🧮 algebra

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

1. The problem states: $\frac{Y}{2} = 4.7$. We need to find the value of $Y$. 2. To solve for $Y$, multiply both sides of the equation by 2 to isolate $Y$.

1. **State the problem:** We have two parabolas given by the equations:

1. **State the problem:** Simplify the expression $$\frac{1}{2+x} - \frac{2-x}{x}$$. 2. **Find a common denominator:** The denominators are $2+x$ and $x$. The common denominator is

1. You asked to use the graph you provided to give the answer. 2. However, I do not have access to any graph or image you mentioned.

1. **State the problem:** You want to graph the system of inequalities: $$y < 2$$

1. The problem is to find the equation to determine how many zeros a function has. 2. The number of zeros of a function corresponds to the number of solutions to the equation $$f(x

1. **Problem statement:** A boat tour company charges 11 for a harbour tour and averages 450 passengers on Saturdays. Every increase of 1 in the price decreases the number of custo

1. The problem is to write the inequality represented by the number line interval from 1 to 4, where 1 is not included and 4 is included. 2. The open circle at 1 means the inequali

1. **State the problem:** Make $n$ the subject of the equation $$n - 2k + 4c^2 = M$$. 2. **Identify the goal:** We want to isolate $n$ on one side of the equation.

1. **State the problem:** Simplify the expression $$-\left(3 - 5\left(x - 2y\right)\right) + 2\left(-2x + y\right)$$. 2. **Apply the distributive property:**