🧮 algebra

1. **State the problem:** Zach paid 8 for an 8-inch diameter pizza, and Aiden paid 12 for a 12-inch diameter pizza. We need to find the percentage increase in price and size, then

1. **Problem 14:** Find the value of $k$ if the slope of the line through points $(3, 2)$ and $(8, k)$ is $\frac{3}{5}$. 2. **Formula for slope:** The slope $m$ between two points

1. **State the problem:** Simplify the expression $$\frac{4x^2 - 2x + 8x - 4}{u x^2 + 1 - u x}$$ and solve the equation $$\frac{2x^2 - 2x - 4}{u x^2 + 1 - u x} = 1$$ for $x$. 2. **

1. **State the problem:** We are given the function $f(x) = x^2 - 2x - 3$ and a table of $x$ values: 0, 1, -1, 3, -2. We need to find the corresponding $y$ values and understand th

1. **Solve the inequalities:** a) $8x \leq x^2 + 12$

1. **Solve the inequalities:** **Problem 1:** Solve $8x \leq x^2 + 12$

1. **State the problem:** Graph the system of inequalities:

1. The problem states: 1/8 of a number is 9, and we need to find the whole number. 2. Let the whole number be $x$.

1. **State the problem:** We need to find a number such that when \(\frac{3}{4}\) of it is added to 9, the result is 27. 2. **Set up the equation:** Let the number be \(x\). The pr

1. **Problem:** Find $x$ in the equation $$105^\circ + x^\circ + 40^\circ + 75^\circ = 360^\circ$$ 2. **Formula:** The sum of angles around a point is always $$360^\circ$$.

1. The problem is to understand how to factorize algebraic expressions. 2. Factorization means writing an expression as a product of simpler expressions called factors.

1. **State the problem:** Solve the inequality $$x\left(\frac{1}{2}-\frac{1}{3}\right)^{-1} + \frac{(x-1)^2}{2} + \frac{1}{2}x^2 \geq 5x\left(\frac{1}{2}+\frac{1}{3}\right)^{-1} +

1. **Problem a:** Berechne $$-2 \frac{1}{4} \cdot \frac{2}{3} - \left[\left(-5 \frac{1}{2}\right) - \left(-1 \frac{1}{2}\right) : \frac{4}{5}\right]$$ 2. **Umwandlung in unechte Br

1. **State the problem:** We are given a piecewise graph and several statements about the function $f$. We need to determine which statements are true. 2. **Analyze the statements:

1. **State the problem:** We need to find the range of a piecewise function described by three horizontal segments: - A segment at $y=3$ extending right from an open circle at $x=1

1. **State the problem:** We need to find the range of a piecewise function whose graph consists of three horizontal pieces with constant y-values -3, 0, and 3. 2. **Recall the def

1. **State the problem:** We are given the formula for cardiac output $D = V \cdot R$, where $D$ is the cardiac output, $V$ is the volume of blood pumped per heartbeat, and $R$ is

1. The problem asks for the domain of a function based on the given graph description. 2. The domain of a function is the set of all possible input values (x-values) for which the

1. The problem states that two divers are underwater, one at a depth of 32 meters, and the other diver's depth $x$ satisfies the equation $$|x - 32| = 11.$$ 2. This is an absolute

1. **State the problem:** Simplify the expression $$\frac{x^6}{x^7}$$ using properties of exponents. 2. **Recall the quotient of powers rule:** When dividing powers with the same b

1. **Problem:** A local print shop charges 0.10 per page to print black and white documents with no flat rate. Find the algebraic model and complete the table. 2. **Formula:** Cost