🧮 algebra

1. Planteamos el sistema de ecuaciones dado: $$\begin{cases} x + y = 2 \\ x - y = 6 \end{cases}$$

1. **State the problem:** Solve the equation $x + y = 2$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $x$ from both sides of the equation. This uses

1. **Problema:** Completar la tabla con términos y grado de los polinomios dados. 2. **Fórmulas y reglas:**

1. **State the problem:** We have a lilac paint mixture where 40% is white paint, 20% is blue paint, and the rest is red paint. Given 4 cups of blue paint, find: a. Cups of white p

1. **Problem 1: What percentage of the fundraising goal has been met?** The fundraising goal is $250000$.

1. **State the problem:** Priyaha has 5 pencils, each of length $x$ inches. When lined up end to end, their total length is 34.5 inches. 2. **Understand the situation:** The total

1. **State the problem:** Find the weight of Kiran's backpack given that it weighs 3 1/2 pounds less than Clare's backpack, which weighs 14 3/4 pounds.

1. The problem states: Mail's water bottle has 24 ounces initially. After she drinks $x$ ounces, the amount left is expressed. 2. We want to find expressions that correctly represe

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.