🧮 algebra

1. **Problem:** Simplify $(3x^4y^2) \cdot (5x^3y^5)$ completely. **Step 1:** Use the product rule for exponents: $a^m \cdot a^n = a^{m+n}$.

1. **Problem:** Factor completely $x^2 + 9x + 20$. Formula: For $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$.

1. **State the problem:** We are given a graph of a function with points and asked to find:

1. **State the problem:** Sydney has $196$ pepper plants and wants to arrange them in a square formation. We need to find how many plants go in each row. 2. **Formula used:** For a

1. **State the problem:** We need to find the length and width of a rectangle where the width is 1 meter greater than the length and the area is 72 square meters. 2. **Define varia

1. **State the problem:** We are given two functions: $$f(x) = |x|$$

1. **State the problem:** We are given the function $$f(x) = \frac{6x^2 - 1}{x^2}$$ and need to evaluate it at three values: $$x=5$$, $$x=-5$$, and $$x=-x$$.

1. **State the problem:** We are given a graph with a function $y=f(x)$ that starts at $(-2,1)$ and passes through $(0,3)$ and $(2,5)$. The shaded region on the y-axis is above the

1. **State the problem:** Determine if the ordered pair $(-9,9)$ satisfies the equation $$5x - 3y = 10$$. 2. **Substitute the values:** Replace $x$ with $-9$ and $y$ with $9$ in th

1. **State the problem:** We are given the sentence: "The y-value is two more than three times the x-value." We need to write this as an equation in two variables $x$ and $y$, then

1. **مقدمة للمشكلة:** سنتحدث عن معاملات ذات الحدين (Binomial coefficients) في درس نظرية ذات الحدين، وكيفية حسابها وفهمها.

1. المشكلة: لدينا مثال رقم $22$ ونريد إيجاد الماج والقياس والسالب على الترتيب من التماثلية.

1. **State the problem:** We need to order the following expressions from least to greatest: $\frac{5\pi}{6}$, $\log_{4}(12)$, $\sqrt{19}$, $4!$, $e^{3}$, $\frac{7}{13}$, $\infty$,

1. **State the problem:** Solve the quadratic equation $$2n^2 - 15n + 7 = 0$$. 2. **Formula used:** The quadratic formula is $$n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $

1. **State the problem:** We are given the marginal cost function $$C(x) = x^2 - 140x + 8000$$ where $x$ is in thousands of mp3 players. We want to find: A. The value of $x$ that m

1. **State the problem:** We want to find the unit price $p$ that maximizes the revenue function $$R(p) = -9p^2 + 18000p$$ and then find the maximum revenue. 2. **Formula and rules

1. **State the problem:** Simplify the expression $$4x^2 - 2y + 7x^2 + 3y - 3x^2 + 5y$$ and verify it equals $$(7 - 3)x^2 + (3 - 5)y$$. 2. **Combine like terms on the left side:**

1. **State the problem:** We need to find all real zeros of the function $f$, which means solving the equation $f(x) = 0$ for real values of $x$. 2. **Formula and rules:** To find

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + 2y - z = 4 \\ x + 2y + z = 2 \\ 2x + y + z = -2 \end{cases}$$

1. Planteamos el problema: Tenemos un comedor con un precio original de $8760 y un descuento del 35%. Queremos encontrar el precio final después del descuento. 2. Fórmula para calc

1. **Problema 8: Cantidad de harina necesaria para 1 kg de huevo** Se sabe que por cada kilogramo de harina se necesitan $0.125$ kg de huevo.