🧮 algebra

1. **Problem:** Simplify the expression $(-3x^2 y^3 z)(4x^6 y^2 z^{-4})$. 2. **Formula and Rules:**

1. **State the problem:** Factor the polynomial equation $$-3x^3 + 27x = 0$$. 2. **Identify common factors:** Both terms have a common factor of $$-3x$$.

1. **Problem statement:** Phil earns 10.50 per hour, worked 3 days a week for 7 months (4 weeks each), earned 5300.98 total, spent 64.50 on jeans and 0.9729 on chocolate. Find hour

1. **State the problem:** Jada works a 5-hour shift (300 minutes) and takes a 15-minute break. We want to find what fraction and percentage of her work shift the break represents.

1. **State the problem:** Jada works a 5-hour shift, which is 300 minutes, and takes a 15-minute break. We want to find what fraction of her total work shift the break represents.

1. Énoncé du problème : Montrer que la suite $(U_n)$ définie par $U_n = an + b$, où $a$ et $b$ sont des réels, est une suite arithmétique. 2. Rappel : Une suite $(U_n)$ est arithmé

1. **State the problem:** Logan has read 180 pages, which is 75% of the total pages $t$ in the e-book. We need to find $t$. 2. **Write the equation:** Since 75% means 75 out of 100

1. **Problem statement:** Susan wants to earn 20 dollars for the Charity Jar. She earned 14 one-half dollars, 22 one-fourth dollars, and 11 one-fifth dollars. We need to find out i

1. The problem states that Logon has read 180 pages, which is 75% of the total pages $t$ in the e-book. 2. The equation given is $$\frac{180}{t} = \frac{75}{100}$$ which relates th

1. **State the problem:** We know that 170 students represent 85% of the total number of students in the program. We want to find the total number of students, denoted as $t$.

1. The problem is to solve for $t$ in the proportion $\frac{16}{t} = \frac{80}{100}$.\n\n2. The formula used here is the property of proportions: if $\frac{a}{b} = \frac{c}{d}$, th

1. The problem is to create a table of values for the linear function $$y=\frac{1}{2}x+2$$. 2. The formula is $$y=\frac{1}{2}x+2$$, which means for each value of $x$, multiply by $

1. a. Simplify \frac{m^2 - n^2}{n - m} Step 1: State the problem.

1. **Stating the problem:** Divide the polynomial $2x^4 - 4x^3 - 5x^2 - 5$ by $x^2 + 2$.

1. **State the problem:** Solve the linear equation $2y + x = 6$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to get $y$ alone on one side of the equa

1. **State the problem:** Solve the linear equation $2y - x = 4$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by per

1. **State the problem:** Simplify or understand the expression $4\sqrt{x}$. 2. **Recall the definition:** The square root function $\sqrt{x}$ represents the principal (non-negativ

1. The problem states that Juan and Ivy have the same number of spring rolls for dinner, with each container holding $r$ spring rolls. 2. From the description, Juan has 4 container

1. Zadání problému: Vyřešte rovnici $$2x + 3 = 7$$. 2. Použitá formule a pravidla: Cílem je izolovat proměnnou $x$ na jedné straně rovnice. To znamená, že musíme odstranit konstant

1. **Stating the problem:** We are given the numbers 24 and 48 and asked to find their ratio to 0 and 8 respectively, which means we want to find the ratio $\frac{24}{0}$ and $\fra

1. **Problem statement:** Evaluate $\log_6 54 + \log_6 2 - \log_6 3$. 2. **Formula used:** The logarithm properties we use are: