🧮 algebra

1. The problem asks to evaluate the expression $ (m + 2)^0 $ where $ m $ is a positive integer. 2. The key rule here is the zero exponent rule: For any nonzero number $ a $, $ a^0

1. **Problem 2:** A is greater than B by 10%, and B is greater than C by 20%. Given C = 20, find A. 2. **Step 1:** Express the relationships using formulas.

1. **Problem:** Find how long the rocket is in the air given the height function $$h = -16t^2 + 128t$$ where $h$ is height in feet and $t$ is time in seconds. 2. **Formula and rule

1. Stating the problem: A is greater than B by 10%, and B is greater than C by 20%. Given C = 20, find A. 2. Important formulas and rules:

1. **State the problem:** We are given a piecewise linear function $f$ and a table with some missing values. We need to complete the table and explain why the equation $f(x) = 4$ h

1. **Problem statement:** In a company, 67.5% of employees are married. 37.5% of employees are female, and 80% of female employees are married. We need to find the percentage $x$ o

1. **Problem statement:** At a school, 60% of the students are girls. 45% of the girls and 15% of the boys are overweight. Find the percentage of overweight students in the school.

1. **State the problem:** Factorize the expression $$8x^4 - 26x^2m^2 + 18m^4$$. 2. **Identify the type of expression:** This is a quadratic form in terms of $x^2$ and $m^2$.

1. The problem asks to solve the equation $1 = 5a + b + c$ step by step. 2. This is a linear equation with three variables: $a$, $b$, and $c$. To solve for one variable, we need va

1. **Problem:** An open-topped rectangular box is made by cutting squares of side $x$ cm from each corner of a $30$ cm by $24$ cm cardboard and folding up the sides. The box volume

1. The problem asks for the gradient (slope) of the line passing through the points (-2, -5) and (2, 5). 2. The formula for the gradient $m$ of a line passing through two points $(

1. **State the problem:** Jenna spent $2 \frac{4}{5}$ hours on homework. The time spent on homework is $1 \frac{1}{3}$ hours more than the time spent on exercising. We need to find

1. **Problem Statement:** Determine whether the system \(\begin{cases} 2x - y = 7 \\ 3x - y = 5 \end{cases}\) is dependent, consistent, or independent. 2. **Formula and Rules:**

1. **Stating the problem:** We are given bounds for $\ln 2$ and $\ln 5$ and asked to estimate values of logarithmic expressions such as $\ln 4$, $\ln(2^5)$, $\ln\left(\frac{5}{2}\r

1. **Stating the problem:** Solve an exponential equation that leads to an algebraic expression. 2. **General approach:** Exponential equations often have the form $a^{f(x)} = b$,

1. **State the problem:** We are given the system of equations: $$-2 - x = \frac{y^2 - 4y + 10}{11}$$

1. **State the problem:** We need to identify which graph corresponds to the system of equations: $$y = (x - 2)^2 + 6$$

1. The problem is to factor the cubic polynomial $x^3 + x + 1$. 2. To factor a cubic polynomial, we first check if it has any rational roots using the Rational Root Theorem. Possib

1. **State the problem:** We need to find the value of the expression $2x(x^2+5)+3$ when $x=2$. 2. **Write the expression:**

1. **Problem:** Find the value of $a$ such that the lines $5x + 3y - 4 = 0$ and $ax + 3y - 5 = 0$ are perpendicular. 2. **Formula and rule:** Two lines $Ax + By + C = 0$ and $A'x +

1. The problem asks to find $(fg)(4)$, which means the composition of functions $f$ and $g$ evaluated at $x=4$. 2. Recall that the composition $(fg)(x)$ means $f(g(x))$, so we firs