🧮 algebra

1. **State the problem:** Solve for $v$ in the equation $\frac{v}{9} = \frac{8}{12}$.\n\n2. **Use the cross-multiplication method:** For equations of the form $\frac{a}{b} = \frac{

1. **State the problem:** Emma wants to find the number of hours $h$ for which the total cost of hiring the local photographer equals the total cost of hiring the out-of-town stude

1. **State the problem:** Shelley starts jogging from the trailhead at 5 miles per hour, while Naomi is already 1.3 miles ahead, walking at 2.4 miles per hour. We need to find how

1. **State the problem:** Simplify the expression $$-12x^2 - 6x^2$$. 2. **Recall the rule:** When combining like terms, add or subtract the coefficients of terms with the same vari

1. **State the problem:** Jackson has quarters (q) and dimes (d). The total value is 12.65 dollars. The number of quarters is seven less than twice the number of dimes. 2. **Define

1. **State the problem:** Express the expression $$\frac{2^n \times 4^{n-1}}{8^{n-2}}$$ as a power with a single base. 2. **Recall the bases and their relationships:**

1. **Problem:** Simplify the expression $$\left(\frac{12x^3 y^2}{9xy}\right) \left(\frac{18x^5 y^3}{4x^2 y^2}\right)$$. 2. **Formula and rules:**

1. Let's start by understanding the problem you want to solve. Since you asked for a simple and easy explanation, I'll explain a basic algebra problem: solving for $x$ in the equat

1. **Stating the problem:** We want to determine if the ratio 2 to 4 is equivalent to the ratio 4 to 8. 2. **Formula used:** Two ratios $\frac{a}{b}$ and $\frac{c}{d}$ are equivale

1. The problem asks if the pair (1, 5) is equivalent to the pair (2, 10). 2. To check equivalence of two pairs, we can compare their ratios: \(\frac{1}{5}\) and \(\frac{2}{10}\).

1. **State the problem:** Solve the system of linear equations using the elimination method: $$5x + 4y = -14$$

1. **Problem:** Solve the equation $3(1.5x + 9) = ?$ by distributing and finding $x$. 2. **Formula:** Use the distributive property: $a(b + c) = ab + ac$.

1. Let's start by stating the problem: Why don't two negatives in the exponent of $e$ turn into a positive? 2. The expression involves the exponential function $e^x$, where $x$ is

1. **State the problem:** Determine whether the function $f(x) = e^{-x^2} \cos x$ is even, odd, or neither. 2. **Recall definitions:**

1. **State the problem:** We need to write an equation in point-slope form to find the total distance $y$ Geoff travels after $x$ hours, given that Geoff paddles at an average spee

1. The problem is to write the equation $y + 5 = 6(x + 7)$ in slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. Start by expanding t

1. **State the problem:** Simplify the expression $$\frac{16p^2 - 64q^2}{\frac{p^2}{\frac{4}{2} - \frac{8}{p}}}$$. 2. **Rewrite the expression:** The denominator is a complex fract

1. **State the problem:** We need to find the features of the graph of the function $$f(x) = \frac{5x^2}{3x^2 + 7x}$$ including horizontal asymptotes, vertical asymptotes, x-interc

1. The problem asks to find the output of the function $f$ at $x=3$, i.e., find $f(3)$. 2. The graph shows a straight line passing through points $(-6,-6)$, $(0,0)$, and $(6,6)$.

1. **State the problem:** We are given two functions: $$f(x) = -4x^2 - 3$$

1. The problem is to understand the expression $-\propto -1$ and what it means. 2. The symbol $\propto$ means "is proportional to." So $a \propto b$ means $a$ is proportional to $b