🧮 algebra

1. **State the problem:** Factor the expression $8^2 - 50$. 2. **Rewrite the expression:** Calculate $8^2$ first.

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both

1. **State the problem:** Simplify the expression $$6 \times (3 - 5 + (-2)) \div (-3)$$. 2. **Apply the order of operations (PEMDAS):** First, simplify inside the parentheses.

1. **State the problem:** Multiply and simplify the expression $$\frac{p^2 - 4}{15p} \times \frac{3}{2 - p}$$ to its lowest terms. 2. **Recall formulas and rules:**

1. **State the problem:** Given that $\alpha + \beta = 2$ and the distance between points $(1, \alpha)$ and $(\beta, 1)$ is 3 units, find the value of $\alpha^2 + \beta^2$. 2. **Re

1. The problem is to solve the inequality $$12 \geq n + 30$$ for $n$. 2. To isolate $n$, subtract 30 from both sides:

1. **State the problem:** We need to find how often a gift bag contains all three items: a hat, a T-shirt, and a backpack. According to the problem, hats are given to every 2nd vis

1. **State the problem:** Two neon lights blink periodically, one every 4 seconds and the other every 6 seconds. We want to find how many times they blink simultaneously in 60 seco

1. The problem is to show the work for solving an algebraic or mathematical expression or equation. 2. Since no specific problem was given, I will demonstrate solving a simple line

1. **State the problem:** We are given the linear equation $$y = 0.37x + 5$$ which models the toll cost $$y$$ based on miles driven $$x$$. 2. **Identify what is asked:** Find the t

1. **State the problem:** Solve the linear equation $$x + 3y = 15$$ for $y$ in terms of $x$ and create a table and graph. 2. **Formula and rules:** To solve for $y$, isolate $y$ on

1. **State the problem:** We need to find how often tours for the National Capitol and the White House leave at the same time, given that National Capitol tours leave every 15 minu

1. **State the problem:** We have two stacks of boxes, one with boxes 12 inches tall and the other with boxes 18 inches tall. We want to find the shortest height at which the two s

1. **State the problem:** Tyee works two jobs: washing cars at 10 per hour and walking dogs at 6 per hour. He worked twice as many hours walking dogs as washing cars and earned a t

1. **State the problem:** We need to find the total volume of lemonade made by mixing 2 1/2 liters of water, 3/4 liters of lemon juice, and 1/4 liters of sugar syrup. 2. **Convert

1. **State the problem:** We have 2 1/2 liters of water, 3/4 liters of lemon juice, and 1/4 liters of sugar syrup mixed together. We need to find the total liters of lemonade made.

1. **State the problem:** Phillip wants to buy pencils and erasers so that the number of pencils equals the number of erasers, with pencils sold in packages of 10 and erasers in pa

1. **State the problem:** Abigail earns 12 commission per phone and 3 commission per accessory. She made a total of 258 commission and sold 6 more accessories than phones. 2. **Def

1. The problem is to analyze the parabola given by the equation $$-12x - 36 = (y - 6)^2$$ and verify the focus, vertex, and endpoints of the latus rectum. 2. First, rewrite the equ

1. **Problemstellung:** Wir sollen die Ausgleichsgerade $y = 0{,}0020114 x + 1{,}0168$ besser skalieren, also die Steigung und den Achsenabschnitt so anpassen, dass sie leichter zu

1. **Problemstellung:** Wir sollen eine Ausgleichsgerade (lineare Regression) für die Punkte $A(5, 1{,}0197)$, $B(10, 1{,}0261)$, $C(12{,}5, 1{,}0484)$ und $D(15, 1{,}0586)$ berech