🧮 algebra

1. **Stel het probleem vast:** We moeten het domein en de nulwaarde van de functie $$f(x) = \frac{2x^2 - 6x + 4}{-x^2 - 3x + 10}$$ bepalen. 2. **Domein bepalen:** Het domein van ee

1. We are asked to determine the domain of the function $$f(x) = \frac{2x^2 - 6x + 4}{-x^2 - 3x + 10}$$. 2. The domain of a rational function is all real numbers except where the d

1. **State the problem:** Evaluate the expression for $x=5$ and $x=10$. 2. **Identify the expression:** Since the expression is not given, let's assume a general example: $y = 2x +

1. **Problem (a):** Given that $\frac{5}{2}$ and $\frac{3}{5}$ are solutions of the quadratic equation $ax^2 + bx + c = 0$ with $a,b,c \in \mathbb{Z}$, find $a$, $b$, and $c$. 2. S

1. **State the problem:** Solve the simultaneous equations for real numbers $x, y$: $$x^2 + 2xy - 8 = 0$$

1. **State the problem:** Find the horizontal asymptote, vertical asymptote, x-intercept, y-intercept, and hole of the function $$f(x) = \frac{3x - 7}{4x + 14}$$. 2. **Horizontal a

1. The problem asks us to determine if the relation shown in the graph is a function. 2. A function is defined as a relation where each input (x-value) has exactly one output (y-va

1. **State the problem:** Find the features of the graph of the function $$f(x) = \frac{4}{2x + 3}$$ including horizontal and vertical asymptotes, intercepts, and holes. 2. **Horiz

1. **State the problem:** We are given two functions: $$f(x) = \frac{x^3 + 2x^2 - 4x - 8}{x^2 - 4} \quad \text{and} \quad g(x) = \frac{x^3 + 6x^2 + 12x + 8}{x^2 + 4x + 4}$$

1. **State the problem:** Solve for $x$ in the equation $$3|2x + 1| - 3 = 9.$$\n\n2. **Isolate the absolute value expression:** Add 3 to both sides:\n$$3|2x + 1| - 3 + 3 = 9 + 3$$\

1. **State the problem:** We need to determine which of the given compound inequalities has no solution. 2. **Recall:** A compound inequality joined by "and" means the solution mus

1. **State the problem:** Solve the equation $$\frac{x + 1}{2} = 2 - \frac{x + 2}{7}$$. 2. **Write down the equation:** $$\frac{x + 1}{2} = 2 - \frac{x + 2}{7}$$.

1. **State the problem:** We are given the rational function $$f(x) = \frac{5}{x+2} - 2$$ and a table of $x$ values: 0.5, 3, 48, 998, 4998. We need to find the corresponding $f(x)$

1. Gegeben ist die Funktion $$f(x) = \frac{5}{x + 2} - 2$$. 2. Wir sollen die Asymptoten der Funktion bestimmen. Eine gebrochen-rationale Funktion hat typischerweise eine vertikale

1. **State the problem:** Factor the quadratic expression $$w^2 + 8w + 15$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look for two numb

1. The problem asks to express 400% as a fraction and as a decimal. 2. Recall that percent means "per hundred," so 400% means 400 per 100.

1. **State the problem:** Solve for $k$ in the equation $$\frac{K+k}{k} = 6.$$ 2. **Rewrite the equation:** Multiply both sides by $k$ to eliminate the denominator:

1. **State the problem:** Factor the quadratic expression $g^2 + 12g - 13$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi

1. The problem asks to write 342% as a fraction and as a decimal. 2. Recall that percent means "per hundred," so 342% means 342 per 100.

1. The problem asks to classify each of the five expressions as functions or not functions. 2. Recall that a function assigns exactly one output for each input.

1. **State the problem:** Darius fills 18 gallons of gas for 45.60. We want to find the cost for Ben to fill 21 gallons. 2. **Formula:** Cost is proportional to gallons. Use unit r