🧮 algebra

1. **Problem statement:** Given sets $A = B = \{x \mid -2 \leq x \leq 2\}$ and functions: a) $f(x) = |x|$

1. We are given the quadratic equation $3x^2 + 4x + 1 = 0$, and our goal is to find the values of $x$ that satisfy this equation. 2. Identify the coefficients: $a = 3$, $b = 4$, an

1. Start with the expression: $$2x^{-1/2}$$. 2. Recall that $$x^{-1/2} = \frac{1}{x^{1/2}} = \frac{1}{\sqrt{x}}$$, so the expression is $$2 \times \frac{1}{\sqrt{x}} = \frac{2}{\sq

1. To determine the feasible solutions, we first need the exact question or the system of inequalities/equations given. 2. If the question involves inequalities, the feasible regio

1. Given the equation $$a^{n^{n}} + bn^{n} + c = 0$$, we want to express $$n$$ in terms of the Lambert W function. 2. First, isolate the term containing $$n$$: $$a^{n^{n}} = -bn^{n

1. **Problem statement:** Given two sets $A = B = \{x \mid -2 \leq x \leq 2\}$, determine whether each function is injective, surjective, or bijective.

1. **State the problem:** Solve the quadratic equation $$3n^2 + 4n + 1 = 0$$. 2. **Identify coefficients:** Here, $a = 3$, $b = 4$, and $c = 1$.

1. The problem asks to fully simplify the given expressions.\n\n2. For part (a): Simplify $2k \times 3 \times 5n$.\n- Multiply the constants: $2 \times 3 \times 5 = 30$.\n- Multipl

1. State the problem: Solve the equation $$22 - 8x = 2x + 9$$. 2. Move all terms involving $x$ to one side and constants to the other side:

1. **State the problem:** Solve the equation $$4m + 5 = 35 - 2m$$ for the variable $$m$$. 2. **Combine like terms:** Add $$2m$$ to both sides to gather the $$m$$ terms on the left:

1. **State the problem:** Solve the equation $5x - 6 = 3x$ for $x$. 2. **Isolate the variable terms:** Subtract $3x$ from both sides to get all $x$ terms on one side:

1. The problem seems to ask why the value is 800 when the maximum number is 56. 2. Let's clarify: if the maximum number in a set is 56, then 800 is not the maximum of that same set

1. **State the problem:** Solve the equation $$17 - 2x = 4x + 5$$. 2. **Move all terms involving $x$ to one side:** Add $2x$ to both sides to get $$17 = 4x + 5 + 2x$$.

1. **State the problem:** We want to evaluate the expression $\left(\frac{6}{2}\right)^2 + 7 \times 2$. 2. **Simplify the division inside the parentheses:** Calculate $\frac{6}{2}

1. We start by clarifying the problem which is to simplify the expression:\n$$\sqrt{2} + \sqrt{3} + \sqrt{2} + (\sqrt{2} + \sqrt{3}) + \sqrt{2} + (\sqrt{2} + (\sqrt{2} + \sqrt{3}))

1. Stating the problem: Solve the equation $$2 \times 9^x - 17 \times 3^x = 9$$ for $x$. 2. Rewrite bases: Note that $9 = 3^2$, so $$9^x = (3^2)^x = 3^{2x}.$$ Substitute into the e

1. **State the problem:** Solve the equation $18 - 2w = 4w$ for $w$. 2. **Isolate variable terms:** Add $2w$ to both sides to move variable terms to one side:

1. The problem states that a number $g$ is rounded to the nearest integer 80. 2. a) To write down the error interval for $g$, note that when rounding to the nearest integer, $g$ li

1. The prompt asks to simplify the solution but does not specify any expression or equation. 2. To proceed, please provide the mathematical expression, equation, or problem that yo

1. The problem asks for the fraction of tennis club members who are aged 30 to 39 years old. 2. From the graph description, the Tennis club has:

1. The problem is to explain how to find the range of a function. 2. The range of a function is the set of all possible output values (values of $y$) that the function can produce.