🧮 algebra

1. **State the problem:** We need to complete the table of values for the functions $f(x) = 5x + 4$ and $g(x) = x^2 + 2x + 3$ at $x = 2, 3, 4, 5$.

1. **State the problem:** Simplify the expression $$\frac{x}{\sqrt{x^2 + y^2}} - \frac{1}{x^2 + y^2}$$. 2. **Identify the common denominator:** The terms have denominators $$\sqrt{

1. **State the problem:** John drives south 8 miles, then east 15 miles, and returns home via a straight road. We need to find the total distance he drives in 7 days. 2. **Use the

1. **Problem:** Simplify the expression $$\frac{1}{3 + \frac{2}{x}}$$. 2. **Formula and rules:** When simplifying complex fractions, combine terms by finding a common denominator o

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Formula and rules:** To simplify a rational expression, factor the numerator and denominator and the

1. The problem is to graph the line given by the equation $$y = \frac{1}{5}x + 8$$ using the slope and y-intercept. 2. The slope-intercept form of a line is $$y = mx + b$$ where $m

1. **State the problem:** We are given that the temperature $y$ in degrees Fahrenheit is a linear function of the number of cricket chirps $x$. When $x=40$, $y=50$, and when $x=80$

1. **State the problem:** We are given two points on a linear function relating chirps per minute $x$ to temperature $y$: $(40, 50)$ and $(80, 60)$. The slope (rate of change) is $

1. **State the problem:** We are given two points on a linear function representing temperature $y$ in degrees Fahrenheit based on the number of cricket chirps $x$. The points are

1. **State the problem:** We need to check if $x=3$ is a solution to the equation $$5(x + 2) = 2x + 19$$ by substituting $x=3$ into both sides and verifying if they are equal. 2. *

1. **State the problem:** We are given that the temperature $y$ in degrees Fahrenheit is a linear function of the number of cricket chirps $x$. Two points on the graph are $(40, 50

1. **State the problem:** Solve the equation $-15 + N = -9$ for $N$. 2. **Formula and rules:** To isolate $N$, add 15 to both sides of the equation to cancel out $-15$ on the left

1. **State the problem:** We need to find the value of $B$ in the equation $15 + B = 23$. 2. **Use the formula:** To isolate $B$, subtract 15 from both sides of the equation.

1. Problem: Find the vertex and y-intercept of the quadratic function $y = x^2 - 6x + 15$. 2. Use the vertex formula $h = -\frac{b}{2a}$ where $a=1$, $b=-6$.

1. **State the problem:** Solve the inequality $$-6u - 17 \leq 7$$ for the variable $u$. 2. **Add 17 to both sides** to isolate the term with $u$:

1. **State the problem:** We have 50 customers, and 45 of them ordered tacos. We want to find what percentage of the customers ordered tacos. 2. **Explain the double number line:**

1. **State the problem:** Alicia and Greg are running with different starting distances and speeds. Alicia starts at 2 miles and runs at 3 mph. Greg starts at 5 miles and runs at 2

1. **State the problem:** Calculate the value of $5^5 \times 40^7$. 2. **Recall the properties of exponents:** When multiplying powers, if the bases are the same, you add the expon

1. **Problem statement:** Reduce the expression $5^2 \cdot (5^4)^3$ to a single power with base 5. 2. **Formula used:** When multiplying powers with the same base, add the exponent

1. **State the problem:** We are given the linear equation $y = -\frac{1}{3}x + 2$ and want to understand its graph and key features. 2. **Formula and rules:** This is a linear fun

1. Let's start by understanding the problem: finding the equation of a function means determining a formula that describes the relationship between the input variable $x$ and the o