🧮 algebra

1. Problema: Avem o progresie aritmetică cu termeni 2, 7, 12, 17, ... și trebuie să găsim rația acestei progresii. 2. Formula pentru rația unei progresii aritmetice este:

1. Problema ne cere să determinăm primii doi termeni ai unei progresii aritmetice în care următorii termeni sunt 10, 13, 16, ... 2. O progresie aritmetică este o succesiune de nume

1. **State the problem:** Solve the equation $$2 = \frac{100}{x}$$ for $x$. 2. **Formula and rules:** To solve for $x$ when it is in the denominator, multiply both sides of the equ

1. The problem involves understanding why the term $(-k+2)$ appears in step 4 of a previous solution. 2. Typically, $(-k+2)$ arises from rearranging or factoring expressions involv

1. Problem: Find the maximum value of the function $f(x) = -6x^2 + 3x - 4$. 2. This is a quadratic function in the form $f(x) = ax^2 + bx + c$ where $a = -6$, $b = 3$, and $c = -4$

1. **State the problem:** Solve for $y$ in terms of $r$ and $t$ in the proportion $$\frac{y - t}{3} = \frac{y - r}{5}.$$\n\n2. **Use cross-multiplication:** Multiply both sides by

1. El problema es resolver la ecuación dada (aunque no se especifica, asumiremos que se refiere a resolver una ecuación algebraica simple). 2. Para resolver una ecuación, usamos la

1. **State the problem:** We need to find the distance the bus travels between Hawkes Meadow and Brunswick Street. 2. **Identify the given information:**

1. **State the problem:** Solve the simultaneous equations for the variables involved. 2. **General approach:** To solve simultaneous equations, we use substitution or elimination

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.