🧮 algebra

1. **State the problem:** Solve the equation $$\left(\frac{7}{13} - \frac{1}{3}\right) - \frac{1}{5} = \left(\frac{105}{\Box} - \frac{65}{\Box}\right) \frac{39}{\Box}$$ where the b

1. **Problem Statement:** Solve the equation $2x^2 - 8x + 6 = 0$ for $x$. 2. **Formula Used:** The quadratic formula is used to solve equations of the form $ax^2 + bx + c = 0$:

1. We are given the equation $\frac{5}{8} - \frac{4}{9} = \frac{45}{\square} - \frac{32}{\square} = \frac{\square}{\square}$ and need to find the missing denominators and the resul

1. The problem is to find the sum of the infinite geometric series $$12 - 6 + 3 - \ldots$$ if it converges. 2. The formula for the sum of an infinite geometric series with first te

1. **State the problem:** We have a geometric sequence defined by the first term $a_1 = 8$ and common ratio $r = \frac{3}{4}$. We need to find the sum of the first 25 terms, $S_{25

1. Problem: Multiply the radicals and simplify. 2. Formula: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \times b}$ and $c\sqrt{a} \cdot d\sqrt{b} = (c \times d) \sqrt{a \times b}$.

1. **State the problem:** We need to find the values of $P$ and $Q$ for the line equation $Px + 2y = Q$ that passes through the point $(-3,5)$ and is perpendicular to the line $2x

Let's solve this step by step! 🎉 **Step 1:** We have the expression $$\frac{n \times n + n}{n} = 10$$

**Step 1:** Imagine you have this: $$x^2 - 4$$ **Step 2:** Think of $$x^2$$ as $$x \times x$$ (like 2 apples side by side) 🍎🍎

1. Imagine you have $x^2$. It means $x$ times $x$. 🟦 🟦 2. Factoring means finding what multiplies to make $x^2$. Here, it's $x \times x$. 🔄

1. **State the problem:** Solve the equation $$\frac{n \times n + n}{n} = 10$$ for $n$. 2. **Rewrite the expression:** The numerator is $n \times n + n = n^2 + n$.

1. **State the problem:** Solve the system of equations using row operations: $$\begin{cases}-6x - 5y - 3z = 17 \\ 3x - 4y + 4z = -19 \\ -6x + 3y - 6z = 30 \end{cases}$$

1. **State the problem:** We have the system of equations: $$\begin{cases} 4x - 5y + 3z = -5 \\ 44x + 17y + kz = -40 \\ -8x - 8y + 3z = 5 \end{cases}$$

1. **State the problem:** Find the y-intercept of the line given by the equation $$-3y - 4x = 15$$. 2. **Recall the y-intercept definition:** The y-intercept is the point where the

1. **State the problem:** Find the equation of the line passing through the point $(3,1)$ with slope $m = -\frac{4}{3}$.\n\n2. **Formula used:** The point-slope form of a line is g

1. **State the problem:** Find the equation of the line passing through the point $(5, -3)$ with slope $\frac{2}{5}$. 2. **Formula used:** The point-slope form of a line is given b

1. **State the problem:** Find the equation of the line passing through the point $(6, -5)$ with slope $m = -\frac{1}{3}$. 2. **Formula used:** The point-slope form of a line is gi

1. **State the problem:** Find the equation of the line passing through the point $(5, 4)$ with slope $2$. 2. **Formula used:** The point-slope form of a line is given by:

1. **State the problem:** Solve the equation $$6^x = 7x + 4$$ for $x$. 2. **Understand the equation:** This is a transcendental equation where an exponential function equals a line

1. **State the problem:** Convert the standard form equation $x + y - 3 = 0$ to slope-intercept form $y = mx + b$. 2. **Recall the formula:** The slope-intercept form is $y = mx +

1. **State the problem:** Kenisha has two salary options: Option 1 is $500 plus 4% commission, Option 2 is $400 plus 5% commission. We want to find the sales amount $x$ where both