🧮 algebra

1. **State the problem:** Max rounded each number to 1 significant figure and multiplied 20 by 500 to get 10,000. We want to find the smallest possible product of the original numb

1. **State the problem:** We need to find the value of $d$ in the equation $$\frac{x^{24}}{x^{d}} = x^{8}.$$\n\n2. **Recall the exponent division rule:** When dividing powers with

1. **State the problem:** We need to find the ratio of juniors to adults given two ratios: juniors to children is 1:3, and children to adults is 5:2. 2. **Write down the given rati

1. **State the problem:** Amir has 80 coins consisting of £1 and 50p coins in a ratio of 3:2. We need to find the total amount of money in pounds. 2. **Set up variables:** Let the

1. **State the problem:** Simplify the expression $$\frac{6h^{5} \times 4h^{3}}{8h^{15}}$$. 2. **Use the laws of exponents and multiplication:** When multiplying terms with the sam

1. Stating the problem: Calculate $\frac{1}{3} \times \left( \frac{9}{3} + \frac{5}{6} \right)$.\n\n2. Use the order of operations: first solve inside the parentheses, then multipl

1. **State the problem:** We have a quartic equation $$x^4 + bx^3 + cx^2 + dx - 2 = 0$$ with roots $$\alpha, \beta, \gamma, \delta$$.

1. **State the problem:** Simplify the expression $120x^8 + 240x^8 + 360x^8$. 2. **Identify like terms:** All terms have the same variable part $x^8$, so we can add their coefficie

1. **State the problem:** Simplify the expression $120x^8 + 240x^8 + 360x^?$ where the exponent of the last term is unknown. 2. **Identify the terms:** The first two terms are like

1. **State the problem:** Simplify the expression $10x \times (4x^4) \times (3x^3)$.\n\n2. **Recall the rules:** When multiplying terms with the same base, add the exponents: $x^a

1. **State the problem:** Simplify the expression $ (16x^3) \times 3x^3 $. 2. **Recall the multiplication rules:** When multiplying coefficients (numbers), multiply them directly.

1. Let's start by defining a simple function to understand how it works. 2. A function is a rule that assigns each input exactly one output.

1. সমস্যাটি হলো: তিনটি সংখ্যার অনুপাত ৩ : ৫ : ৬ এবং তাদের যোগফল ৬৩০। আমাদের বৃহত্তম ও ক্ষুদ্রতম সংখ্যার পার্থক্য বের করতে হবে। 2. অনুপাত অনুযায়ী, তিনটি সংখ্যা হবে $3x$, $5x$, এবং

1. **State the problem:** We are given the equation $$4x^2 + y^2 - 32x + 4y + 64 = 0$$ and need to analyze it.

1. The problem asks to find 50% of 820. 2. The formula to find a percentage of a number is: $$\text{Percentage value} = \frac{\text{Percentage}}{100} \times \text{Total number}$$

1. **State the problem:** Simplify the expression $$\frac{1}{2} - \frac{1}{3} \times \frac{7}{2} + \frac{15}{8} \times \frac{4}{5} - 3 \div \frac{3}{4} \times \frac{3}{2}$$. 2. **R

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both

1. The problem asks which division results in a positive quotient among the options: A. $-18 \div 3$

1. The problem states that the population increases exponentially at a rate of 1.6% per year. 2. The formula for exponential growth is $$P = P_0 e^{rt}$$ where:

1. **State the problem:** Solve the equation $$4 + \log\left(\frac{x}{4}\right) = \log(x^2)$$ for $x$. 2. **Recall logarithm properties:**