🧮 algebra

1. **State the problem:** Solve the equation $$\frac{x - 5}{4} = -1$$ for $x$. 2. **Use the formula:** To solve for $x$, multiply both sides of the equation by 4 to eliminate the d

1. **State the problem:** Solve the equation $4x - 5 = -10$ for $x$. 2. **Add 5 to both sides:**

1. **Problem statement:** We have a large rectangle ABCD composed of two smaller rectangles joined horizontally. The length AB (and CD) is $x$ cm. The width BC (and AD) is divided

1. The problem asks to write an equation that models the relationship between the two columns of numbers in each table. 2. We will use the linear equation form $$y = mx + b$$ where

1. **Problem:** Use transformation to sketch the graph of $$y = 3\sqrt{-(x + 5)} - 10$$ and state the domain and range. 2. **Base function:** The base function is $$y = \sqrt{x}$$,

1. **Planteamiento del problema:** Factorizar el polinomio $$P(x,y) = x^2 - 2x - y^4 + 1$$. 2. **Reorganización del polinomio:** Agrupamos términos para facilitar la factorización:

1. **State the problem:** We want to find how many people would have died from AIDS in 2003 if the number of deaths grew exponentially from 1600 in 1983 with a growth factor of 2.2

1. El problema nos da la expresión $P(x,y) \equiv x^2 - 2x - y^4 + 1$ y nos pide identificar cuáles afirmaciones sobre esta expresión son falsas. 2. Primero, analicemos la expresió

1. **State the problem:** Solve the equation $46 - 16 - 4 - x = 8 + 13x$ for $x$. 2. **Simplify the left side:** Combine the constants on the left side.

1. Evaluate the expression \(\left(\frac{3}{5}\right)^{-4}\). 2. Recall the rule for negative exponents: \(a^{-n} = \frac{1}{a^n}\).

1. **State the problem:** Factor the polynomial $$g(x) = 3x^2 - 5x^4 + 2x - 7$$. 2. **Rewrite the polynomial in standard form:** Arrange terms in descending powers of $$x$$:

1. **State the problem:** Complete the square for the expression $r^2 - 6r + 9$ and rewrite it as a perfect square. 2. **Recall the formula:** To complete the square for an express

1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the rule (function) that relates $x$ to $y$. 2. **Given values:**

1. Stating the problem: We need to verify if the factorizations given are correct. 2. For part B, the original expression is $$27n + 36 - 18n^3$$ and the proposed factorization is

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{\frac{(x+2)!}{x!}} = \sqrt{3! \times 7}.$$\n\n2. **Recall factorial properties:** The factorial function $n!$ is the

1. **State the problem:** We need to find the rule of the exponential function passing through the points $(0,1)$ and $(1,4)$. 2. **Recall the general form of an exponential functi

1. **State the problem:** Solve the equation $x - 3 = 2$ for $x$. 2. **Formula and rules:** To isolate $x$, add 3 to both sides of the equation. This uses the addition property of

1. The problem asks to describe the end behavior of the function $$f(x) = -3x^5 + 2x^2 - 1x - 2$$. 2. For polynomial end behavior, the term with the highest degree dominates as $$x

1. **State the problem:** We need to find the average rate of change in the number of living wage jobs from 1997 to 1999. 2. **Formula for average rate of change:**

1. Planteamiento del problema: Determinar si los subconjuntos dados forman una base para $\mathbb{R}^3$ y expresar el vector $\begin{bmatrix}5 \\ -1 \\ 3\end{bmatrix}$ como combina

1. The problem asks to find the slope of the line passing through the points (1, 0) and (6, 10). 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ i