🧮 algebra

1. **State the problem:** Solve the equation $$\left(a+\sqrt{2}\right)^2 + \left(\sqrt{2}a - 1\right)^2 = 6$$ for the variable $a$. 2. **Expand each squared term:**

1. **State the problem:** We want to find the year when the value of Sean's car, initially 20000, depreciates to approximately 5000 given a 19% annual depreciation rate. 2. **Formu

1. The problem asks to convert the logarithmic equation $\log 10 = 1$ into its equivalent exponential form. 2. Recall the definition of logarithm: $\log_b a = c$ means $b^c = a$.

1. **State the problem:** Solve the equation $$2\sqrt{7} + (x-2)(\sqrt{7} + x) = 0$$ for $x$. 2. **Expand the product:** Use the distributive property to expand $(x-2)(\sqrt{7} + x

1. **State the problem:** Evaluate the expression $\left(\log_3 27 + (5^2)^2\right) - \log_3 9$.\n\n2. **Recall logarithm rules and exponentiation:**\n- $\log_b a$ means the logari

1. **State the problem:** We are given that $P(x) = Q(x) \cdot (x - 3)$ and asked which of the statements A, B, C, or D must be true. 2. **Recall the property of multiplication:**

1. **State the problem:** We need to determine the end behavior of the function $f(x) = \ln(x - 3)$. 2. **Recall the domain and properties of logarithmic functions:** The natural l

1. **Problemstellung:** Berechne die Gesamtkosten für einen Fußball mit einem Durchmesser von 22 cm, wenn die Fixkosten pro Ball 5,63 und die zusätzlichen Materialkosten 78,35 pro

1. **Evaluate** $ (8+2)^2 \div 2(3) - (-5) $. Step 1: Calculate inside the parentheses: $8+2=10$.

1. **Problem:** Put the numbers $2.3 \times 10^2$, $\sqrt{400}$, $5^3$, $0.4$, and $1 \times 10^3$ in order from least to greatest. 2. **Step 1:** Calculate each number.

1. **State the problem:** Simplify or analyze the quadratic expression $3x^2 - 4x + 1$. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the sol

1. **Énoncé du problème :** Trouver trois couples solutions pour chaque équation donnée. 2. **Formule et règles :** Une solution $(x,y)$ satisfait l'équation linéaire. Pour trouver

1. Énonçons le problème : Résoudre la question 2, partie c. 2. Supposons que la question 2 porte sur une équation ou un système donné (puisque le détail n'est pas fourni, je vais i

1. **State the problem:** Solve the absolute value equation $$3|x + 7| - 18 = 0$$ for $x$. 2. **Isolate the absolute value expression:**

1. **State the problem:** We have a quadratic function represented by a table of values with $x$ and $y$ values. 2. **Identify key features:**

1. **State the problem:** We analyze the function $f(x) = |x - 4| + 2$ to determine its key features such as intervals of increase/decrease, intercepts, domain, and range. 2. **Rec

1. **State the problem:** Solve the equation $$-3|6x - 4| = 54$$ for $$x$$. 2. **Isolate the absolute value:** Divide both sides by $$-3$$ to isolate $$|6x - 4|$$.

1. The problem states that the function describing the lengths of paddle boards is $$v(x) = |x - 10|$$ where $x$ is the length in feet and $v$ is the variation. 2. The vertex of an

1. **State the problem:** Simplify the expression $$2(a+2) + (2a+1)(a-1)$$. 2. **Use distributive property:**

1. **Stating the problem:** Vi har 6,5 liter muffinsmet och varje muffinsform fylls med 7,2 cl. Vi ska räkna ut hur många muffins vi kan göra.

1. **State the problem:** Simplify the expression $$x \approx y + z + x + y + u + o$$. 2. **Combine like terms:** Group the terms with the same variables together.