🧮 algebra

1. **State the problem:** We want to prove algebraically whether the ordered pair $(2,1)$ is a solution to the inequality $$3x - 2y > 4$$.

1. **State the problem:** We analyze the quadratic function $$f(x) = x^2 + 2x - 3$$ to find its domain, range, vertex, axis of symmetry, intercepts, and key attributes. 2. **Formul

1. **Problem Statement:** We are given two examples involving functions and asked to analyze their domain, range, and whether they are discrete or continuous.

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 5$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **State the problem:** The distance a jet travels varies directly with the number of hours it flies. A jet traveled 3420 miles in 6 hours. We need to write an equation to model

1. **Stating the problem:** Find the slope of lines parallel and perpendicular to the x-axis and y-axis.

1. **State the problem:** We have a rectangle where the length is seven less than twice the width. The area is 15 square meters. We need to find the width $x$. 2. **Define variable

1. **State the problem:** Solve the equation $$\frac{x + 3}{8} = -2$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. Since

1. **State the problem:** Solve the equation $$12 + \frac{x}{5} = 20$$ for $x$. 2. **Isolate the variable term:** Subtract 12 from both sides to isolate the term with $x$.

1. **State the problem:** Simplify the expression $$\frac{2^{n-1}}{3^n}$$. 2. **Recall the properties of exponents:**

1. **State the problem:** Simplify the expression $3x - y + 8 + x + y - 2$. 2. **Combine like terms:** Group the terms with $x$, the terms with $y$, and the constant terms separate

1. **State the problem:** We need to find Lyla's total profit over two days, given that Monday's activity is -4 (money spent) and Tuesday's activity is 10 (money earned). 2. **Form

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. **Stating the problem:** John drives 200 km at steady speeds of 60 km/h and 100 km/h. The graph shows fuel consumption for these speeds: segment l1 ends at (25 km, 275 litres) f

1. **State the problem:** Find the zeros of the function $$g(x) = 4x^2 - 484$$. The zeros are the values of $$x$$ where $$g(x) = 0$$. 2. **Set the function equal to zero:**

1. **Problem (a):** Find the original price of an oven sold at 25% off with a sale price of 251.85. 2. The formula for discount price is:

1. **State the problem:** We need to find which expressions are equivalent to the expression $$ (x - y) \frac{5}{8} - \frac{1}{4} x + y $$. 2. **Rewrite the original expression:**

1. **Problemstellung:** Gegeben ist die Parabel $y = 0,5x^2 + 2x$. Wir sollen die Schnittpunkte mit der x-Achse bestimmen und die Parabel skizzieren. 2. **Formel und Regeln:** Die

1. **State the problem:** Determine if $y$ varies directly with $x$ given the pairs $(-2,6)$, $(1,3)$, and $(4,8)$. If yes, write the direct variation equation in the form $y = kx$

1. The problem asks to write the equations of a house-like graph composed of lines and curves using square roots, absolute values, and quadratic forms, with vertical and horizontal

1. **Stating the problem:** In a class, there are girls and 30 boys. 28 boys pass, all girls pass. The total passing students are 95% of the class. Find the number of girls and boy