🧮 algebra

1. **State the problem:** Rationalize the denominator of the expression $$\frac{\sqrt{10}}{3\sqrt{2}}$$. 2. **Recall the rule:** To rationalize a denominator containing a square ro

1. **Problem:** Solve the system using substitution for part (a): $$\ell_1: y = 3x - 4$$

1. Masalah: Hitung nilai dari $16^{\frac{1}{2}} + 27^{\frac{2}{3}} - 125^{\frac{1}{3}}$. 2. Rumus dan aturan penting:

1. The problem is to find the value of $p$ in a given question. 2. Since the specific question details are not provided, I will explain the general approach to find $p$ in algebrai

1. The problem states that the width of the shaded regions is $x-8$. 2. To understand this, we need to know what $x$ represents and how the width is calculated.

1. **State the problem:** We need to find the product of $4X^2$ and $3X^2$. 2. **Formula used:** When multiplying terms with the same base, multiply the coefficients and add the ex

1. **State the problem:** Simplify the expression $-10X + (-4X)$. 2. **Recall the rule:** When adding terms with the same variable, add their coefficients.

1. **State the problem:** We need to simplify the expression by adding the terms involving $x^2$, specifically $8x^2 + (-5x^2)$. 2. **Recall the rule for adding like terms:** When

1. **State the problem:** Simplify and solve the equation $$30 = \frac{x^2 - 9}{3 - x} + \frac{x}{2} \cdot \frac{x - 3}{x - 3}$$ where the second fraction simplifies to 1 since num

1. **State the problem:** Simplify and understand the expression $$62.5 \cos(2\pi 60 t) \left( \frac{2\pi 60 e^{-t} \cos(2\pi 60 t) - e^{-t} \sin(2\pi 60 t)}{1 + (2\pi 60)^2} - \fr

1. **Problem statement:** (a) Determine which carton size of Smiley Orange Juice is the better buy based on cost per ml.

1. The problem asks to write the domain of the given graph as an inequality. 2. The domain of a function is the set of all possible input values (x-values) for which the function i

1. **State the problem:** Tamika wants to find when the total cost to fish at Floyd's Catfish Farm equals the total cost at Miller's Catfish Farm.

1. Énonçons le problème : Résoudre l'équation $$-1,5x^2 + 45x + 20 = 5$$ et arrondir les solutions aux centièmes. 2. Simplifions l'équation en ramenant tout à zéro :

1. **State the problem:** Solve the equation $x + 5 = \sqrt{5x + 21}$ for $x$. 2. **Recall the formula and rules:** To solve equations involving square roots, we isolate the square

1. **State the problem:** Solve the equation $x + 5 = \sqrt{5x + 21}$ for $x$. 2. **Recall the formula and rules:** To solve equations involving square roots, isolate the square ro

1. **Stating the problem:** We are given a table of height $y$ in meters versus time $x$ in seconds: $$\begin{array}{c|c}

1. The problem asks to write an equation in the form $y = mx + b$ for the given graph. 2. The graph shows a line passing through the origin $(0,0)$ and points increasing by 20 unit

1. **State the problem:** We need to find a four-digit number $ABCD$ where each digit is a perfect square (0, 1, 4, 9). 2. **Given conditions:**

1. **Problem statement:** We have a rectangular enclosure divided by a fence parallel to two of its sides, using a total of 600 meters of fencing. We want to find the dimensions th

1. The problem states that the 3rd graph is not a function because it passes through 2 points with the same x-coordinate. 2. A function is defined as a relation where each input (x