🧮 algebra

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

1. Let's define variables: Let $A$ be the number of cookies Anna had initially, and $E$ be the number of cookies Elsa had. 2. After Anna baked another 340 cookies, Anna's total coo

1. The problem asks to identify the value or meaning of $d$ in the given context. 2. However, the question does not provide any equations, expressions, or context where $d$ appears

1. Let's define variables for the number of cookies baked by Elsa and Anna. Let $A$ be the number of cookies Anna baked.

1. The problem is to understand the logarithm of numbers less than 1. 2. Recall the definition of logarithm: for $\log_b(x)$, it answers the question "to what power must we raise $

1. The problem is to understand the logarithm of numbers greater than 1. 2. Recall that the logarithm function $\log_b(x)$ answers the question: "To what power must the base $b$ be

1. **State the problem:** Wema drove from town A to town B in 48 minutes at an average speed of 90 km/h. Aisha took 32 minutes to drive the same distance. We need to find the diffe

1. The problem gives a piecewise function: $$f(x) = \begin{cases} 4 - x & \text{if } x < 3 \\ 7 & \text{if } x = 3 \\ x^2 - 8 & \text{if } x > 3 \end{cases}$$

1. **State the problem:** Convert the recurring decimal $0.3$ (where 3 repeats indefinitely) to a fraction in simplest form. 2. **Set up an equation:** Let $x = 0.3333\ldots$ (the

1. **Stating the problem:** A person starts with an initial amount of money. 25% is stolen in a bus, 10% of the remainder is lost through a hole in the pocket, then 50% of the new

1. Let's clarify the problem to understand why the answer should be 80 instead of 77. 2. Please provide the original problem or equation so we can verify the calculations step-by-s

1. The problem involves analyzing inequalities with absolute values: (i) $|r + a - \sigma| > |r + a + \sigma|$

1. **Stating the problem:** A person starts with an initial amount of money. 25% is stolen, 10% of the remainder is lost, then 50% of the new remainder is spent on food, and finall