🧮 algebra

1. We are asked to determine the function rule (voorschrift) of a homographic function given certain conditions. 2. A homographic function has the general form:

1. Let's clarify the concept of "rise over run." 2. "Rise over run" is a way to describe the slope of a line in coordinate geometry.

1. **State the problem:** Solve the equation $x(x + 5) - 12 = x^2 + 3x$. 2. **Write the equation:**

1. **State the problem:** Solve the equation $3 + x = 1 + 4x$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the inequality $x > 7 - 4$ and represent the solution on a number line. 2. **Simplify the inequality:**

1. **State the problem:** Solve the inequality $$-6 \leq x - 5 < 1$$. 2. **Understand the inequality:** This is a compound inequality involving $x$. We want to find all values of $

1. **State the problem:** Simplify the expression $$\frac{x^3}{2y^2} \cdot \frac{6y^4}{xy}$$. 2. **Write the expression:** $$\frac{x^3}{2y^2} \times \frac{6y^4}{xy}$$.

1. **State the problem:** Simplify the expression $$\frac{a + 1}{a^{2}-4} + \frac{1 - a^{2}}{(a-1)^{2} + 3}$$. 2. **Recall important formulas and rules:**

1. **State the problem:** Simplify the expression $$\frac{16x^2 + 24x + 9}{3x^2 + 13x - 10} \cdot \frac{6x^2 + 25x - 25}{4x^2 - 13x - 12}$$

1. **Problem:** Solve the equation $$|1 - 2m| = m + 2$$ and verify the solutions. 2. **Formula and rules:** The absolute value equation $$|A| = B$$ implies two cases if $$B \geq 0$

1. Problema: Rasti funkcijos $f(x) = e^{4x+7}$ pirmykštę. 2. Naudojama formulė: Jei $f(x) = e^{g(x)}$, tai pirmykštė yra $$F(x) = \frac{1}{g'(x)} e^{g(x)} + C,$$ kur $g'(x)$ yra $g

1. **State the problem:** Evaluate the sum $$\frac{3}{4} + \frac{5}{6}$$. 2. **Formula and rules:** To add fractions, they must have a common denominator. Find the least common den

1. **Stating the problem:** Raheem takes $\frac{21}{4}$ hours to make a basket and $\frac{11}{2}$ hours to make a mat. He works a maximum of 22.5 hours per week. We need to show th

1. Let's state the problem: Determine when a system of linear equations has one solution, no solution, or infinitely many solutions. 2. Consider a system of two linear equations in

1. **State the problem:** Solve the system of linear equations: $$x+(b-1)y-z=4$$

1. **State the problem:** Prove the identity $$2\cosh(3x)\cosh(x) = \cosh(4x) + \cosh(2x)$$. 2. **Recall the formula for hyperbolic cosine product:**

1. **State the problem:** Solve the inequality $3x + 4 < 7x + 24$. 2. **Write down the inequality:**

1. **State the problem:** Solve the inequality $|2b - 1| \leq 3$. 2. **Recall the definition of absolute value inequality:** For any expression $x$, $|x| \leq a$ means $-a \leq x \

1. **State the problem:** We need to find a possible value of $x$ such that the point $(x, 53)$ satisfies the system of inequalities: $$y > 14$$

1. **State the problem:** Solve the quadratic equation $2x^2 + 3x - 2 = 0$ for $x$. 2. **Formula used:** The quadratic formula is given by

1. **State the problem:** Solve the system of equations using diagonal methods (Cramer's Rule): $$\begin{cases} x + y + z = 0 \\ x - 2y + 2z = 4 \\ x + 2y - z = 2 \end{cases}$$