🧮 algebra

1. **Evaluate each expression with negative exponents:** **a)** $(-10)^{-2} = \frac{1}{(-10)^2} = \frac{1}{100}$

1. **State the problem:** Solve the equation $4\log_5 X = \log_5 625$ for $X$. 2. **Recall the logarithm properties:**

1. **State the problem:** Solve for $x$ in the equation $\log x + \log 12 = \log 8$. 2. **Recall the logarithm property:** $\log a + \log b = \log (a \times b)$. This means we can

1. **State the problem:** Write the expression $$\frac{3}{2x-1} - \frac{2}{x+3}$$ as a single fraction, given that $$x \neq \frac{1}{2}$$ and $$x \neq -3$$. 2. **Formula and rules:

1. **State the problem:** We are given that $x-2$ is a factor of the polynomial $3x^2 + kx - 6$. We need to find the value of $k$. 2. **Use the Factor Theorem:** If $x-2$ is a fact

1. **Problemstellung:** Löse die Gleichung $2x + 3 = 7$. 2. **Formel und Regeln:** Um eine lineare Gleichung zu lösen, isolieren wir die Variable $x$ auf einer Seite der Gleichung.

1. **Stel het probleem vast:** We willen de kosten berekenen voor 5 kwartier parkeren in twee garages: Pleingarage en Stationsgarage. 2. **Gegeven informatie:**

1. **Stel het probleem vast:** We willen weten hoeveel er gemiddeld per leerling is opgehaald in klas 2B over de drie maanden april, mei en juni samen. 2. **Gegeven:**

1. **State the problem:** Find the lowest common multiple (LCM) of the numbers $$A = 2^3 \times 3 \times 5 \times 7^2$$

1. **State the problem:** We need to describe the transformations applied to the graph of $y=f(x)$ to obtain the graphs of the given functions. 2. **Recall transformation rules:**

1. The problem asks to describe the transformations applied to the graph of $y=f(x)$ to obtain each new function. 2. Recall the general transformation rules:

1. The problem asks to identify which statement does NOT describe the explicit arithmetic formula. 2. The explicit arithmetic formula for an arithmetic sequence is given by:

1. The problem states that the function $f(x) = 52x - 33$ is rotated clockwise, and we need to find a possible equation for the transformed function $g(x)$. 2. When a linear functi

1. **Stating the problem:** Adam běžel 10 km za 50 minut stálým tempem.

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. The quadratic formula is:

1. **State the problem:** We are given that $y$ is inversely proportional to the square of $(x+3)$, i.e., $y \propto \frac{1}{(x+3)^2}$. When $x=2$, $y=5$. We need to find the form

1. **Problemstellung:** Gegeben ist die Kostenfunktion eines Kinderstuhls $$K(x) = 0{,}05 \cdot x^2 + 6 \cdot x + 260$$ und der Preis pro Stück ist 20. Gesucht sind die Fixkosten,

1. **Problemstellung:** Gegeben ist die Gewinnfunktion $$G(x) = -x^3 + 16x^2 - 27x - 252$$. Gesucht sind die Nullstellen, die Gewinnzone, der maximale Gewinn und der Wendepunkt der

1. Énoncé du problème : Si $a > -3$, déterminer quelle inégalité parmi les propositions suivantes est vraie : - $-2a < -6$

1. Problemet: Vi skal omskrive formlen for omkredsen af en cirkel, som er givet ved $$O = 2 \cdot \pi \cdot r$$, så vi isolerer radius $r$.\n\n2. Formel: Start med formlen $$O = 2

1. Problemet er å løse ligningen $$\frac{8}{x} + 7 = 11$$ for $x$. 2. Vi starter med å isolere brøkdelen ved å trekke 7 fra begge sider: