🧮 algebra

1. **State the problem:** We need to find the equation of a line with slope $-\frac{1}{2}$ and y-intercept at the point $(0,3)$. 2. **Recall the formula:** The slope-intercept form

1. **State the problem:** Simplify the expression $\sqrt{\frac{25}{4} + 16}$.\n\n2. **Recall the formula:** The square root of a sum is not the sum of the square roots, so we first

1. Let's start by stating the problem: You want to understand how to "move" the numerator and denominator in fractions to isolate variables or expressions. 2. The key formula to re

1. The problem is about understanding how to manipulate fractions and move numerators and denominators across an equal sign in an equation. 2. When you have an equation like $$\fra

1. **State the problem:** Simplify the expression $4x - 14$. 2. **Identify common factors:** Both terms $4x$ and $14$ have a common factor of $2$.

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: