🧮 algebra

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

1. The problem asks to find the original price of a television that is on sale for 1485 during a Black Friday sale. 2. We assume the sale price is a discounted price from the origi

1. **State the problem:** You asked where the points (0,20), (20,0), and (10,10) come from in the context of the daycare revenue problem.

1. Let's clarify the question: You want to understand how the number $-1$ becomes $+1$ in the context of coordinates $(x,y)$, specifically in step 3 of a problem. 2. In coordinate

1. **Problem Statement:** Find the domain and range of the function $y = \frac{2x+3}{x-1}$. 2. **Domain:** The domain is all real numbers except where the denominator is zero becau

1. **State the problem:** Simplify the expression $5(11 \times 10^3)$ using standard notation. 2. **Recall the multiplication rule:** When multiplying numbers, multiply the coeffic

1. **Stating the problem:** We are given the function $$y = \left(\frac{1}{3}\right)^x$$ and want to understand its behavior and graph.

1. **State the problem:** Walmart charges a delivery fee of 3% of the total grocery bill. We need to find the total price including the delivery fee for groceries worth 140. 2. **F