🧮 algebra

1. **State the problem:** Calculate the value of $2 \times 5^2$. 2. **Recall the order of operations:** Exponents are evaluated before multiplication.

1. The problem is to multiply the variable $d$ by 4. 2. The multiplication operation means adding $d$ to itself 4 times, or simply scaling $d$ by 4.

1. **State the problem:** Calculate the value of the expression $10 \times (6 - (5 - 1))$. 2. **Understand the order of operations:** According to the rules of arithmetic, operatio

1. **State the problem:** Solve the quadratic equation $$x^2 + 16 = 0$$ for $x$. 2. **Formula and rules:** To solve equations of the form $$x^2 + c = 0$$, isolate $x^2$ and then ta

1. Planteamos el problema: calcular el valor de $$\left(-\sqrt[3]{-8} + \sqrt[5]{32}\right) \left(\sqrt[3]{64} - \sqrt{100}\right)$$. 2. Recordemos las propiedades de las raíces:

1. **State the problem:** Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of $ (2 - 5x)^8 $ and simplify each term.

1. **State the problem:** Rearrange each linear equation into the form $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept. 2. **Formula and rules:** The slope-intercept

1. **State the problem:** Jack starts with 450 in his savings account and withdraws 25 each week. He wants to have at least 100 left at the end of the summer. We need to find how m

1. Planteamos el problema: hallar todos los valores $c$ en el intervalo $[0,2]$ tales que $f(c)=0$. 2. Para resolver $f(c)=0$, necesitamos conocer la expresión explícita de $f(x)$,

1. **State the problem:** Jack starts with 450 in his savings account and wants to have at least 100 left after withdrawing 225 each week. 2. **Set up the inequality:** Let $w$ be

1. The problem is to simplify $\sqrt{\sqrt{625}}$. 2. Recall that $\sqrt{a}$ means the square root of $a$, and $\sqrt{\sqrt{a}}$ means the square root of the square root of $a$.

1. **State the problem:** Calculate the fifth root of the product of -32 and -243, i.e., find $$\sqrt[5]{(-32) \times (-243)}$$. 2. **Recall the formula:** The nth root of a produc

1. **State the problem:** Find the roots of the cubic polynomial $$x^3 + 4x^2 - 17x - 60$$ and verify them. 2. **Formula and rules:** To find roots of a cubic polynomial, we can tr

1. **Problem statement:** Given the cubic equation $x^3 - 8x - 1 = 0$, it has a real root between two consecutive integers $n$ and $n+1$. The function values $f(x) = x^3 - 8x - 1$

1. **State the problem:** Solve the equation $$\sqrt{n} + 10 + 2 + \sqrt{n} - 5 = 0$$ for $n$. 2. **Simplify the equation:** Combine like terms.

1. **State the problem:** Solve the equation $$1 - \left(x + \frac{x}{2} + \frac{x}{5}\right) = 20$$ for $x$. 2. **Rewrite the equation:** Combine the terms inside the parentheses:

1. **State the problem:** Simplify the algebraic expression $$\frac{3x^2}{x+4} + \frac{5z}{x+64}$$ and $$\frac{2x-3}{x^2+5x+6} + \frac{4}{x+3}$$ and $$\frac{6}{x+4} + \frac{2x+8}{x

1. **State the problem:** Simplify the function $$f(x) = \frac{1 - \sin^2(x)}{\cos(x)}$$. 2. **Recall the Pythagorean identity:** $$\sin^2(x) + \cos^2(x) = 1$$, which implies $$1 -

1. **State the problem:** We need to find the rule for the table where $X$ is the input and $Y$ is the output: $$\begin{array}{c|c}

1. **State the problem:** Graph the two linear equations on the same coordinate plane: a) $2x + y = 2$

1. **State the problem:** We are given the equation $y = 2$ and asked to analyze its graph and points related to it. 2. **Rewrite in standard form:** The equation $y = 2$ can be wr