🧮 algebra

1. **State the problem:** Solve the equation $4y + 2x = 754$ for $y$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving other terms to t

1. **State the problem:** Simplify the expression $$\frac{2}{x+5} + \frac{2}{x^2-25}$$. 2. **Recognize the formula and rules:** The expression involves adding two rational expressi

1. **State the problem:** We need to find a one-to-one correspondence (bijection) function from set $A=[0,1]$ to set $B=[1,2]$. 2. **Recall the definition:** A function $f:A \to B$

1. The first question asks which options about asymptotes are correct. 2. Recall the rules for asymptotes of rational functions $f(x) = \frac{P(x)}{Q(x)}$ where $P$ and $Q$ are pol

1. **State the problem:** Simplify the expression $$\frac{2}{x+5} + \frac{2}{x^2+25}$$. 2. **Identify the denominators:** The denominators are $x+5$ and $x^2+25$.

1. **State the problem:** Greg fills his mug and pours it into jug A three times, and Martin fills his mug and pours it into jug B six times. We need to find how many more millilit

1. **State the problem:** Calculate the value of $$5^{-4} \div \left(3^{3} \div 5^{7}\right)$$. 2. **Recall the rules:**

1. **State the problem:** Calculate the value of the expression $$5^{-4} \div \left(3^{3} \div 5^{7}\right)$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $x^2 + 1 = 0$ for $x$. 2. **Recall the formula:** To solve quadratic equations of the form $ax^2 + bx + c = 0$, we use the quadratic fo

1. مسئله را بیان می‌کنیم: می‌خواهیم ترکیب توابع (gf) \circ (fg)، (gf) \circ (gf) و (fg) \circ (fg) را روی زوج مرتب (m,n) بررسی کنیم که شامل عبارات لگاریتمی و کسرهایی با مخرج‌هایی ب

1. **State the problem:** Solve the equation $x^2 + 1 = 5$ for $x$. 2. **Use the formula:** To solve for $x$, isolate $x^2$ by subtracting 1 from both sides:

1. **State the problem:** Solve the equation $$2x + 3 = 11$$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse o

1. Problem statement: Determine the correct expression among the options for $\log_a x$. 2. Formula: Use the change of base formula.

1. **State the problem:** We need to find the numbers to replace the boxes in the equation: $$\square x(x+3) + 9x(2x+1) = 5x(\square x + 6)$$

1. Problem Q10: You have black and white socks in the ratio 4:3. How many socks must you pull to be certain of having a single pair of the same color? 2. To solve this, use the Pig

1. The problem asks for the smallest possible product of two numbers that round to 20 and 300 respectively when rounded to 1 significant figure. 2. When rounding to 1 significant f

1. **Stating the problem:** We are given that the length of a string, $L$, is 30 cm when rounded to the nearest 10 cm.

1. **Problem Statement:** Prove by mathematical induction that $$3 + 3^2 + 3^3 + \cdots + 3^n = 0.5(3^{n+1} - 3)$$ for all positive integers $n$. 2. **Base Case:** Check for $n=1$.

1. **Stating the problem:** Solve the linear equation $x + 4y = 2$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. Thi

1. **State the problem:** Calculate the total amounts of tomatoes, onions, and cooking oil needed for beef and beans for two occasions combined, then find the total cost for each,

1. **Énoncé du problème :** Déterminer l'ensemble de définition $D_f$ de la fonction $f$ dans chacun des cas suivants : a) $f(x) = \ln(x-1)$