🧮 algebra

1. Factorize the odd-numbered problems: 1. Factorize $4x^2 - 2x^3 - 6x$:

1. সমস্যাটি বুঝিঃ কৃষকের কাছে ২৫০ শতাংশ জমি রয়েছে। এর মধ্যে - ধানের জমি = $\frac{3}{8}$ অংশ

1. Problem 1: Solve for $x$ in the equation $$3(5x - 29) - 9 = -6$$ Step 1: Distribute 3 into terms inside parentheses:

1. The problem asks to find the value of $$(-12) \div (-3) + (-6) \times (-2)$$. 2. First, compute the division: $$(-12) \div (-3) = 4$$ because dividing two negative numbers resul

1. **State the problem:** Mayerlin has $x$ dimes and $y$ nickels. She has no more than 20 coins combined:

1. Let's define variables for the number of guests helped by each server: Let $x$ be the number of guests the second server helped.

1. The user wrote "With solution" but did not specify a math problem, so I will provide a short example problem with a solution. 2. Problem: Solve the quadratic equation $x^2 - 5x

1. **Stating the problem:** We need to find the equation of a straight line passing through the origin $(0,0)$ and approximately passing near $(-6,-2)$ and $(6,4)$. 2. **Identify t

1. We are given the expression $5c + 2$ and the value $c = 6$. 2. Substitute $6$ for $c$ in the expression: $$5 \cdot 6 + 2$$

1. Problem: Find the domain of the functions \( f(x) = \sqrt{x+2} \) and \( g(x) = \frac{1}{x^2 - x} \). 2. For \( f(x) = \sqrt{x+2} \), the expression inside the square root must

1. Stating the problem: Simplify the expression \( \frac{3}{10} - \frac{1}{10} \). 2. Since the denominators are the same, simply subtract the numerators:

1. The problem is to add the mixed number $1 \frac{1}{2}$ and the fraction $\frac{3}{8}$. 2. First, convert the mixed number to an improper fraction. $1 \frac{1}{2} = \frac{2 \time

1. State the problem: Add the fractions $\frac{2}{3}$ and $\frac{1}{4}$. 2. Find a common denominator for the fractions. The denominators are 3 and 4, so the least common denominat

1. The problem is to evaluate the expression $\frac{6}{11} - 2 \frac{3}{4}$. 2. First, convert the mixed number $2 \frac{3}{4}$ to an improper fraction.

1. We need to subtract the fractions $\frac{3}{4}$ from $\frac{5}{6}$.\n2. Find a common denominator. The denominators are 6 and 4. The least common denominator (LCD) of 6 and 4 is

1. State the problem: Simplify the expression $5 \frac{9}{11} - \left(-\frac{6}{11}\right)$.\n\n2. Convert the mixed number to an improper fraction:\n$$5 \frac{9}{11} = 5 + \frac{9

1. **Problem:** If you have $\frac{3}{4}$ of a chocolate bar and you want to divide it into portions each of size $\frac{1}{2}$ of a chocolate bar, how many portions can you get? *

1. The problem is to evaluate the expression $-1 \frac{3}{7} - \frac{2}{3}$. 2. First, convert the mixed number $-1 \frac{3}{7}$ into an improper fraction. Since it is negative, we

1. Let's evaluate the expression $$\frac{-23 - (-14)}{-1 + 2(-1)}$$ step by step. - Compute the numerator: $$-23 - (-14) = -23 + 14 = -9$$

1. Let's clarify what "use the proper solution for division" means. Division is the operation of splitting a number into equal parts or groups. It is often expressed as $a \div b$

1. We are asked to simplify the expression $\frac{4}{9} - \frac{7}{9}$. 2. Since both fractions have the same denominator 9, subtract the numerators directly: $4 - 7 = -3$.