🧮 algebra

1. **Problem Statement:** We are given the function $y=\frac{2}{x}$ and asked to:

1. The problem is to express a number or result as a fraction. 2. A fraction is a way to represent a number as a ratio of two integers, written as $\frac{a}{b}$ where $a$ is the nu

1. **State the problem:** Find the equation of the straight line passing through the points (3, 10) and (7, 28) in the form $y = mx + c$. 2. **Formula used:** The slope $m$ of a li

1. **State the problem:** Find the equation of the straight line passing through points (5, 4) and (8, 19). 2. **Formula used:** The equation of a straight line is $y = mx + c$, wh

1. **State the problem:** We need to find the y-intercept of the straight line passing through the points $(2, 13)$ and $(8, 37)$. 2. **Formula for slope:** The slope $m$ of a line

1. **State the problem:** Simplify the expression $$\left(\frac{25a^{12}}{t^{15}}\right)^{-\frac{2}{3}}$$. 2. **Recall the rule for negative exponents:** $$x^{-n} = \frac{1}{x^n}$$

1. **State the problem:** Simplify the expression $7\sqrt{40}$.\n\n2. **Recall the rule:** The square root of a product can be written as the product of the square roots: $$\sqrt{a

1. The problem asks: "45 is which square?" This means we want to find if 45 is a perfect square, and if so, which number squared equals 45. 2. The formula for a perfect square is:

1. **State the problem:** Solve the inequality $3k + 8 \geq 26$. 2. **Understand the inequality:** We want to find all values of $k$ such that when multiplied by 3 and added to 8,

1. The problem is to solve the compound inequality $$4 < \frac{x + 7}{2} \leq 8$$ and then represent the solution on a number line. 2. To solve the inequality, multiply all parts b

1. **Problem Statement:** We need to find the y-intercept of the straight line passing through the points $(2, 13)$ and $(8, 37)$. 2. **Formula for slope:** The slope $m$ of a line

1. **State the problem:** Solve the compound inequality $$4 < \frac{r - 8}{5} \leq 9$$ for the variable $r$. 2. **Understand the inequality:** This is a compound inequality where t

1. The problem is to simplify the expression $$81x^6 - 16y^2$$. 2. Recognize that this is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$.

1. **Stating the problem:** We are given a pyramid-like arrangement of numbers and need to determine the correct answer from the given options based on the pattern or relationship

1. **State the problem:** We need to find the y-intercept of the straight line passing through the points $(2, 13)$ and $(8, 37)$. 2. **Formula for slope:** The slope $m$ of a line

1. **State the problem:** We need to find the gradient (slope) of the straight line passing through the points (7, 6) and (11, 16). 2. **Formula for gradient:** The gradient $m$ of

1. **Stating the problem:** Simplify the expression involving the fractions and integers given: $$\frac{43}{17}, -\frac{1}{7}, -7, 35, 5, -\frac{1}{14}, \frac{1}{7}, -14, \frac{1}{

1. **State the problem:** We need to find the gradient (slope) of the straight line passing through the points $(6, 4)$ and $(11, 39)$. 2. **Formula for gradient:** The gradient $m

1. **State the problem:** We need to find the equation of line G that passes through the point (8, 11) and is parallel to the line given by $$y = 3(4x + 3)$$. 2. **Rewrite the give

1. **State the problem:** Find the equation of a straight line with gradient $5$ passing through the point $(3, 9)$. 2. **Formula used:** The equation of a straight line in slope-i

1. **State the problem:** We need to find the equation of line A that passes through the point $(-2, 5)$ and is parallel to the line given by $y = 3x + 9$. 2. **Recall the formula