🧮 algebra

1. **مشكلة:** أكمل التعريفات والعبارات المتعلقة بالدوال والمصفوفات والاحتمالات. 2. **الدالة الخطية تعرف بما يلي:**

1. **Problem:** Given matrices \(P = \begin{pmatrix}3 & -4 \\ 5 & 1\end{pmatrix}\) and \(Q = \begin{pmatrix}2 \\ 8\end{pmatrix}\), find \(P^{-1}\). 2. **Formula for inverse of a 2x

1. **State the problem:** We need to determine which number line correctly displays the points $\{-1.70, \frac{1}{2}, -1.25, -\frac{3}{5}\}$ in order from left to right. 2. **Conve

1. **Problem statement:** A batsman has an average of 37 runs after 17 innings. We want to find how many runs he should score in the next innings so that his average increases by 6

1. **Problem statement:** A batsman has an average of 37 runs after 17 innings. We want to find how many runs he should score in the next innings so that his average increases by 6

1. The problem asks to determine the truth value of several algebraic and geometric statements. 2. Statement 1: For any integers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

1. **State the problem:** We are given the polynomial $$34z^{14} + bz^7 + 70$$ where $b$ is a positive integer. We want to find the greatest possible value of $b$ such that the pol

1. **State the problem:** We have line $h$ with slope $\frac{3}{5}$ and x-intercept at $(17,0)$. Line $k$ is line $h$ translated down 4 units. We need to find the y-coordinate of t

1. **State the problem:** Simplify the expression $$\left(\frac{1}{3}\right)^{-3} - \left(\frac{1}{3}\right)^{-4}$$. 2. **Recall the rule for negative exponents:** For any nonzero

1. Problem: Simplify the expression $$\frac{\frac{1}{3}x - 3}{\frac{1}{3}x^{-4}}$$. 2. Formula and rules: To divide by a quantity multiply by its reciprocal, so $$\frac{A}{B}=A\cdo

1. Problem statement. Problem: Solve the inequality $$ (2 - 5x)^2 > 4 (x - 3)^2 $$.

1. **Problem:** Find the point of intersection of the lines \(y = 2x + 1\) and \(y = -2x - 2\). 2. **Formula and rule:** At the point of intersection, the \(y\)-values of both line

1. The first problem is to solve the equation $$7r + 2 \times 7r + 3 = -(7)(-2r)$$ for $r$. 2. First, simplify the left side by distributing and combining like terms.

1. **State the problem:** Simplify the expression $-5 - (-5) +$. 2. **Understand the expression:** The expression contains subtraction and addition with negative numbers.

1. **State the problem:** Simplify the expression $-2 + 8(-3) - (-12)$. 2. **Apply the order of operations:** First, multiply $8$ by $-3$.

1. **Problem:** Solve the equation using logarithmic laws: $$\log_4 x + \log_4 (x - 6) = 2$$ 2. **Formula and rules:** Recall the logarithmic product rule: $$\log_b A + \log_b B =

1. The user requests more math questions without answers, taken from the "Smart Math" book for the brevet level. 2. Since the user asks for questions only, no solutions or answers

1. نبدأ بكتابة المسألة: قسم ٣٦٠ بنسبة 1_2 3 : 1_2 4. 2. نفهم أن النسبة 1_2 3 : 1_2 4 تعني 1.23 : 1.24.

1. **Stating the problem:** We have an equilateral triangle with side length $4a + 2$ millimeters and a square with side length $2a + 7$ millimeters. We want to compare their perim

1. **State the problem:** Joseph deposited an unknown amount of money on Monday, then deposited 700 on Tuesday, withdrew 300 and 200 on Wednesday and Thursday respectively, and fin

1. The problem is to solve an equation step by step and learn the process. 2. Since no specific equation is given, let's consider a simple example: Solve for $x$ in the equation $2