🧮 algebra

1. The problem is to simplify the expression $1101_2$ which is a binary number. 2. To simplify or understand a binary number, we convert it to decimal (base 10).

1. **State the problem:** Solve for $m$ in the equation $$4^{m+2} + 4^{m+5} = 65.$$\n\n2. **Recall the properties of exponents:** For any base $a$ and exponents $x$ and $y$, $$a^{x

1. **Énoncé du problème :** Développer $P(x)=x^2-9+(x-3)(3x+5)$, résoudre $P(x)=-24$, montrer que $P(x)=4(x-3)(x+2)$, factoriser $Q(x)=(x+2)^2-4x-8$, déterminer les valeurs de $x$

1. **State the problem:** Solve the inequality $$|x^2 - x + 1| \geq 1$$. 2. **Recall the definition of absolute value inequality:** For any expression $A$, $$|A| \geq 1$$ means $$A

1. Problem: Find the month with the highest percentage change in rice price in Kabupaten Sejahtera in 2022. 2. Formula: Percentage change between two months is calculated as

1. The problem is to solve the inequality $|x^2+2| \le 11$. 2. Recall that the absolute value inequality $|A| \le B$ means $-B \le A \le B$.

1. The problem is to find the value of $\lfloor 2.5 \rfloor$. 2. The floor function $\lfloor x \rfloor$ gives the greatest integer less than or equal to $x$.

1. **Problem statement:** We are given the function $b(x) = \frac{3}{3x - 4}$ defined on the interval $\left[\frac{4}{3}, +\infty\right[$. We want to understand its behavior and gr

1. The problem is to evaluate or understand the expression involving the floor function: $\lfloor x \rfloor 2.5$. 2. The floor function $\lfloor x \rfloor$ returns the greatest int

Let's solve the equation step by step! 🎉 1. Here is the equation:

1. The problem is to solve the algebraic expression $3y^3 - 2y^2 + 5y - 6$ by factoring or finding its roots. 2. We use the factoring method to solve cubic expressions. The goal is

1. **Stating the problem:** OSIS MAN IC has a maximum initial capital of 900000 Rupiah to buy one variant of drink in size M or S from Pak Amir. They sell the drinks at 9000 Rupiah

1. The problem is to find the radius $r$ of the 2nd blade given the equation $r(2 + \text{theatre}) = 60$. 2. We start with the equation:

1. **State the problem:** Simplify the expression $5\frac{a}{b}x - 3 + 3\frac{a}{b}x + 7 + 1\frac{a}{b}2$. 2. **Rewrite mixed fractions as improper fractions:**

1. Problem 1: If 5 machines take 10 hours to produce 100 widgets, how long will 10 machines take to produce the same number? Formula: Work = Rate × Time

1. **Problem Statement:** Mukasa travels from town B to village A at 15 km/hr, leaving at 1:06 pm and arriving at 3:06 pm.

1. The problem is to analyze the given list of integers: $3, +3, 0, -1, +8, -5, +4, -4$ and $-132, -12, -7, -5, +16, +200, -200, 10$. 2. Since the problem does not specify a partic

1. **State the problem:** We know 3 workers take 4 days to build a wall. We want to find how many days 6 workers will take to build the same wall, assuming they work at the same ra

1. **Problem 1: Factor the trinomial** $x^2 + 5x + 6$. 2. The general formula for factoring a trinomial of the form $x^2 + bx + c$ is to find two numbers that multiply to $c$ and a

1. **Problem:** Solve the determinant of the matrix \(\begin{bmatrix} x - y & y \\ -y & x + y \end{bmatrix}\). 2. **Formula:** The determinant of a 2x2 matrix \(\begin{bmatrix} a &

1. **Problem (a):** Given $p^3 + q^3 + r^3 = 1$, prove that $$\left(\frac{x^p}{x^{-q}}\right)(p^2 - pq + q^2) \times \left(\frac{x^q}{x^{-r}}\right)(q^2 - qr + r^2) \times \left(\f