🧮 algebra

1. **State the problem:** We need to evaluate each expression in the 3x3 grid and then order the results from least to greatest. 2. **Evaluate each expression:**

1. **State the problem:** Simplify the expression $$\frac{c^2 d^2 - 2 c d x + x^2}{c d - x}$$. 2. **Recognize the numerator:** The numerator is a perfect square trinomial. It can b

1. **State the problem:** Simplify the expression $$\frac{-1\pm\sqrt{1-4+16}}{2}$$. 2. **Simplify inside the square root:** Calculate the value under the square root (discriminant)

1. The problem is to simplify the expression $\frac{e^x}{2} + \frac{e^{-x}}{2}$.\n\n2. We start by recognizing that the expression is a sum of two terms, each divided by 2. We can

1. **Problem statement:** We have a quadratic function $f(x) = a \cdot x^2 + b \cdot x + c$. We know the vertex (toppunkt) is $T(2,14)$ and the tangent line at point $P(0,6)$ is $y

1. Das Pascalsche Dreieck ist ein dreieckiges Zahlenmuster, bei dem jede Zahl die Summe der beiden Zahlen direkt darüber ist. 2. Die erste Zeile ist 1, die zweite Zeile ist 1 1, di

1. **State the problem:** Solve the equation $$10^{8t} \times 10^{2 - t} = 11$$ for $t$. 2. **Use the property of exponents:** When multiplying powers with the same base, add the e

1. **Problem statement:** Factorize the expressions: (c) $25x^2 - 49$

1. **Problem statement:** We have the system of equations: $$y = 4x + 3$$

1. **State the problem:** We have a compound whose mass decreases over time according to the formula $$M(t) = 18e^{-kt}$$ where $k$ is a constant.

1. **State the problem:** We need to find the two double inequalities that define the shaded rectangular region on the coordinate plane. 2. **Identify the boundaries:** The shaded

1. **Énoncé du problème :** Résoudre le système linéaire suivant selon les paramètres $m$, $\alpha$, et $\beta$ : $$\begin{cases} m x + 9 y = \alpha \\ x + m y = \beta \end{cases}$

1. Problemet är att bestämma konstanterna $a$ och $b$ i ekvationen $$x^2 - ax + b = 0$$ så att lösningarna är $x_1 = 2$ och $x_2 = 7$. Konstanterna $a$ och $b$ är positiva tal. 2.

1. **State the problem:** Order the numbers $4 \frac{2}{5}$, $\frac{35}{8}$, $4.49$, and $4.461$ from least to greatest. 2. **Convert all numbers to decimals for easy comparison:**

1. **State the problem:** We need to order the numbers 6 7/11, 6.18, 53/8, and 6.635 from least to greatest. 2. **Convert all numbers to decimals for easy comparison:**

1. **State the problem:** We want to find the unknown time $t$ (in days) it takes for 18 meters of snow to fall, given a proportion relating time and snow depth. 2. **Set up the pr

1. **State the problem:** We need to find the unknown amount of tuna $A$ (in kilograms) using a proportion with the given values $A$, 36, 8, and 9. 2. **Set up the proportion:** Th

1. **State the problem:** A satellite travels 350 kilometers in 56 seconds. We want to find how far it travels in 8 seconds at the same rate. 2. **Set up the proportion:** Let $d$

1. **Stating the problem:** We need to find the distance a satellite travels in 8 seconds using a proportion from part (a). 2. **Understanding proportions:** A proportion states th

1. **State the problem:** We are given two functions $f(x) = x - 5$ and $g(x) = \frac{1}{x} - 1$. We need to find the composition $fg(x)$, which means $f(g(x))$. 2. **Recall the co

1. El problema es entender por qué la ecuación $x + \sqrt{3} y = 2$ se transforma en la forma pendiente-intersección $y = -\frac{1}{\sqrt{3}} x + \frac{2}{\sqrt{3}}$. 2. Para despe