🧮 algebra

1. **State the problem:** Solve the system of simultaneous linear equations using the substitution method: $$2x + 3y = -12$$

1. Problema: Vom explica ce este o funcție de ordin exponențial. 2. Definiție: O funcție exponențială este o funcție de forma $$f(x) = a^x$$, unde $$a$$ este o constantă pozitivă d

1. The problem states: Solve the equation $\frac{n-6}{4} = 5$ for $n$. 2. The formula used here is to isolate the variable $n$ by undoing the operations step-by-step.

1. The problem is to find the value of $x$ in the proportion $\frac{118}{18} = \frac{83}{x}$. 2. The formula for solving proportions is to cross multiply: $a/b = c/d \implies a \ti

1. The first problem given is to simplify or analyze the expression $a^2 + 53a - 14$. 2. This is a quadratic expression in standard form $ax^2 + bx + c$ where $a=1$, $b=53$, and $c

1. The problem is to understand what "all of polynomials" means in algebra. 2. Polynomials are expressions consisting of variables and coefficients combined using addition, subtrac

1. **State the problem:** Find the equation of a straight line passing through the point $(-2,-1)$ and perpendicular to the line given by $6x - 4y = 8$. 2. **Rewrite the given line

1. The problem is to solve for $y$ in an equation involving $y$ (the exact equation is not provided, so we will explain the general approach). 2. To solve for $y$, isolate $y$ on o

1. **State the problem:** Calculate the value of the expression $$\sqrt[3]{-2} \times (-37) - \{ -2 \times (-3) + 8 \times (-2) - 8 \times 2 \} + 5^2$$. 2. **Recall important rules

1. The problem is to understand the meaning or use of the variable $T=4$. 2. Typically, $T$ can represent a period in physics or mathematics, such as the period of a wave or oscill

1. **State the problem:** Given the value $a=3$, we want to understand or use this value in a mathematical context. 2. **Explanation:** The variable $a$ is assigned the value 3. Th

1. **State the problem:** We are given the equation $c=\frac{3x}{2x-11}$ and need to make $x$ the subject. 2. **Write the equation:**

1. **State the problem:** Emily has a budget of 720 and wants to rent from either Company A or Company B. Company A charges a setup fee of 80 plus 135 per day. Company B charges 13

1. The problem is to find the relation between variables $x$, $y$, and $z$ given the equation $3309x + 6442y = 3z = 13682$. 2. First, note that the equation as written is ambiguous

1. **Problem statement:** We want to find the minimum value of $$S = \frac{12 x^3}{y^2} + \frac{y}{x^2} + 3y$$

1. The problem asks for the possible values of $x$ and $y$, but no specific equation or condition is given. 2. To find possible values of variables, we need an equation or inequali

1. **State the problem:** Simplify the expression $$\frac{\sqrt{24x^3}}{\sqrt{3x^2}} - \sqrt{50x}$$. 2. **Use the property of radicals:** $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{

1. **State the problem:** Solve the linear equation $$3309x + 6442y = 13682$$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two var

Given the user's request to remove numbering and explanations, here is the solution only: Solve the equation $2x + 3 = 7$.

1. **State the problem:** We are given values $a = \sqrt{81}$, $b = -\frac{3}{4}$, and $c = \pi$. We need to determine which set represents the irrational numbers among the options

1. The problem is to express the decimal number 0.5 as a fraction. 2. Recall that decimals can be converted to fractions by considering the place value of the decimal digits. For 0