🧮 algebra

1. The problem is to add two irrational numbers and simplify the result. 2. First example: $\sqrt{3} + (-\sqrt{3}) = \sqrt{3} - \sqrt{3} = 0$.

1. **State the problem:** We are given the function $$y = \log_2 |x - 2|$$ and asked to analyze it. 2. **Understand the function:** This is a logarithmic function with base 2, wher

1. The problem asks to determine if each table of values represents a function. 2. A relation is a function if every input $x$ has exactly one output $y$.

1. Problem: Determine if the mapping from domain \{0,1,2,5,6\} to range \{5,6,7,8\} with arrows 0→5, 1→7, 2→6, 5→7, 6→8 is a function. Step: Each domain element maps to exactly one

1. **State the problem:** Determine whether each set of ordered pairs, graph points, tables, and mapping diagrams represent functions. ---

1. The first diagram maps each domain element to exactly one range element: 0→5, 1→6, 2→7, 5→8, 6 has no mapping shown. Since no domain element maps to more than one range element,

1. **State the problem:** Determine if each set of ordered pairs, graph points, tables, and mapping diagrams represent functions. ---

1. The problem is to find the remainder when -41 is divided by 9, i.e., compute $-41 \bmod 9$. 2. Recall that the modulo operation finds the remainder after division, and the resul

1. **Stating the problems:** We have four equations involving the variable $P$:

1. **State the problem:** We have two functions: $$f(x) = -\frac{1}{2}x^2 + x + \frac{3}{2}$$

1. The problem asks to express the given numbers in standard form, which means writing them as a product of a number between 1 and 10 and a power of 10. 2. For part (a), 51720:

1. **State the problem:** We are given the graph of a function $f$ and need to estimate:

1. **Problem b:** Simplify the expression $x^3 + xy$. Since this is already simplified, the expression remains $x^3 + xy$.

1. Problem: Solve the system \(\{2x + 11y = -2, x - 3y = -1\}\). 2. From the second equation, express \(x\) in terms of \(y\):

1. نبدأ بقراءة السؤال: لدينا دالة س(ص) = ص + ٩ - ١ ٩ - ١ = (س, ص) مع جدول أرقام مرفق. 2. المطلوب هو إيجاد المجال والمدى والاطراد للدالة س.

1. **State the problem:** Simplify the expression $2x^2y + 6x^2 + 4xy^2 + 12xy$ by factoring. 2. **Group terms:** Group terms with common factors:

1. **State the problem:** You have 72 apples in total, with 38 red apples and the rest green. Among all apples, 46 have worms and cannot be used for cooking. We want to find the ma

1. **State the problem:** Bert has some amount of cents. If he had 3 cents more, he would have twice as much as Georgia. If he had 4 cents less, he would have the same amount as Ge

1. The problem is to find the missing number in the series: __ 85 81 83 79 81 77. 2. Observe the pattern by looking at the differences between consecutive numbers:

1. **حل النهاية:** لدينا النهاية $$\lim_{x \to 3} \frac{3 - x + x^2}{3 - 2x}$$.

1. **Problem:** Find the domain of the piecewise function \( د(س) = \begin{cases} س + ٣ & -٣ \leq س < ٢ \\ ١ - س & س \geq ٢ \end{cases} \). Step 1: The domain includes all \( س \)