🧮 algebra

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

1. The problem is to determine if I can handle algebra. 2. Algebra involves working with variables, expressions, equations, and functions to solve problems.

1. **State the problem:** Calculate the value of $34 + 65 \div 6 \times 4$. 2. **Recall the order of operations:** According to the order of operations (PEMDAS/BODMAS), division an

1. The problem is to find the values of the function $y=2x-1$ for given $x$ values and understand how to plot the graph. 2. The formula is $y=2x-1$, which is a linear function wher

1. **State the problem:** Solve the equation $$\frac{5}{2(y-3)} = \frac{10 - y}{(y-3)^2}$$ for $y$. 2. **Identify the formula and rules:** We have a proportion between two fraction

1. **State the problem:** Solve the equation $((4x+3)\cdot 2)+(6x+3)=69$ for $x$. 2. **Write the equation clearly:**

1. **State the problem:** Solve the linear equation $3x = 4x + 1$ for $x$. 2. **Recall the rule:** To solve for $x$, we want to isolate $x$ on one side of the equation.