🧮 algebra

1. **State the problem:** Solve the cubic equation $$x^3 + 3x^2 - 25x - 75 = 0$$. 2. **Formula and approach:** To solve a cubic equation, we can try to find rational roots using th

1. **State the problem:** Solve the cubic equation $$x^3 + 3x^2 - 25x - 75 = 0$$. 2. **Formula and approach:** To solve a cubic equation, we can try to find rational roots using th

1. **State the problem:** Solve the equation $(4x - 14) \times 4 = 24$ for $x$. 2. **Write the equation:**

1) Soient $a$ et $b$ deux nombres réels tels que $a \in [-2, 5]$ et $-3 < b < -1$. **a)** Encadrement de $2a + 7$, $3b - 14$, $3b - a$ :

1. Simplify and evaluate each expression without a calculator. **a)** Simplify $$\dfrac{9}{5} \times \dfrac{-15}{21} \div \left(\dfrac{-45}{14}\right)$$

1. **State the problem:** Simplify and evaluate $\frac{(6^2)^8}{(6^4)^2}$. 2. **Recall exponent laws:**

1. **Problem:** Evaluate $f(0)$ given the piecewise function: $$f(x) = \begin{cases} -x + 3 & x > 2 \\ 2x & 0 \leq x \leq 2 \\ 2x - 1 & x < 0 \end{cases}$$

1. **State the problem:** Solve the system of equations using the elimination method: $$4x + y = 9$$

1. **Problem Statement:** We have a six-pointed star with a central hexagon labeled 118. Around it are six small triangles with numbers 5, 2, 5, 3, 4, and 6 adjacent to the hexagon

1. **State the problem:** Solve the equation $$2 \arcsin(x^2 - 3x + 1) + \pi = 0$$ and find the sum of all values of $x$ that satisfy it. 2. **Isolate the arcsin term:**

1. The problem asks to find the equation of a line with slope $\frac{3}{5}$ and y-intercept $-4$. 2. The slope-intercept form of a line is given by the formula:

1. **Stating the problem:** We are given a graph showing the plumber's fees as a function of hours worked. The graph is a straight line passing through points (0,30), (3,105), and

1. The problem is to understand and identify negative integers. 2. Negative integers are whole numbers less than zero, represented as $-1, -2, -3, \dots$.

1. **State the problem:** Simplify the expression $(-6)(-3) + (-6)(3)$ and verify the distributive property. 2. **Recall the distributive property:** For any numbers $a$, $b$, and

1. مسئله: در جدول سمت چپ، هر عدد با یک عملیات ریاضی به عدد متناظر در جدول سمت راست تبدیل شده است. باید قانون تبدیل را پیدا کنیم و جدول سمت راست را کامل کنیم. 2. برای یافتن قانون، ب

1. Тодорхойлж байна: y = x^{1/2} ба y = \frac{1}{\sqrt{x}} функцууд адилтгал тэнцүү эсэхийг шалгах. 2. Формул болон дүрэм:

1. Állítsuk fel a problémát: Egy új autó ára 12000 euró, és az éves fenntartási költségek az autó korától függenek az adott táblázat szerint. 2. A cél az, hogy az 5 év alatt a nett

1. **Problem statement:** A roll of crimson ribbon is $5 \frac{2}{5}$ meters long. The length of a roll of crimson silk strip woven from this ribbon is $\frac{2}{3}$ of the length

1. **State the problem:** We need to find the length and width of a rectangular room where the length is 5 yards more than the width, and the area is 150 square yards. 2. **Define

1. **State the problem:** We want to find the partial fraction decomposition of the rational expression $$\frac{9x^2 - x + 14}{(x+1)(x^2+5)}.$$\n\n2. **Formula and setup:** Since t

1. **State the problem:** Simplify the rational expression $$\frac{x^2}{(x-5)^2 (x+1)}$$. 2. **Understand the expression:** The numerator is $$x^2$$ and the denominator is the prod