🧮 algebra

1. The problem is to simplify the expression $5^7 + 5^9$. 2. Notice that both terms have a common base of 5, so we can factor out the smallest power, which is $5^7$.

1. **State the problem:** We are given that the product of $x$ and $y$ is 23, i.e., $xy=23$. 2. **Interpretation:** To find the value of $x$, we need either a value or an expressio

1. We are given the function $$f(x)=\sqrt{x-5}$$ and need to determine whether it is even, odd, or neither. 2. Recall the definitions:

1. The problem is to simplify and rewrite the expression: $$\left(\frac{-2}{5}\right)^{-2} \cdot \left(\frac{-5}{2}\right)^{-3}$$

1. **State the problem:** We need to find how many hours Salma and Mary each take to read a 120-page book. 2. **Find Salma's reading rate:**

1. Given: $\log_2(x) = 3$ and $\log_2(y) = 5$. 2. We need to find $\log_2\left( \frac{4x^2}{y} \right)$.

1. **Exercice 2 - Problème 1** Déterminer la fonction polynôme du second degré $f$ telle que : $f(0)=4$, $f'(0)=3$ et $f(1)=3$.

1. The problem is to determine whether the function $f(x) = 5x^3$ is even, odd, or neither. 2. Recall definitions:

1. The problem is to simplify the expression $$\frac{2x^3}{3x^2} \times \frac{4x^3}{6x}$$ and find the simplified result. 2. Start by rewriting the expression:

1. Énoncé du problème : Développer et simplifier la fonction $f(x) = (2x^2 + 1)(3x - 1)^2$, puis étudier les autres fonctions données. 2. Développons $(3x - 1)^2$ :

1. **Stating the problem:** Marwan's car needs 5 liters of gasoline to cover 50 km. We need to find how much gasoline is required for a 200 km trip.

1. First, state the problem: Ahmed’s mother uses 2 oranges and 4 spoons of sugar to make 1 cup of orange juice. 2. We want to find how many oranges and spoons of sugar are needed t

1. First, identify the function described by the graph in the image. The graph appears to be a parabola, so it likely represents a quadratic function. 2. Use the standard form of a

1. **Statement of the problem:** Given:

1. لنقم بفهم المسألة: نريد حساب حاصل ضرب $2\sqrt{8}$ في $\sqrt{2}$. 2. نبدأ بتبسيط التعبيرات الجذرية: \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}.

1. The problem is to simplify the expression $2\sqrt{x} \times 8 \times \sqrt{x} \times 2$. 2. First, rewrite the expression grouping coefficients and square root terms: $2 \times

1. The problem is to find the domain of the function $$f(x) = \frac{x+4}{\sqrt{4x+8}}.$$\n\n2. The domain includes all values of $x$ for which the function is defined. Since there

1. لنبدأ بتحديد المعادلة التي تريد حلها. 2. من فضلك اكتب المعادلة رياضيًا لأتمكن من مساعدتك في حلها بشكل دقيق.

1. نُعطى الدالة $y=f(x)$ بحيث \(y^2 = a x + 2\). 2. المطلوب إيجاد قيمة الثابت $a$ بحيث تكون $y = 3$ و $y < 0$ لجميع قيم $x$ الممكنة.

1. The problem is to analyze the equation $$\frac{x^2 + x - 6}{x - 2} = x + 3$$ and identify what is wrong with it. 2. First, factor the numerator:

1. Let's state the problem: Solve the quadratic equation $$2x^2 - 5x + 2 = 0$$. 2. Identify coefficients: Here, $$a=2$$, $$b=-5$$, and $$c=2$$.