🧮 algebra

1. **State the problem:** We are given the polynomial expression $$12t^5 - 20t^4 + 8t^2 - 16$$ and want to analyze its structure, possibly factor it, and understand its behavior.

1. **State the problem:** We have an arithmetic sequence with the first three terms: $8p$, $7p - 3$, and $4p + 2$. The sum of the first $n$ terms is $-1914$. We need to find the va

1. **State the problem:** Solve the exponential equation $$\left(\frac{1}{9}\right)^{3x+5} = \left(\frac{1}{243}\right)^{x-6}$$ for $x$. 2. **Rewrite bases as powers of a common ba

1. **State the problem:** Calculate the value of $$\left(\frac{1}{3} + \frac{1}{2}\right) \cdot 0.06 + \frac{1}{25} \div 1 \frac{1}{5}$$. 2. **Rewrite mixed numbers and decimals:**

1. The problem asks us to calculate the value of the function $f(x)$ at $x = -\frac{1}{4}$. 2. To solve this, we need the explicit formula for $f(x)$, which is not provided in the

1. **Problem statement:** Evaluate each expression and give the final answers as exact simplified fractions. 2. **Recall important rules:**

1. The problem is to find the equation of the line passing through the points $A(2,3)$ and $B(4,7)$. 2. The formula for the slope $m$ of a line through two points $(x_1,y_1)$ and $

1. The problem involves finding the missing values (either a circle or a square) in rectangles where the product of the top and bottom numbers equals the number inside the rectangl

1. **Problem Statement:** Ronda plays a game guessing an integer between 0 and 100. Her score after one guess $x$ is given by the function $$f(x) = -|x - 57| + 300$$ where 57 is th

1. Planteamos el problema: Resolver un sistema de ecuaciones lineales usando el método de Gauss-Jordan. 2. El método de Gauss-Jordan consiste en transformar la matriz aumentada del

1. **State the problem:** Solve the system of linear equations: $$3n - 4n + 2o = 5$$

1. **Stating the problem:** We are given two inequalities involving $x$ and $y$: $$2x + 3y < 60$$

1. **Problem Statement:** Identify a possible degree of the polynomial based on the given graph and explain the choice.

1. **Problem Statement:** Identify a possible degree of the polynomial based on the graph's behavior and explain the choice.

1. The problem is to find the value of a function or expression at $x=0$. 2. To solve this, we need the function or expression definition. Since it is not provided, let's consider

1. **State the problem:** Simplify the expression $$\frac{t - \frac{1}{t}}{t + t} \div \frac{t^2 - 2t + 1}{t}$$ where $t \neq 0$. 2. **Rewrite the expression:** The expression can

1. Let's start by stating the problem: We want to understand why at $x=0$, the value of $y$ is 20 and not 32. 2. Usually, the value of $y$ at a specific $x$ depends on the function

1. **State the problem:** We need to solve the equation $$0 = x^3 - 2x^2 - 7x + 14$$ which means finding all values of $x$ such that $f(x) = 0$. 2. **Recall the function:** The fun

1. **State the problem:** Convert the fractions (a) $\frac{1}{5}$, (b) $\frac{3}{4}$, and (c) $\frac{7}{2}$ into percentages. 2. **Formula used:** To convert a fraction to a percen

1. **Stating the problem:** Convert the given decimals into percentages. 2. **Formula:** To convert a decimal to a percentage, multiply the decimal by 100 and add the percentage sy

1. **State the problem:** Solve the equation $5x + 6 = 2x + 30$ for $x$. 2. **Write down the equation:**