🧮 algebra

1. **State the problem:** Solve the equation $x + 0.5y = 6$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to move $x$ to the other side and then divide

1. **State the problem:** Solve the equation $$2|4 - x| + 3|4 - x| = 25$$ for the positive value of $x$. 2. **Combine like terms:** Since both terms involve $|4 - x|$, add the coef

1. **Énoncé du problème :** Émile reçoit 0,10 par bouteille retournée et veut gagner 25. Combien de bouteilles doit-il retourner ?

1. **State the problem:** We have a function $h(x) = a^x + b$ where $a$ and $b$ are positive constants. The graph passes through points $(0, 10)$ and $\left(-2, \frac{325}{36}\righ

1. **State the problem:** Solve the system of linear equations by graphing: $$2x + 5y = 1$$

1. The problem is to find the sum of the series $1 + 2 + 3 + 4 + 5 + \ldots + 1000$. 2. This is an arithmetic series where the first term $a_1 = 1$, the last term $a_n = 1000$, and

1. The problem asks: For which values of $n$ does the parabola $y = nx^2 + 4x - 2$ intersect the $x$-axis? 2. To find where the parabola intersects the $x$-axis, we set $y=0$ and s

1. Let's start by stating the problem: You want to know if there is an easy method to simplify algebraic expressions. 2. The general approach to simplification involves combining l

1. Muammo: $y = nx^2 + 4x - 2$ parabola $OX$ o'qiga qachon tutashadi? 2. Parabola $OX$ o'qiga tutashishi uchun $y=0$ bo'lganda ildizlar mavjud bo'lishi kerak.

1. The problem is to simplify the fraction $\frac{700}{8}$. 2. To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator.

1. **State the problem:** Solve the quadratic equation derived from the expression $(2 - y)^2 = -3y(2 - y)$. 2. **Rewrite the equation:** Expand both sides:

1. Let's start by understanding the problem: you want a detailed explanation of the steps leading up to step six in a solution process. 2. Since the original problem or context isn

1. Let's start by understanding the three topics: fractions, percentages, and standard form. 2. Fractions represent parts of a whole and are written as $\frac{a}{b}$ where $a$ is t

1. **State the problem:** Multiply the fractions $\frac{2}{7}$ and $\frac{14}{16}$. 2. **Formula:** To multiply fractions, multiply the numerators together and the denominators tog

1. Problema: Calculați rezultatul expresiei $$24 : (-9 + 5 \cdot 3)$$. 2. Formula și reguli: Ordinea operațiilor este importantă: mai întâi înmulțirea, apoi adunarea/scăderea, și î

1. **State the problem:** Fully factorise the expression $15p^2 + 24p$. 2. **Identify the greatest common factor (GCF):** The coefficients 15 and 24 have a GCF of 3, and both terms

1. **State the problem:** Fully factorise the expression $3k^2 + 9k$. 2. **Identify common factors:** Both terms have a common factor of 3 and $k$.

1. **Problem statement:** Show that the percentage error in approximating the sum to infinity of a geometric series by the sum of the first $n$ terms is given by

1. **State the problem:** Fully factorize the expression $x^2 + 12x$. 2. **Identify the common factor:** Both terms $x^2$ and $12x$ have a common factor of $x$.

1. **State the problem:** We are given a line passing through points approximately $(-9,5)$ and $(9,-5)$ and asked to find the slope of the line in simplest form. 2. **Formula for

1. **State the problem:** We need to find the slope of the line passing through the points $(-10,6)$ and $(0,-4)$ and express it in simplest form. 2. **Recall the slope formula:**