🧮 algebra

1. **State the problem:** Simplify the expression $1 - 1$. 2. **Recall the subtraction rule:** Subtracting a number from itself results in zero.

1. **State the problem:** Simplify or factor the quadratic expression $x^2 + 6x + 9$. 2. **Recall the formula:** A quadratic expression $ax^2 + bx + c$ can be factored using the me

1. Solve the equation $\frac{1}{2}(2f - 3) + \frac{1}{3}(f - 4) = 0$. Start by distributing the fractions:

1. The problem asks for the 12th term of the harmonic sequence with terms 6, 4, 3, ... 2. A harmonic sequence is a sequence whose terms are the reciprocals of an arithmetic sequenc

1. Problem Set A: Simplify the system of linear equations given: Original system:

1. **State the problem:** We need to find the value of $k$ such that the terms $2k+7$, $6k-2$, and $8k-4$ form an arithmetic progression (AP). 2. **Recall the property of an AP:**

1. نبدأ ببيان المشكلة: لدينا عددان حقيقيان $X$ و $Y$ مع الشروط التالية: $$5 \leq X \leq 7$$

1. **State the problem:** We need to evaluate the expression $$\frac{595}{4.08^2 + 5.3}$$ and determine which answer, 27.1115 or 271.115, is correct by approximating the value. 2.

1. **State the problem:** Find the number of terms in the arithmetic progression (AP) 6, 9, 12, ..., 78. 2. **Recall the formula for the nth term of an AP:**

1. The problem is to simplify the expression $\frac{8!}{7!}$.\n\n2. Recall the definition of factorial: for any positive integer $n$, $n! = n \times (n-1) \times (n-2) \times \cdot

1. **State the problem:** We are given an arithmetic progression (AP) where the first term $a_1 = 8$ and the 21st term $a_{21} = 108$. We need to find the 7th term $a_7$. 2. **Reca

1. **Problem statement:** Berenika wants to buy 35 T-shirts, each costing 5.80. She estimated the cost by calculating $40 \times 6 = 240$.

1. **State the problem:** In a class, $\frac{3}{5}$ of the students are girls and the rest are boys. Among the girls, $\frac{2}{9}$ are absent, and among the boys, $\frac{1}{4}$ ar

1. The problem is to plot the function $y = x^3 + 3x$ over the interval $x \in [-100, 100]$. 2. The function is a cubic polynomial, which means it can have up to three real roots a

1. The problem is to plot the function $y = x^3 + 3x$. 2. This is a cubic polynomial function where the highest degree term is $x^3$.

1. ปัญหาคือการเขียนกราฟของฟังก์ชันที่กำหนดในโจทย์ก่อนหน้า 2. สมมติว่าโจทย์ก่อนหน้าคือฟังก์ชัน $y=f(x)$ เราจะใช้ฟังก์ชันนี้ในการเขียนกราฟ

1. Let's start by stating the problem: You want to see how both sides of an equation are divided by 12. 2. Suppose we have an equation of the form $$12x = 36$$.

1. **Problem statement:** We need to find the width of a rectangular plot where the length and width are in the ratio 2:1, and the total cost of fencing the plot is 1500. The cost

1. **State the problem:** We are given the function $f(x) = x^3 - 3x$ and want to analyze it. 2. **Formula and rules:** This is a cubic polynomial function. Important features to f

1. **State the problem:** We have a two-digit number where the sum of its digits is 8. When the digits are interchanged, the new number is 36 greater than the original number. 2. *

1. The problem is to understand the function notation $f(x)$ and what it represents. 2. The notation $f(x)$ means a function named $f$ with input variable $x$.