🧮 algebra

1. **State the problem:** Rohan ordered 5 kg of premium coffee and some quantity $x$ kg of ordinary coffee. The price per kg of premium coffee is three times the price per kg of or

1. **State the problem:** Rohan ordered 5 kg of premium coffee and some ordinary coffee. The price per kg of premium coffee is three times that of ordinary coffee. When the quantit

1. **State the problem:** Rohan ordered 5 kg of premium coffee and some quantity $x$ kg of ordinary coffee. The price per kg of premium coffee is three times the price per kg of or

1. **Problem statement:** Given an arithmetic progression (AP) with first term $a_1=5$ and 25th term $a_{25}=25$, find: (i) the common difference $d$,

1. Problem statement: Rohan ordered 5 kg of premium coffee and some additional kilograms of ordinary coffee. The price per kg of premium coffee is three times that of ordinary coff

1. The problem gives parametric equations: $$y = t^6 - 5$$ and $$x = 4^3 - 1$$. 2. First, simplify the expression for $$x$$ since it does not depend on $$t$$: $$4^3 = 64$$, so $$x

1. نبدأ بكتابة التعبير الرياضي المعطى: $$77^{10} \times 26^{8} \times 52 \div (20^{9} \times 91^{8} \times 7) - 40$$

1. **Problem statement:** A drum contains chemicals P, Q, and R in the ratio 3:5:2. After removing 30 litres of the blend, 12 litres of P and 8 litres of Q are added. The final qua

1. **Problem statement:** A drum contains chemicals P, Q, and R in the ratio 3:5:2. Let the initial total quantity be $x$ litres. 2. The quantities of P, Q, and R initially are:

1. The problem asks to expand the logarithm $\log_2 5x$. 2. Recall the logarithm product rule: $\log_b (MN) = \log_b M + \log_b N$.

1. **State the problem:** We need to calculate $$\frac{2.37 \times 10^{8}}{6.83 \times 10^{-3}}$$ and express the answer in standard form to 3 significant figures. 2. **Rewrite the

1. **State the problem:** We need to calculate $$\frac{7.45 \times 10^{-12}}{2.12 \times 10^{-5}}$$ and express the answer in standard form to 3 significant figures. 2. **Divide th

1. **State the problem:** We need to subtract two numbers in scientific notation: $7.26 \times 10^{-10}$ and $2.82 \times 10^{-11}$.\n\n2. **Rewrite the numbers with the same power

1. **State the problem:** We need to multiply the numbers $6.4 \times 10^{-4}$ and $9.3 \times 10^{11}$ and express the result in standard form. 2. **Multiply the coefficients:** M

1. Let's start by stating the laws of exponents and logarithms clearly. 2. Laws of Exponents:

1. The problem is to simplify the expression \(14 \div x \div a \times 45\). 2. Division and multiplication are performed from left to right.

1. The problem asks to find the product of a variable $a$ and the number 9. 2. Multiplying $a$ by 9 is written as $9a$.

1. **Stating the problem:** We need to find the value of $z$ from the equation:

1. The problem is to understand the function $y=3x^2+1$ and explain its mathematical properties. 2. This is a quadratic function where $y$ depends on $x$ squared, multiplied by 3,

1. The problem is to understand the function $y=3x^2+1$ and explain its components and behavior. 2. This is a quadratic function where $y$ depends on $x$.

1. The average rate of change of a function $f(x)$ over an interval $[a,b]$ measures how much the function's output changes per unit change in input between $a$ and $b$. 2. It is c