🧮 algebra

1. The problem is to simplify the expression $\sqrt{2} (7 + \sqrt{3})$. 2. We use the distributive property: $a(b+c) = ab + ac$.

1. সমস্যাটি হলো: শতকরা বার্ষিক সরল সুদের হার কত হলে 10 বছরে সুদ, মূলধনের \frac{2}{5} অংশ হবে। 2. সরল সুদের সূত্র হলো: $$S = P \times r \times t$$ যেখানে \(S\) হলো সুদ, \(P\) হলো মূ

1. **State the problem:** We are given the equation $32\sqrt{2} = 2x^a$ and need to find the value of $a$. 2. **Rewrite the equation:** Note that $32 = 2^5$ and $\sqrt{2} = 2^{\fra

1. **State the problem:** We need to estimate $\sqrt{0.05}$ to the nearest hundredth using a number line, then calculate it to the nearest thousandth. 2. **Recall the formula:** Th

1. **State the problem:** Solve the quadratic equation $h^2 + 5h + 4 = 0$ for $h$. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the solution

1. **State the problem:** Solve the equation $$-6\log x - 5n + 3 = -21$$ for $x$ assuming $n$ is a constant. 2. **Rewrite the equation:** Move constants to one side:

1. **State the problem:** Solve the equation $$-6\log x - 5n + 3 = -21$$ for the variable $n$ assuming $\log$ is the logarithm function and $x$ is a constant or known value. 2. **R

1. **Stating the problem:** We are given a sequence starting with 34, 55, followed by four unknown terms. We need to find two expressions involving terms of this sequence:

1. **State the problem:** Simplify the expression $$\frac{6}{6^{1/4}}$$. 2. **Recall the exponent rule:** When dividing powers with the same base, subtract the exponents:

1. **Problem Statement:** Calculate the percent increase or decrease given the starting and final values. 2. **Formula:** Percent Change = $$\frac{\text{Final Value} - \text{Starti

1. The problem is to simplify the expression $\left(9^2\right)^{\frac{1}{3}}$ using the properties of rational exponents. 2. Recall the power of a power property: $\left(a^m\right)

1. We are asked to find the real solution(s) of the equation $$\frac{1}{3} x^4 = 27$$. 2. The equation involves a quartic term $x^4$. To solve for $x$, we first isolate $x^4$ by mu

1. **Problem (a):** Sara rides her bicycle at a speed of 420 metres per minute. We need to convert this speed to kilometres per hour (km/h). 2. **Formula and rules:**

1. **State the problem:** Given the system of equations: $$a+b+c=5$$

1. **Problem statement:** (a)(i) Find the total cost of 4 cinema tickets if one ticket costs 6.30.

1. **Problem:** Given $34^2 = 1156$, find the value of $\frac{(0.34)^2}{10^2}$. 2. **Formula and rules:** We know that $0.34 = \frac{34}{100}$ and $10^2 = 100$. So,

1. **State the problem:** We need to evaluate the division of two decimal numbers: $0.004560 \div 2.13$. 2. **Formula used:** Division of decimals can be done by converting the div

1. Masalani bayon qilamiz: Sizdan algebraik ifodani yechish yoki muammoni hal qilish so'ralmoqda. 2. Masalan, tenglama yechish uchun umumiy formulani ko'rib chiqamiz: $$ax+b=0$$, b

1. **Problem:** Multiply the given numbers by powers of 10. Formula: Multiplying by $10^n$ shifts the decimal point $n$ places to the right if $n$ is positive, or $|n|$ places to t

1. **Stating the problem:** We are given the sequence 25, 32, 37, 47, 58, ? and need to find the next number. 2. **Analyze the differences between terms:** Calculate the difference

1. **State the problem:** We need to find the mass in kilograms of one barrel of oil carried by a supertanker. 2. **Given data:**