🧮 algebra

1. Problem 11: Evaluate the square roots. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **Problem Statement:** Determine whether each rational number is a perfect square and evaluate the given square roots. 2. **Recall:** A perfect square is a number that can be ex

1. The problem is to evaluate the expression $1 - 4(1 - 4)$. 2. According to the order of operations (PEMDAS/BODMAS), we first solve the expression inside the parentheses.

1. The problem asks if the expression $1-4(1-4)$ equals 13. 2. First, apply the order of operations: parentheses, then multiplication, then subtraction.

1. **Stating the problem:** Simplify the expression $$74 - \{6 + (-16) - (-16) + 25\}$$ step by step. 2. **Recall important rules:**

1. The problem is to solve the equation $1o = \frac{4x}{3}$ for $x$. 2. First, clarify the equation: it seems "1o" might be a typo for "10". So the equation is $10 = \frac{4x}{3}$.

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 $$S = \frac{12 x^3}{y^2} + \frac{y}{x^2} + 3y$$