🧮 algebra

1. The problem is to analyze and understand the function $$y = -3|x - 2| + 4$$ and its key features such as vertex and points. 2. The formula involves an absolute value function, w

1. **State the problem:** Simplify the expression $$\frac{4^3 \div 2^2}{2^0 \times (2^3)^3}$$. 2. **Recall the exponent rules:**

1. **State the problem:** We are given two functions $g$ and $f$ with their domains and ranges, and we need to find the domain and range of the composition $f \circ g$. 2. **Recall

1. **State the problem:** Simplify the expression $$\frac{512^3 \times 2^{-9} \div 2^8}{9^2 \div 9 - 5^0}$$. 2. **Rewrite the expression:**

1. Problem A: Complete the perfect square trinomial $x^2 - 30x + \_\_\_$. 2. The formula for a perfect square trinomial is $$a^2 - 2ab + b^2 = (a - b)^2$$.

1. **State the problem:** Solve the equation $-16 + 3n = -8 - 5n$ for $n$. 2. **Write down the equation:**

1. **State the problem:** We are given a recursive sequence defined by $a_1 = 5$ and $a_n = -2a_{n-1}$ for $n \geq 2$. We need to find the value of $a_6$. 2. **Understand the formu

1. **State the problem:** Simplify the expression $$\left( \frac{p^2 t^7}{10} \right)^3$$. 2. **Recall the exponent rule:** When raising a quotient to a power, apply the power to b

1. **State the problem:** Solve the system of linear equations: $$6x - 5y = 8$$

1. **State the problem:** Thirty-five more than 0.8 times a number is the same as 43 less than the product of -7 and the number.

1. **State the problem:** Newton recycled 79,270 tons of material this year, and the amount increases by 8% each year. We want to find how much material will be recycled 10 years f

1. **State the problem:** Isabelle pays 2.50 each time she rides the bus, or she can buy a bus pass for 15 plus 1.00 per ride. We want to find after how many rides the total cost i

1. The problem is to simplify the expression $$\left| \frac{1}{\sqrt{54}} - \frac{1}{\sqrt{50}} \right|$$. 2. First, simplify the square roots in the denominators:

1. **Problem Statement:** Find the inverse of the function $f_1(x) = -3x^2 + 4$. 2. **Recall the formula and rules:** To find the inverse function $f_1^{-1}(x)$, we swap $x$ and $y

1. The problem is to find the piecewise linear function $F(x)$ that passes through the points $(-4,0)$, $(-2,0)$, $(0,3)$, $(2,2)$, and $(4,0)$. 2. Since the function is piecewise

1. **Problem Statement:** Determine the domain and range for both $f(x)$ and its inverse from the given piecewise graph.

1. **State the problem:** We are given the function $$h(x) = \frac{2x^2 - 7x + 3}{x^2 - x - 6}$$ and need to analyze its properties including intercepts, asymptotes, and intervals

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} x^2 + 2 & \text{if } x < 1 \\ x - 5 & \text{if } x \geq 1 \end{cases}$$

1. **State the problem:** Simplify the expression $$(3x^2y^5)(6x^3y^6)$$. 2. **Recall the rules:** When multiplying terms with the same base, add the exponents: $$a^m \times a^n =

1. **State the problem:** Find the key features of the function $$g(x) = \frac{x^2 + x - 6}{2x^2 + 2x - 4}$$ including intercepts, asymptotes, holes, and intervals where the functi

1. The problem is to simplify an expression or equation (please provide the specific expression if needed). 2. To simplify, we use algebraic rules such as combining like terms, fac