🧮 algebra

1. The problem asks for the unit rate of water usage in cubic feet per hour. 2. The unit rate is the amount of water used per one hour.

1. **State the problem:** We need to find the unit rate of water usage in cubic feet per minute based on the graph showing water used over time. 2. **Identify the given data:** Fro

1. **State the problem:** Simplify and analyze the rational expression $$\frac{x^{2} - 12x + 27}{x^{2} - 10x + 9}$$ and understand its behavior. 2. **Factor numerator and denominat

1. The problem is to find 33 percent of 65. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percent}}{100} \times \text{number}$

1. The problem asks to find 33 percent of 87.12. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percent}}{100} \times \text{num

1. **Stel het probleem vast:** We hebben een grote rechthoek die is verdeeld in drie kleinere rechthoeken naast elkaar. De hoogte van elke kleine rechthoek is $a$, en de breedte is

1. **State the problem:** Calculate the value of the expression $\frac{2}{3} + 5$. 2. **Recall the rule:** To add a fraction and a whole number, convert the whole number to a fract

1. **State the problem:** We need to graph the inequality $y > -2x - 1$ on the coordinate axes. 2. **Understand the inequality:** The inequality $y > -2x - 1$ means that $y$ is gre

1. **State the problem:** We need to graph the linear inequality $$3x + y \leq -3$$ on the Cartesian coordinate system. 2. **Rewrite the inequality in slope-intercept form:** To gr

1. **State the problem:** Simplify the expression $$\frac{x^{2} + 14x + 49}{x^{2} + 15x + 56}$$. 2. **Recall the factoring formula:** For a quadratic expression $ax^2 + bx + c$, we

1. **State the problem:** We need to graph the linear inequality $$3x + y \leq -3$$ on a coordinate plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, express

1. **Problem Statement:** We need to graph the linear inequality $$3x + y \leq -3$$ on the coordinate plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, expres

1. **State the problem:** Solve for the positive value of $x$ in the equation $$2|4 - x| + 3|4 - x| = 25.$$\n\n2. **Combine like terms:** Since both terms have $|4 - x|$, add the c

1. **State the problem:** Solve the equation $$\frac{7}{2} - \frac{7}{2x} = 7$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fractions, find a common den

1. **State the problem:** Solve the equation $$\frac{7}{2} + \frac{5}{2x} = 3$$ and understand the rectangle with length $x+2$ and width $x$ positioned in the first quadrant. 2. **

1. **State the problem:** Solve the equation $$\frac{6x - 18}{8} = \frac{2x + 3}{8x}$$ for $x$. 2. **Understand the equation:** We have a rational equation where both sides are fra

1. **State the problem:** We need to sketch the graph of the quadratic function $$f(x) = 2x^2 - 4x - 2$$. 2. **Recall the general form and properties:** A quadratic function is gen

1. **State the problem:** We have two functions, A and B, with different rates of change (slopes). We want to find the equation of a new linear function whose slope is an integer b

1. **Problem Statement:** We need to sketch the graph of the quadratic function $$f(x) = 2x^2 - 4x - 2$$.

1. **Stating the problem:** We want to create an exponential function that fits given $x$ and $y$ coordinates. 2. **Formula used:** An exponential function generally has the form $

1. **Problem 1:** Solve the equation $$\frac{3x}{x-2} - \frac{6}{x-2} = \frac{3(x-2)}{x-2}$$ Since the denominators on the left side are the same, combine the fractions: