🧮 algebra

1. **Problem Statement:** We are given revenue and cost functions for REDs limited and need to determine the maximum profit. 2. **Formula:** Profit $P(x)$ is given by the differenc

1. **Problem Statement:** We are given a set of points $(x, f(x))$ and asked to approximate the function $f(x)$ using one of the given forms: a. $f(x) = 15x^2$

1. The problem asks us to find an expression equivalent to $ (7x^3)(7x^4) $. 2. We use the rule for multiplying powers with the same base: $$ a^m \times a^n = a^{m+n} $$

1. **Stating the problem:** Tina has 48 rabbits in total.

1. **Stating the problem:** We are given a survey of 60 pupils about their favorite drinks: cola, milk, and water. We know the number of boys and girls who prefer each drink and ne

1. **State the problem:** Simplify the expression $\left(7x^2\right)^2 \left(x^3\right)^{\frac{1}{2}}$ and find which option it matches. 2. **Recall the exponent rules:**

1. **Stating the problem:** We have a table of values for $x$ and $y$: $$\begin{array}{c|ccccccc}

1. Problem: Finn divisoren når dividenden og kvotienten er gitt. 2. Formelen for divisjon er:

1. **State the problem:** We need to find the equation of the line passing through the points (-5, -5), (-2, -2), (3, 3), and (7, 7). 2. **Formula used:** The equation of a line in

1. **State the problem:** Solve the equation $$\frac{1}{3x} - \frac{2}{x+2} = \frac{x}{x+2}$$ for $x$. 2. **Identify the common denominator:** The denominators are $3x$ and $x+2$.

1. The problem is to find the intersection point of the lines $x=3$ and $y=-2$ on a Cartesian coordinate plane. 2. The line $x=3$ is a vertical line passing through all points wher

1. **State the problem:** We are given the 5th term ($a_5$) and the 11th term ($a_{11}$) of an arithmetic progression (AP) and need to find the 8th term ($a_8$). 2. **Recall the fo

1. **State the problem:** Solve the equation $$\frac{1}{3}x - \frac{2}{x+2} = \frac{x}{x+2}$$ for $x$. 2. **Identify the common denominator:** The denominators are $3$, $x+2$, and

1. The problem is to find the equation of a horizontal line passing through the point where $y = -2$. 2. Recall that the equation of a horizontal line is always of the form $$y = c

1. **Stating the problem:** We are given three people: Jinadasa, Siridasa, and Amaradasa. Siridasa is 8 years younger than Jinadasa, Amaradasa is 3 years older than Siridasa, and t

1. The problem asks for the equation of a vertical line crossing the x-axis at $x=10$. 2. A vertical line has an equation of the form $x = a$, where $a$ is the x-coordinate where t

1. **Problem Statement:** Find the x-coordinate of every point along the given vertical line and determine the equation of the line.

1. **State the problem:** Multiply the fractions $\frac{4}{7}$ and $3 \frac{1}{3}$ and express the answer as a fraction in its lowest terms. 2. **Convert the mixed number to an imp

1. **State the problem:** Find the value of $\log \frac{1}{8}$. 2. **Recall the logarithm rule:** $\log \frac{a}{b} = \log a - \log b$.

1. We are asked to factor the quadratic expression $x^2 - x - 30$. 2. The general form of a quadratic expression is $ax^2 + bx + c$. Here, $a=1$, $b=-1$, and $c=-30$.

1. **State the problem:** Simplify the expression $2x (x-3) + (x-3)$. 2. **Identify the common factor:** Notice that both terms contain the factor $(x-3)$.