🧮 algebra

1. **State the problem:** We are given two functions: $$f(x) = 3x - 30$$

1. **State the problem:** We are given the linear equation $5x - 4y = 5$ and asked to express $y$ in terms of $x$, then identify the correct graph based on the slope and y-intercep

1. **State the problem:** We are given two functions $f(x) = x^2 - 8x + 7$ and $g(x) = x - 1$. We need to find the values of $(f + g)(0)$, $(f - g)(1)$, $(f \cdot g)(2)$, and $\lef

1. **State the problem:** We have an exponential model of the form $$y = a \cdot b^x$$ that passes through points $(3,5)$ and $(4,10)$. We need to find which of the given points al

1. **State the problem:** Solve the equation $5x - 4y = 5$ for $y$ and express it in slope-intercept form $y = mx + b$. 2. **Rewrite the equation:** Start with the given equation:

1. **State the problem:** We are given a parabola with vertex at $(-1,-4)$, crossing the y-axis at $(0,3)$, and x-axis at approximately $(-3,0)$ and $(1,0)$. We need to find: (a) $

1. **State the problem:** Solve the equation $$-\frac{1}{2}(y - 3) = \frac{25}{4}$$ for $y$. 2. **Use the distributive property:** Multiply both sides by $-2$ to eliminate the frac

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Solve the equation $$-\frac{1}{2}(y - 3) = \frac{25}{4}$$ for $y$. 2. **Write down the formula and rules:** To solve for $y$, we need to isolate $y$ on on

1. **State the problem:** We have a function $f(x) = -ax + b$ where $a$ and $b$ are constants.

1. **State the problem:** Write the equation $$5q^2 - 2q = 4q^2 - 6q + 45$$ in standard form and solve for $q$. 2. **Write the equation in standard form:** Move all terms to one si

1. **State the problem:** Solve the quadratic equation $6q^2 - 4q = 5q^2 - 7q + 54$. 2. **Rewrite the equation in standard form:** Move all terms to one side by subtracting $5q^2 -

1. **State the problem:** Given the equation $$\sqrt{15} - 9x = 48$$, find the value of $$x$$. 2. **Rewrite the equation:** The problem states $$\sqrt{15} - 9x = 48$$. Note that $$

1. **State the problem:** Solve the equation $\frac{x}{2} + \frac{x}{3} = 9$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to comb

1. **State the problem:** We need to graph three lines on the same coordinate grid and identify the shape they form. 2. **List the equations:**

1. **State the problem:** Solve the equation $\frac{X}{2} + \frac{X}{3} = 9$ for $X$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to comb

1. **State the problem:** We need to write an equation relating the total cost $C$ to the number of slices of pie $r$ eaten, given an admission fee and a per-slice cost.

1. The problem asks to write the intervals shown on the number line in interval notation. 2. The intervals given are:

1. **State the problem:** We need to write the intervals shown on the number line in interval notation. 2. **Analyze the graph:**

1. **State the problem:** Write a piecewise function for the absolute value of $x+3$. 2. **Recall the definition of absolute value:** For any expression $A$, the absolute value $|A

1. **State the problem:** Solve the equation $$\frac{6x}{x^2 - 9} = \frac{18}{x + 3}$$ for $x$. 2. **Recall the formula and rules:** The denominators are $x^2 - 9$ and $x + 3$. Not