

1. El problema nos pide evaluar la función $$g(x) = -8x - 1$$ en $$x = 3$$. 2. La fórmula para evaluar una función en un valor dado es sustituir $$x$$ por ese valor y simplificar.

1. Planteamos el sistema de ecuaciones dado: $$\begin{cases} x + 2y = 10 \\ 2x - y = 6 \end{cases}$$

1. The problem is to use the distributive property to simplify the expression $26 \times 3 + 26 \times 7$. 2. The distributive property states that $a \times b + a \times c = a \ti

1. **State the problem:** We are given the function $y=3^{2x}+8x-1$ and asked to analyze it. 2. **Understand the function:** This function combines an exponential term $3^{2x}$ and

1. **State the problem:** We are given the function $y = f(x) = \frac{2}{x - 5}$ and need to find its vertical and horizontal asymptotes. 2. **Vertical asymptote:** Vertical asympt

1. **State the problem:** We have a geometric sequence: 20, 100, 500, 2500, ... We want to find:

1. El problema es simplificar la expresión $$\frac{21}{25} \cdot \frac{100}{3}$$. 2. Para multiplicar fracciones, multiplicamos los numeradores entre sí y los denominadores entre s

1. **Planteamiento del problema:** Resolver el sistema de ecuaciones por el método de reducción: $$\begin{cases} x + 2y = 10 \\ 2x - y = 5 \end{cases}$$

1. **State the problem:** Solve the inequality $3x - 5 + 5 \leq 7 + 5$. 2. **Simplify both sides:** Combine like terms.

1. **State the problem:** Solve the linear equation $2x + 5y = 7$ for one variable in terms of the other. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the