🧮 algebra

1. Le problème est de factoriser une expression algébrique donnée. 2. La factorisation consiste à écrire une expression sous forme d'un produit de facteurs plus simples.

1. **State the problem:** We are given the proportion $$\frac{576}{512} = \frac{a}{32}$$ and need to solve for $a$. 2. **Formula used:** In a proportion $$\frac{x}{y} = \frac{m}{n}

1. Let's start by understanding the problem: you want to know why the answer to a WAEC question is $\frac{11}{2}$. Without the exact question, I'll explain a common scenario where

1. We are given the proportion $$\frac{14}{32} = \frac{r}{80}$$ and need to solve for $r$. 2. The formula for solving proportions is to cross multiply: $$a/b = c/d \implies ad = bc

1. **State the problem:** Solve for $d$ in the proportion $$\frac{d}{7} = \frac{42}{49}$$. 2. **Recall the rule for proportions:** If $$\frac{a}{b} = \frac{c}{d}$$, then the cross

1. **State the problem:** Solve for $n$ in the proportion $$\frac{n}{98} = \frac{20}{35}$$. 2. **Formula and rule:** In a proportion $\frac{a}{b} = \frac{c}{d}$, the cross products

1. **State the problem:** We need to solve for $y$ in the proportion $$\frac{48}{72} = \frac{y}{69}$$. 2. **Formula used:** In proportions, if $$\frac{a}{b} = \frac{c}{d}$$, then $

1. The problem is to solve for $v$ given the equation $5 = \frac{30}{50} v$. 2. The formula used here is to isolate $v$ by multiplying both sides of the equation by the reciprocal

1. **State the problem:** Solve for $p$ in the proportion $$\frac{15}{25} = \frac{21}{p}.$$\n\n2. **Recall the property of proportions:** If $$\frac{a}{b} = \frac{c}{d},$$ then the

1. **State the problem:** Simplify the expression $$36\frac{1}{2} \times 64 - \frac{1}{3} \times 5^0$$. 2. **Recall important rules:**

1. Énoncé du problème : Comparer les deux nombres $A = \frac{n+2}{n+3}$ et $B = \frac{n+3}{n+4}$ où $n$ est un entier naturel.

1. **Problem Statement:** Prove that if $$ (1 + x)^n \geq 1 + nx $$ for $$ x > -1 $$ and $$ n \in \mathbb{N} $$, then $$ (1 + x)^{n+1} \geq 1 + (n + 1)x $$.

1. **State the problem:** Lauren starts with 25 gallons in her truck's gas tank. The pump fills the tank at 35 gallons per minute. We want to write an equation for the amount of ga

1. **State the problem:** Simplify the expression $$\frac{n+2}{n+3} - \frac{n+3}{n+4}$$. 2. **Formula and rules:** To subtract two fractions, find a common denominator and then sub

1. **Stating the problem:** We are given several polynomials and asked to factor them or determine if they are factorable using the difference of squares pattern. We also need to i

1. **State the problem:** Find the slope of the line passing through the points $(-2, -3)$ and $(1, 3)$. 2. **Formula for slope:** The slope $m$ of a line through two points $(x_1,

1. **State the problem:** Find the slope of the line passing through the points $(7, -4)$ and $(4, -6)$. 2. **Formula for slope:** The slope $m$ of a line passing through points $(

1. **State the problem:** Calculate the value of the expression $7 \times 0.007 \times \sqrt{0.0435}$.\n\n2. **Recall the formula and rules:**\n- Multiplication of decimals is stra

1. **State the problem:** Evaluate the expression $9 \circ 0.4 \sqrt{0.019}$ where $\circ$ denotes multiplication. 2. **Recall the formula:** Multiplication is associative and comm

1. **State the problem:** We are given the linear equation $y = -\frac{1}{3}x + 6$ and want to understand its properties such as slope, y-intercept, and x-intercept. 2. **Formula a

1. **Problem statement:** We are given the arithmetic sequence: $-4, -10, -16, -22, \ldots$ and need to find the explicit formula for the $n^{th}$ term $a_n$. 2. **Formula for arit