🧮 algebra

1. The problem is to solve for $r$ in the equation $$\frac{3}{5} r = 2.$$\n\n2. To isolate $r$, divide both sides of the equation by $\frac{3}{5}$. The formula used is $$r = \frac{

1. **State the problem:** We have a curve defined by the equation $$y = (2k - 3)x^2 - kx - (k - 2)$$ where $k$ is a constant. We are told the line $$y = 3x - 4$$ is tangent to this

1. El problema nos da un modelo exponencial para la propagación del virus COVID-19 en Argentina durante marzo, con la función $$f(t) = (1.24)^t$$ donde $t$ es el número de días des

1. **Δίνεται το πρόβλημα:** Έχουμε τις εξισώσεις $x + y = 19$ και $x^3 + y^3 = 6346$.

1. **State the problem:** Solve the equation $$(1 - x)(x + 90) - (2x + 1)(x + 90)(x - 2x) = 50.$$\n\n2. **Understand the terms:** We have two products subtracted, and the right sid

1. **State the problem:** We have a sequence defined by $u_1 = 6$ and the recursive formula $u_{n+1} = k u_n + 3$, where $k$ is a positive constant. 2. **Find an expression for $u_

1. **State the problem:** Solve the inequality $$9 + x < 8$$ for $$x$$. 2. **Write the inequality:** $$9 + x < 8$$

1. **State the problem:** We are given the first three terms of the binomial expansion of $ (1 + kx)^{16} $ as $1$, $-4x$, and $px^2$, where $k$ and $p$ are constants.

1. Problem: Znajdź wartość $m$ dla prostej $y = -2x + (3m + 3)$, która przecina oś Oy w punkcie $(0, 2)$. 2. Wzór na punkt przecięcia z osią Oy to $y$ dla $x=0$, czyli $y = 3m + 3$

1. **Problem (i):** A geometric sequence has first term $4$ and common ratio $6$. Find the minimum $n$ such that the $n^{th}$ term is greater than $10^{100}$. 2. The $n^{th}$ term

1. The problem asks to write an expression for the quotient of 24 and 4 without solving it. 2. The quotient means division, so we use the division symbol or fraction form.

1. The problem asks to write an expression for the product of 7 and 15 without solving it. 2. The product of two numbers means multiplying them together.

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: $$6X - 10Y = 12$$