🧮 algebra

1. The problem asks about the slope of vertical and horizontal lines. 2. The slope of a line is defined as the change in $y$ divided by the change in $x$, or $$m=\frac{\Delta y}{\D

1. The problem asks to find the value of the function $s(t) = -3t + 8$ at $t = -2$. 2. The formula to evaluate a function at a given input is to substitute the input value into the

1. **Problem Statement:** Determine the domain and range of the graph described, which starts near (-3, -2), crosses the x-axis near (1,0), and ends at (4, 2). 2. **Understanding D

1. **State the problem:** We are given two sets of points and need to find the equations of the lines they represent. 2. **Identify the points:**

1. **State the problem:** Find the equation of the line passing through the points $(-2,3)$ and $(-1,1)$ in slope-intercept form $y=mx+b$. 2. **Find the slope $m$:** Use the formul

1. **State the problem:** Rose needs 200 litres of water to make 5 litres of iced tea. We want to find out how much water she needs to make 300 ml (which is 0.3 litres) of iced tea

1. **State the problem:** Find the equation of the line passing through points (0, 4) and (4, 2) in slope-intercept form $y=mx+b$. 2. **Formula:** The slope $m$ is given by $$m=\fr

1. The problem asks what output will be displayed if the user inputs 0 for the area of a square. 2. The pseudocode is:

1. **State the problem:** We are given two points representing profits after certain years: (1, 3) and (4, 15), where $x$ is years in business and $y$ is profit in millions. We nee

1. **State the problem:** We are given two points $(86,113)$ and $(176,239)$ and need to find the linear equation relating $R$ and $C$ in the form $R = mC + b$.

1. **State the problem:** Calculate the value of the expression $$2^3 + 5(-2)^2$$. 2. **Recall the order of operations:** We first evaluate exponents, then multiplication, and fina

1. **State the problem:** Solve the equation $$2 - \frac{x + 3}{4} = \frac{x - 1}{8}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fractions, multiply b

1. **State the problem:** We need to find the equation of the line passing through the points $(-1,0)$ and $(0,-4)$. 2. **Formula used:** The equation of a line can be found using

1. **State the problem:** Solve for $x$ given the function $f(x) = \frac{x^2 - 5}{x - 2}$ and $f(x) = 4$. 2. **Write the equation:**

1. **State the problem:** We are given a logarithmic function $$f(x) = -3 \log_{0.5}(x + 4) + 2$$ and a quadratic function $$g(x) = 5(x - 2)^2 + 7$$ which is said to be the inverse

1. Problem: Add the integers given in each expression. 2. Formula: For any two integers $a$ and $b$, addition is $a + b$.

1. **State the problem:** Simplify the expression $\frac{5x^2}{5x}$.\n\n2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} =

1. Problem: Add the integers given in the first expression: $(+73) + (+64)$. 2. Formula: Integer addition is straightforward: add the numbers if they have the same sign, subtract i

1. **State the problem:** Solve the quadratic equation $$5x^2 + 10x - 45 = 0$$ by completing the square. 2. **Divide the entire equation by 5** to simplify the coefficient of $$x^2

1. **Problem 1: List subsets of the set \{4, 5, 6\}** The subsets of a set include the empty set, single-element sets, two-element sets, and the full set itself.

1. **State the problem:** Solve the quadratic equation $x^2 + 6x - 14 = -2$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero: