🧮 algebra

1. **Stating the problem:** Förenkla uttrycket $$3y(2y + 3) - y(y + 5)$$.

1. **State the problem:** We need to find the coordinates of another point on the line $h$ which has a slope of 4 and passes through the point $(20,12)$. 2. **Formula used:** The e

1. Problemet är att förenkla uttrycket $$3a(b - 2) - a(b + 3)$$. 2. Använd distributiva lagen: $$x(y + z) = xy + xz$$ för att multiplicera varje term.

1. The problem is to simplify the expression or equation given previously. 2. To simplify, we combine like terms, factor where possible, and reduce fractions.

1. **Problem statement:** We need to find the cost function $K(x)$ given the derivative(s) and initial conditions for each part.

1. **State the problem:** We need to fill in the boxes with digits 1 to 9 (each digit used once) to create logarithmic expressions that produce an integer, an irrational number, an

1. **State the problem:** Solve the equation $$\frac{1}{1 - e^x} = 5$$ for $$x$$. 2. **Rewrite the equation:** Multiply both sides by $$1 - e^x$$ to clear the denominator:

1. **State the problem:** We need to determine if the variables $x$ and $y$ are proportional based on the graph provided. 2. **Recall the definition of proportionality:** Two varia

1. The problem asks to rewrite the exponential equation $$3^{-4} = \frac{1}{81}$$ as a logarithmic equation. 2. Recall the definition of logarithms: If $$a^x = b$$, then $$\log_a(b

1. **State the problem:** Simplify the expression $$\frac{x^6 z^3}{x^2 z^5}$$. 2. **Recall the rule for dividing powers with the same base:** $$\frac{a^m}{a^n} = a^{m-n}$$.

1. **Énoncé du problème** : Résoudre le système d'équations \(\begin{cases}-2x + 3y = -1 \\ -7x + 5y = 16 \end{cases}\) par substitution ou méthode de Gauss et vérifier graphiqueme

1. **Problem Statement:** Complete the table for the graph of $$y=\frac{3x-2}{2}$$ and draw the graph of $$y=\frac{3}{2}x - 1$$.

1. **State the problem:** We want to find how to use the numbers 4, 30, 36, 52, and 57 to get the total 119. 2. **Understand the problem:** We need to check if any combination of t

1. **State the problem:** Solve the inequality $3x - 4 < x + 10$. 2. **Write the inequality:**

1. **Stating the problem:** We are demonstrating Theorem (14) which involves expanding a 3×3 determinant using minors and cofactors. 2. **Formula used:** The determinant of a 3×3 m

1. **Problem statement:** Ein Lift darf maximal 450 kg oder 6 Personen befördern. Wieviel Gewicht wird maximal für eine Person angenommen? 2. **Formel:** Um das maximale Gewicht pr

1. **Problem:** Find the value of $x$ such that $h(x) = 2$ where $h(x) = 8 \cdot 2^x$. 2. **Formula:** We use the equation $h(x) = 8 \cdot 2^x = 2$.

1. **State the problem:** We need to find the maximum value of the quadratic function $A(x)$ modeling the area of a rectangle based on the side length $x$, given data points and a

1. **State the problem:** We are given average monthly high temperatures for certain months and a sinusoidal model predicting temperature as a function of month number $t$. We need

1. The problem involves finding the equation of a line given points and verifying or using linear functions. 2. For a linear function, the general form is $y = mx + b$, where $m$ i

1. The problem defines the set $S = \{3x - 1 \mid x \in \mathbb{N} \wedge 5 \leq x \leq 8\}$. 2. This means $S$ contains values of the expression $3x - 1$ where $x$ is a natural nu