🧮 algebra

1. **State the problem:** We are given the quadratic function $h(t) = -5t^2 + 20t + 2$ and need to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $h

1. **Problem Statement:** Multiply and divide integers as per the given operation. 2. **Important Rules:**

1. **Problem Statement:** Solve the equation $x^2 - 5x + 6 = 0$. 2. **Formula and Rules:** This is a quadratic equation of the form $ax^2 + bx + c = 0$.

1. The problem asks us to evaluate the expression $$(3.4 \times 10^2) \times (2 \times 10^3)$$ and express the result in the form $a \times 10^b$. 2. Recall the rule for multiplyin

1. **State the problem:** Evaluate the expression $$(2.5 \times 10^3) \times (3 \times 10^2)$$ and express the result in the form $[?] \times 10$. 2. **Recall the multiplication ru

1. **State the problem:** We are given the quadratic function $h(t) = -5t^2 + 20t + 2$ and want to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $h

1. **Stating the problem:** The problem statement is incomplete. Please provide the full problem or equation to solve. Since no specific problem or equation was given, I cannot pro

1. **State the problem:** Solve the equation $$2x^4 - x^3 - 6x^2 - x + 2 = 0$$ using the quadratic formula. 2. **Identify the approach:** This is a quartic equation, not a quadrati

1. **Problem Statement:** We have a function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x + 1$. We need to check if $f$ is injective, surjective, or bijective. 2. **Definiti

1. **Problem statement:** We have a function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x + 1$. We need to check if $f$ is injective, surjective, or bijective. 2. **Definiti

1. **Problem statement:** We have a function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x + 1$. We need to check if $f$ is injective, surjective, or bijective. 2. **Definiti

1. **State the problem:** A farmer stocked a pond with 1000 fish fingerlings. The fish population grows by a constant factor $x$ each year. After 2 years, the population is 36000.

1. **Problem statement:** We have a function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x + 1$. We need to check if $f$ is injective, surjective, or bijective. 2. **Definiti

1. **State the problem:** Given $x = 3 + \sqrt{8}$, find the value of $x - \frac{1}{x}$. 2. **Recall the formula and rules:** To find $x - \frac{1}{x}$, we need to calculate $\frac

1. **State the problem:** Given $x = 3 + \sqrt{8}$, find the value of $x - \frac{1}{x}$. 2. **Recall the formula:** To find $x - \frac{1}{x}$, we can use the expression directly by

1. Let's solve a challenging factorial problem: Calculate $$\frac{10!}{8!}$$. 2. Recall the factorial definition: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 1$$.

1. The problem asks why $10! = 10 \times 9 \times 8!$. 2. The factorial of a number $n$, written as $n!$, is the product of all positive integers from $n$ down to 1.

1. The definite integral from 3 to 10 of $x$ dx is calculated using the formula for the integral of $x$, which is $\frac{x^2}{2}$. Evaluating from 3 to 10: $$\int_3^{10} x \, dx =

1. The problem is to create a challenging factorial problem for practice. 2. Factorials are denoted by $n!$ and represent the product of all positive integers from 1 to $n$.

1. The problem is to solve a system of equations with 1, 2, and 3 unknowns. 2. For 1 unknown, the equation is usually of the form $ax = b$. To solve, divide both sides by $a$ to ge

1. **Problem Statement:** Find Shabnam's age when Aftab's age is 23 years, given Shabnam is 3 years older than Aftab. 2. **Formula:** Shabnam's age $s = a + 3$, where $a$ is Aftab'