🧮 algebra

1. **State the problem:** We need to solve the quadratic equation $$18abx^2 + (5a^2 - 7b^2)x - 9ab = 0$$ for $x$ using the quadratic formula.

1. **State the problem:** Solve the quadratic equation $$12abx^2 - \left(9a^2 - 8b^2\right)x - 6ab = 0$$ for $x$ using the quadratic formula. 2. **Recall the quadratic formula:** F

1. **Problem Statement:** Identify which graphs represent pairs of inverse functions. 2. **Key Concept:** Two functions $f$ and $g$ are inverses if and only if their graphs are sym

1. **State the problem:** We need to find the value of $n$ when $n$ arithmetic means are inserted between $a$ and $100$, the ratio of the first mean to the last mean is $1:7$, and

1. The problem is to add the fractions $\frac{1}{2}$ and $\frac{2}{4}$.\n\n2. To add fractions, they must have a common denominator. The denominators here are 2 and 4.\n\n3. The le

1. **State the problem:** Solve for $x$ in the equation:

1. **State the problem:** Simplify the expression $$\frac{2 - \frac{3}{5}}{1 \frac{3}{10} + 5}$$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Simplify the expression $$\frac{3.2 - \frac{3}{5}}{1 \frac{3}{10} + 5}$$. 2. **Convert mixed numbers and decimals to improper fractions:**

1. **Problem 1: Minimum number of bread loaves for packing** The baker can pack bread in boxes of $15$ or $20$ loaves. We want to find the minimum number of bread loaves that can b

1. **State the problem:** Tom cleans his room every $12$ days and Jerry every $16$ days. They start cleaning today (day $0$). We want to find the next day when both clean their roo

1. **State the problem:** Calculate the value of $$A=801324000(1+0.15)^{10}$$. 2. **Formula used:** This is a compound interest formula where $$A=P(1+r)^n$$, with $$P=801324000$$,

1. **State the problem:** Solve the equation $$\sqrt{x^2 - 4x + 13} + \sqrt{x^2 - 4x + 8} = 5$$ for $x$. 2. **Rewrite the expressions inside the square roots:**

1. **State the problem:** We need to find the equation of a parabola that passes through the points $(-4, 0)$, $(2, 6)$, and $(8, 0)$.

1. **Problem statement:** Compute the value of the expression $(-8)(-6)$. 2. **Formula and rules:** Multiplying two negative numbers results in a positive number.

1. **Understanding the problem:** Factoring means rewriting an expression as a product of simpler expressions called factors. 2. **Common factoring methods:**

1. **Problem:** Compute $(-4) + 2$. Formula: Addition of integers.

1. **State the problem:** Rationalize the denominator of the expression $$\frac{9}{4} \div (3\sqrt{5} + 6)$$. 2. **Rewrite the expression:** Division by a number is the same as mul

1. **State the problem:** Rationalize the denominator of the expression $$\frac{4}{3\sqrt{5} + 6} \cdot \frac{3\sqrt{5} - 6}{3\sqrt{5} - 6}$$. 2. **Formula and rules:** To rational

1. **Memahami masalah:** Seorang anak menabung dengan jumlah yang bertambah tetap setiap bulan, artinya tabungan tiap bulan membentuk barisan aritmetika.

1. **Nyatakan masalah:** Seorang anak menabung dengan jumlah uang yang bertambah tetap setiap bulan. Jumlah tabungan selama 12 bulan adalah 306000 dan selama 18 bulan adalah 513000

1. **State the problem:** Simplify the expression $$40-[3^2\times 3+2\times 2^3\times 2-(-10)\times 2]+90\div(-9)$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exp