🧮 algebra

1. **State the problem:** Simplify the expression $$\sqrt{3 + \sqrt{3}} - \sqrt{|1|} - \sqrt{1}$$. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $$\sqrt{3 + \sqrt{7}} - \sqrt{|1 - \sqrt{7}|}$$. 2. **Recall important rules:**

1. The problem is to simplify $$\left( \frac{x^{-2}}{x^5} \right)^0$$ using only positive exponents. 2. Recall the rule: Any nonzero expression raised to the power of 0 equals 1, i

1. **State the problem:** Simplify the expression $$\frac{m^9}{m^4}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, subtr

1. **Problem Statement:** We need to find an expression equivalent to $$\frac{r^3}{t}$$. 2. **Understanding the Expression:** The expression is a fraction with numerator $$r^3$$ an

1. **Problem Statement:** We are given the set $C = \{x \in \mathbb{R} \mid -3 < x < 3\}$ and asked to understand its meaning and graph.

1. The problem is to simplify the expression $$\frac{m^3}{m^5}$$ using only positive exponents. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-

1. **State the problem:** Simplify the expression $$\left(\frac{x^{-2}}{x^{5}}\right)^{0}$$ using only positive exponents. 2. **Recall the zero exponent rule:** Any nonzero base ra

1. **State the problem:** Simplify the expression $$\frac{m^9}{m^4}$$. 2. **Recall the rule for division of powers with the same base:** When dividing powers with the same base, su

1. **Stating the problem:** Simplify the expression $-[ -[ -[ -4 \div [8(\frac{1}{2} + \frac{1}{3})]] - 1] + 1]$. 2. **Identify the operations and order:** We will simplify inside

1. The problem is to solve a system of equations by substitution. 2. The substitution method involves solving one equation for one variable and then substituting that expression in

1. **State the problem:** We are given the x-intercepts of a parabola at $(-2,0)$ and $(3,0)$ and the vertex at $(0.5,-12.5)$. We need to find the equation of the parabola. 2. **Fo

1. **State the problem:** Find the value of $x$ when $f(x)$ is 4 more than $g(x)$. 2. **Write the functions:**

1. **State the problem:** We want to analyze and understand the function $$y = \frac{1 + x^2}{x}$$. 2. **Rewrite the function:** We can split the fraction to simplify understanding

1. **Problem statement:** Calculate the profit percentage when an article costing 612 is sold at a marked price of 1275 with a 28% discount.

1. **State the problem:** We know that $x$ is inversely proportional to $y$. Given $y=27$ when $x=14$, find $x$ when $y=21$. 2. **Formula and rule:** If $x$ is inversely proportion

1. **Problem Statement:** Find the function and analyze the expression $y = (x + 1)^3 - 1$. 2. **Formula and Rules:** This is a cubic function shifted horizontally and vertically.

1. **Stating the problem:** Find the result of $$\frac{(3^3 p^4)^3}{3 p^2}$$.

1. The problem asks us to identify which number in the set $\{-49, \frac{7}{22}, 3\pi, -2.5, 0.1\dot{2}\}$ is irrational. 2. Recall that an irrational number is a number that canno

1. **Problem Statement:** Given the graph of $y = f(x)$ with vertices at $(-6, -2)$, $(-2, 4)$, and $(2, 2)$, we need to draw the graph of $y = -f(x)$. 2. **Understanding the Trans

1. **State the problem:** Calculate the value of the expression $4640 \times 0.083 + 0.0000020 \times 5585000 \sqrt{0.083}$.\n\n2. **Recall formulas and rules:**\n- Multiplication