🧮 algebra

1. **State the problem:** Factor the expression $ (2x-1)(4x^2-2x+1) $ completely. 2. **Recall the distributive property:** To factor or expand a product of two expressions, multipl

1. **State the problem:** Factor the polynomial expression $$3x^4 - 24x$$. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $$3x$$.

1. **State the problem:** We need to order the fractions $\frac{1}{2}$, $\frac{7}{10}$, and $\frac{5}{8}$ from least to greatest. 2. **Formula and rules:** To compare fractions, co

1. **State the problem:** We need to put the fractions $\frac{1}{10}$, $\frac{2}{3}$, and $\frac{5}{11}$ in order from least to greatest. 2. **Formula and rules:** To compare fract

1. **State the problem:** We need to put the fractions $\frac{1}{2}$, $\frac{7}{10}$, and $\frac{2}{3}$ in order from least to greatest. 2. **Formula and rules:** To compare fracti

1. **State the problem:** We need to order the fractions $\frac{1}{2}$, $\frac{5}{11}$, and $\frac{2}{5}$ from least to greatest. 2. **Formula and rules:** To compare fractions, we

1. **State the problem:** We need to put the fractions $\frac{1}{2}$, $\frac{4}{5}$, and $\frac{3}{4}$ in order from least to greatest. 2. **Formula and rules:** To compare fractio

1. **State the problem:** We need to order the fractions $\frac{2}{3}$, $\frac{1}{2}$, and $\frac{4}{7}$ from least to greatest. 2. **Formula and rules:** To compare fractions, we

1. **State the problem:** We need to order the fractions $\frac{3}{5}$, $\frac{3}{7}$, $\frac{3}{4}$, and $\frac{3}{8}$ from least to greatest. 2. **Formula and rule:** To compare

1. **State the problem:** We are given the quadratic functions $y=5x^2$ and $y=\frac{1}{4}x^2$ and need to fill in tables of values by squaring $x$, multiplying by the coefficient

1. **Énoncé du problème :** Une entreprise fabrique des poutres métalliques vendues 2,3 milliers d'euros la tonne. Le coût de production en milliers d'euros est donné par $$C(x) =

1. The problem is to evaluate the expression $8 \times e^8$ where $e$ is the base of the natural logarithm, approximately equal to 2.71828. 2. The formula used here is simple multi

1. **Énoncé du problème :** Une entreprise vend des poutres métalliques à 2,3 milliers d'euros la tonne. Le coût de production en milliers d'euros est donné par la fonction $$C(x)

1. The problem is to solve the inequality $y > 3$. 2. This inequality means we are looking for all values of $y$ that are strictly greater than 3.

1. **State the problem:** We need to graph the inequality $$y \leq \frac{2}{3}x - 5$$. 2. **Formula and rules:** The inequality is in slope-intercept form $$y = mx + b$$ where $$m

1. **State the problem:** Simplify the expression \(\frac{(x^3)(x + 5)}{x - 9} \cdot \frac{(x - 9)(x + 8)}{3x^3}\). 2. **Write the formula and rules:** When multiplying fractions,

1. The problem asks: What is the percentage of 2 in 17? 2. To find the percentage of a number $a$ in another number $b$, we use the formula:

1. **State the problem:** Solve the exponential equation algebraically. 2. **General approach:** For an equation of the form $$a^{x} = b^{x}$$ or $$a^{f(x)} = b^{g(x)}$$, we use pr

1. **State the problem:** Solve the exponential equation $$5^{x^x} = 5^x + 26$$. 2. **Analyze the equation:** The equation involves an exponential expression with a variable expone

1. Das Problem: Du möchtest wissen, wie man den Wert von $k$ findet. 2. Allgemein hängt die Methode zur Bestimmung von $k$ vom Kontext ab, z.B. ob $k$ eine Konstante in einer Gleic

1. Das Problem besteht darin, den Wert von $k$ zu bestimmen, wobei die offizielle Lösung $k=11$ ist. 2. Um $k$ zu finden, müssen wir die gegebene Gleichung oder den Zusammenhang ke