🧮 algebra

1. Das Problem lautet: Bestimme die Variable $b$ mit der pq-Formel. 2. Die pq-Formel wird verwendet, um die Lösungen der quadratischen Gleichung $x^2 + px + q = 0$ zu finden.

1. **State the problem:** We have a car purchased for 20700 dollars that depreciates at 13.75% per year. We want to find its value after 12 years.

1. **State the problem:** Simplify the expression $$-0.4^2 \times (-1.3) / 0.8 - 0.62$$. 2. **Recall order of operations:** Exponents first, then multiplication and division from l

1. **Stel het probleem vast:** We hebben drie winkels: supermarkt (S), apotheek (A) en boekhandel (B).

1. **State the problem:** Simplify the composite functions given by \(m(x) = x^3 - x\), \(n(x) = \frac{5}{x}\), \(p(x) = 3x - 6\), and \(q(x) = \frac{x^2}{x - 5}\). Find \((p \circ

1. **State the problem:** Evaluate the function $L(x) = -x^3 + 2x^2 - x - 1$ at $x = -1$ and $x = 3$. 2. **Recall the function:**

1. Problem: Evaluate and find the domain of the composite functions given: a. $f(x) = \sqrt{x - 2}$ and $g(x) = 5x$, find $(f \circ g)(x)$ and its domain.

1. **State the problem:** Simplify the expression $x^3 \cdot x^4$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents.

1. **State the problem:** Simplify the expression $2 (2\sqrt{4})^{-2}$. 2. **Recall the rules:**

1. **State the problem:** We need to evaluate the composite functions \((f \circ g)(4)\) and \((g \circ f)(3)\) using the graphs of \(f(x)\) and \(g(x)\). 2. **Recall the definitio

1. **State the problem:** Solve the equation $$6x - 7 = 14 - x$$. 2. **Write down the formula and rules:** To solve linear equations, we aim to isolate the variable $x$ on one side

1. Let's start by understanding what it means for a number or expression to be "undefined" in mathematics. 2. A value is "undefined" when it does not have a meaningful or valid res

1. **State the problem:** We have two rectangles P and Q.

1. **Evaluate (f \circ g)(6)** using the table. - First find $g(6)$ from the table: $g(6) = 4$.

1. The problem is to simplify the expression $\frac{x}{2}$. 2. The expression $\frac{x}{2}$ means $x$ divided by 2.

1. **State the problem:** Find the center point and radius of the circle represented by the equation $ (x+2)(x-6)+(x+8)(x-2) $. 2. **Expand the terms:**

1. **State the problem:** Solve the equation $x = 12 + \frac{2x}{2}$ for $x$. 2. **Rewrite the equation:** The equation is $x = 12 + \frac{2x}{2}$.

1. **Stating the problem:** We have two curves representing pressure $P$ as a function of flow rate $Q$: - System curve: $P = a Q^2 - b Q + c$

1. **State the problem:** Determine if the function $f(x) = \sqrt{x^2 - 1}$ has any asymptotes. 2. **Recall the definition of asymptotes:**

1. **Problem statement:** We need to fill the five empty circles inside the star with the numbers 1, 2, 3, 4, and 5 so that the sum of the four numbers along any line (which includ

1. **State the problem:** We need to find a quadratic model for a bridge shaped as a concave down arc. The bridge's arc passes through point $(0,3)$, has a width of 240 meters, and