🧮 algebra

1. **State the problem:** Simplify the expression $4(5n - 2) - 3(4n + 5)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Solve the equation $$\log_{10} \frac{x^2 - 24}{x} = 1$$. 2. **Recall the definition of logarithm:** If $$\log_b A = C$$, then $$A = b^C$$.

1. **State the problem:** We are given the linear function $y = 3x - 2$ and asked to understand its properties and graph. 2. **Formula and rules:** The equation $y = mx + b$ repres

1. **Problem Statement:** Analyze the properties of graph a), which is a straight line with positive slope crossing the y-axis at about $y = -2$ and the x-axis at about $x = 2$. 2.

1. The problem is to simplify the expression $5\sqrt{2} + 5\sqrt{2}$.\n\n2. We use the property of like terms in algebra: terms with the same radical part can be added by adding th

1. **Problema:** Calcolare per la funzione $y=\frac{x^2+6x+5}{3x-1}$ il dominio, il segno, le intersezioni con gli assi e gli asintoti. 2. **Dominio:** Il denominatore non può esse

1. We are asked to solve the equation $$\frac{x - 2}{x + 3} = 0$$ for $x$. 2. Recall that a fraction equals zero if and only if its numerator is zero and the denominator is not zer

1. **Stel het probleem vast:** We hebben het stelsel van vergelijkingen: $$x^2 - y^2 = 0$$

1. **State the problem:** Layla's gas tank capacity is 10 gallons. After driving for 4 hours, 5 gallons remain. We need to write an equation for $G$ (gallons remaining) in terms of

1. Nyatakan masalah: Selesaikan ungkapan pecahan berikut: $$\frac{2xyz}{5a} \div \frac{8xy^2}{20ab}$$

1. Il problema non è stato specificato chiaramente, quindi assumiamo che tu voglia una guida generale su come risolvere un'equazione algebrica. 2. Per risolvere un'equazione algebr

1. **State the problem:** We need to find the value of $a$ in the equation $$\frac{\sqrt{3}}{5} + \frac{2}{\sqrt{3}} = a\sqrt{3}$$ where $a$ is a fraction. 2. **Rewrite the equatio

1. **State the problem:** We have the distance function $$D = -60t + 240$$ where $$D$$ is the distance from City A in miles and $$t$$ is the time in hours after Stella leaves her h

1. **State the problem:** Solve the equation $$\frac{x^2}{25}+\frac{(mx+5m)x^2}{9}=1$$ for $x$ in terms of $m$. 2. **Rewrite the equation:**

1. **State the problem:** We need to find the equation of line K which is parallel to the line $y=\frac{2}{5}x - 10$ and passes through the point $(15, 20)$. 2. **Recall the formul

1. Le problème demande de trouver une équation du second degré pour modéliser une situation où une personne a payé 180 pour un certain nombre de bouteilles, mais pour 200, elle aur

1. The problem is to find an approximate solution to the equation $$x^3 - 3x + 1 = 0$$ using the iterative formula $$x_{n+1} = - \frac{1}{x_n^2 - 3}$$ starting with $$x_1 = 0.5$$.

1. **State the problem:** Solve the quadratic equation $x^2 - 7x + 11 = 0$ and then find the integer values of $x$ that satisfy the inequality $x^2 - 7x + 11 < 0$. 2. **Recall the

1. **State the problem:** Solve the simultaneous equations for real numbers $p, q \neq 0$: $$4p + q = 10$$

1. **State the problem:** We need to write an equation for the total cost $C$ of using a computer for $t$ minutes at an internet cafe. 2. **Given information:**

1. **State the problem:** Simplify the expression $$\frac{5y^2 - 35y}{49 - y^2}$$ and find the restrictions on the variable $y$. 2. **Factor numerator and denominator:**