🧮 algebra

1. **State the problem:** We have a rectangular pool where the length is 2 meters shorter than twice its width. We need to write an expression for the perimeter and then find the p

1. **Problem Statement:** We are given the function $y = (3 - 2x)(2 + x)$ and a linear equation $3y - 5x + 6 = 0$. We need to analyze these graphs and solve related questions.

1. **Problem Statement:** We are given data points $(x_i, y_i)$ and want to fit a quadratic model $$y = b_0 + b_1 x + b_2 x^2$$ using the least squares method.

1. **State the problem:** We are given data points for the value of an investment $x$ and the number of years $y$ it took to reach that value. We want to find the logarithmic regre

1. **Exercice N°1** **Problème :** Calculer les termes et la raison d'une suite arithmétique donnée.

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. **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