🧮 algebra

1. **Problem Statement:** (a) Find the Highest Common Factor (HCF) of 54 and 90.

1. **State the problem:** Solve the quadratic equation $$3x^2 + x - 20 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where the equ

1. **Stating the problem:** We have 10 triangles, each with three numbers at the vertices and one number inside a circle at the center. We need to analyze the relationship between

1. The problem is to find the value of 200 multiplied by 3/4 percent. 2. Recall that percent means per hundred, so 3/4% is equal to $\frac{3}{4} \times \frac{1}{100} = \frac{3}{400

1. **Problem Statement:** 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 slope-inte

1. The problem is to determine which value or expression should be placed in the blank space. 2. To solve this, we need more context or the equation where the blank appears.

1. **State the problem:** We are given a vertical line passing through points (7, 5) and (7, -4).

1. **State the problem:** We are given a polynomial $$p(x) = 2x^3 + ax^2 - 24x + b$$ with two conditions: - $$x + 3$$ is a factor of $$p(x)$$.

1. **State the problem:** We need to find how many socks weigh the same as one oven mitt. 2. **Given information:** The balance scale shows one oven mitt on the left side and five

1. **State the problem:** Solve for $x$ and $y$ in the equation $$\frac{x \cdot \sqrt{y}}{2} = \sqrt{\frac{3}{2}} \cdot \sqrt{\frac{9}{2}}$$ without using a calculator.

1. **State the problem:** Madison plans to cover a total distance of $1 \frac{4}{5}$ miles on a treadmill. She has already walked $\frac{2}{5}$ miles and wants to find out how far

1. **Stating the problem:** We are given the implicit equation $$ (x^2 + y^2)^2 = xy $$ and asked to analyze or understand it. 2. **Understanding the equation:** This is an implici

1. Let's start by stating the problem: Solve the equation given previously (assuming it was a quadratic or algebraic equation). 2. The general formula for solving a quadratic equat

1. The problem asks: Which number is 3 units backwards forward from -2? 2. To solve this, we need to understand the number line and the concept of moving units forward or backward.

1. Problemi: Zgjidhni ekuacionin me vlerë absolute të formës $|ax + b| = c$ ku $a$, $b$, dhe $c$ janë numra realë dhe $c \geq 0$. 2. Formula dhe rregullat: Vlera absolute $|x|$ ësh

1. **Problem statement:** Find the number 6 units backwards from 3 on the number line. 2. **Formula and rule:** Moving backwards on the number line means subtracting the number of

1. **State the problem:** Solve the equation $$|x - 1| - |x - 2| = 1$$ for $x$. 2. **Recall the definition of absolute value:** For any real number $a$, $$|a| = \begin{cases} a & \

1. **Stating the problem:** Solve the equation $$4x + 3y = \ln(4x - 3y)$$ for variables $x$ and $y$ or analyze its properties. 2. **Understanding the equation:** This is a transcen

1. Problem: Find the absolute values of the expressions: - (f) $\sqrt{\frac{5}{4}} - \frac{\sqrt{18}}{\sqrt{8}}$

1. **Stating the problem:** We are given the equation $\ln(xy) = x^2 + y^2$ and asked to analyze or solve it. 2. **Recall the logarithm property:** $\ln(xy) = \ln x + \ln y$ for $x

1. **State the problem:** We need to find the expression for $h(x+1)$ given the function $h(x) = 3x^4 + x^3 - 4x^2 + x - 2$. 2. **Formula and rule:** To find $h(x+1)$, substitute e