🧮 algebra

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:**

1. **Stating the problem:** We are given an expression involving logarithms with base 7: $$\log_7 174 = 7 \log_7 174 + 7 \log_7 174$$ and need to analyze or simplify it. 2. **Recal

1. **Problem statement:** Show that the equation $3x^2 - 4y^2 + 3x + 16y - 18 = 0$ represents a hyperbola. Then find its eccentricity and the equations of its asymptotes. 2. **Rewr

1. **Problem:** Solve the system of equations: $$\begin{cases} 4x - 3y = 20 \\ 2x - y = 5 \end{cases}$$

1. **Stating the problem:** Given matrices

1. The problem is to find 10% of 78. 2. The formula to find a percentage of a number is: $$\text{Percentage value} = \frac{\text{percentage}}{100} \times \text{total value}$$

1. **State the problem:** Calculate the retail price given the cost and mark-up percentage using the formula: $$\text{Retail Price} = \text{Cost} + (\text{Cost} \times \text{Mark-u

1. **State the problem:** We want to find the number of miles $m$ you can drive a Gambelli Agency car so that the total cost is less than renting from McDougal Rental.

1. **State the problem:** We need to find the percentage of women in a cycling club with 1254 members, where 342 are women. 2. **Formula:** The percentage of women is given by

1. **State the problem:** Simplify the expression $$2 \frac{5}{8} - \left(-\frac{1}{5}\right) \div \left(-\frac{8}{5}\right) + \frac{1}{4}$$. 2. **Convert mixed number to improper