🧮 algebra

1. **State the problem:** We want to find the price per ounce when 48 fluid ounces cost 7.20. 2. **Formula:** Price per ounce = \frac{\text{Total price}}{\text{Total ounces}}

1. **State the problem:** We want to find the price per ounce when 42 fluid ounces cost 7.20. 2. **Formula:** Price per ounce = \frac{\text{Total price}}{\text{Total ounces}}

1. **State the problem:** We need to find two consecutive even integers whose difference of squares is 68. 2. **Define variables:** Let the first even integer be $x$. Since the int

1. The user requests to "Complete on a graph," which is unclear without a specific function or equation. 2. To assist effectively, please provide the function or equation you want

1. We are asked to write the quadratic expression $w^2 + 9w - 5$ in completed square form. 2. The general form of a quadratic is $ax^2 + bx + c$. Here, $a=1$, $b=9$, and $c=-5$.

1. **Problem Statement:** Graph the quadratic functions:

1. **Problem 1:** Write $x^2 + 8x + 5$ in the form $(x + a)^2 + b$ where $a,b$ are integers. 2. **Formula:** To complete the square for $x^2 + bx + c$, use:

1. **Problem statement:** Given that $a$, $b$, $c$, and $d$ are in continued proportion, prove that $$\frac{a-2b}{b-2c} = \frac{3b+4c}{3c+4d}.$$\n\n2. **Recall the definition of co

1. **Stating the problem:** We want to understand the concept of continued proportion, which is a sequence of numbers where each term is in proportion to the next. 2. **Definition:

1. Let's clarify the problem you are referring to and verify the solution. 2. If the problem involves solving an equation or expression where the answer is claimed to be 2, we need

1. **State the problem:** Solve the equation $$-7x - 9 = -2x + 31$$ for $x$. 2. **Write down the equation:** $$-7x - 9 = -2x + 31$$

1. **State the problem:** Solve the linear equation $2.25x + 70 = 193.75$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtrac

1. **State the problem:** A group of friends has 69.75 to spend on parking and admission to an amusement park. Parking costs 17.25, and each ticket costs 17.50. We want to find the

1. **State the problem:** Robert buys cheese and lemons, paying a total of 24.36. The cheese costs 5.31, and he buys 5 bags of lemons at the same price each. We need to find the co

1. The problem asks to write down the two inequalities describing the unshaded region on the graph. 2. The graph shows two lines:

1. **State the problem:** The lacrosse team raised 1775.50 to go to a tournament. They rented a bus for 901.50 and budgeted 46 per player for meals. We need to find the number of p

1. The problem involves understanding and interpreting inequalities involving $x$ and $y$. 2. Inequalities like $x - y < 4$ and $x - y > 4$ describe regions in the coordinate plane

1. **State the problem:** We need to write the two inequalities that describe the unshaded region on the coordinate plane. 2. **Identify the lines:**

1. **Problem 7:** The value of $y$ varies directly with $x$. Given $x=5$ and $y=-15$, find the constant of variation and the value of $y$ when $x=9$. 2. **Direct Variation Formula:

1. **State the problem:** We need to find the inequalities describing the unshaded region on the graph. 2. **Identify the lines:**

1. **Problem statement:** The value of $y$ varies directly with $x$. When $x=5$, $y=-15$. We need to find the constant of variation and then find $y$ when $x=9$. 2. **Formula for d