🧮 algebra

1. **Énoncé du problème :** Montrer que la somme

1. The problem asks for the change in temperature when the temperature drops from -2 to -4 degrees. 2. To find the change in temperature, subtract the final temperature from the in

1. Let's state the problem: We want to analyze the expression $$\frac{2n^2 - 3}{n^2 + 3}$$ and explain why this expression is limited (bounded). 2. First, observe the expression's

1. Problem statement: Jawad has two fish tanks, one larger and one smaller. The smaller tank initially has 35 fish.

1. State the problem: Find the number $x$ such that when it is added to 5, the result is the same as when $\frac{2}{3}$ of it is subtracted from 6. 2. Set up the equation based on

1. **State the problem:** Matt and Ming sold small and large boxes of oranges at a fundraiser. Matt sold 3 small and 14 large boxes for 203, and Ming sold 11 small and 11 large box

1. **State the problem:** We need to find the length and width of a rectangle given that its perimeter is 152 meters and the width is 22 meters less than the length. 2. **Define va

1. We are given the expression $$\frac{2^n}{3 - 2^{-n}}$$ and asked to find its smallest term. 2. First, rewrite the expression for clarity:

1. The problem asks us to find all factors of 40. 2. A factor of a number is any integer that divides that number exactly without leaving a remainder.

1. We start with 240 loaves of bread at the beginning of Monday. 2. On Monday, the bakery sold $\frac{1}{4}$ of the loaves, so the number of loaves sold is:

1. The problem is to find all multiples of 5 that are less than 51. 2. Multiples of 5 are numbers that can be written as $5n$, where $n$ is a positive integer.

1. **State the problem:** We need to solve the equation $$\frac{1}{3} - 4 = \frac{T}{5} + 1$$ for the variable $T$. 2. **Simplify the left side:** Convert $4$ into a fraction with

1. We need to expand the expression $ (4x + 5y)^2 $. 2. Recall the identity for the square of a binomial: $ (a+b)^2 = a^2 + 2ab + b^2 $.

1. We need to find the smallest term of the expression $$2n + \frac{512}{n^2}$$ where $n$ is a positive real number. 2. To find the minimum value, we take the derivative of the exp

1. **State the problem:** Express the numbers 16 and 14 as powers or combinations of base 2. 2. **Express 16 with base 2:**

1. We are asked to determine if the given statements are TRUE or FALSE and justify the answers. (i) Distance between points $(3x, -3x)$ and $(-x, -6x)$ is $-5x$ if $x<0$.

1. We are asked to factorize the quadratic expression $6t^2 - 7t - 20$. 2. First, multiply the leading coefficient and the constant term: $6 \times (-20) = -120$.

1. The problem is to find the smallest value of the expression $3n^2 - 10n - 14$ for integer values of $n$. 2. This is a quadratic expression in standard form $an^2 + bn + c$ with

1. State the problem: Solve the equation $$\frac{7x - 6}{x - 18} = -\frac{2}{3}$$ for $x$. 2. Cross-multiply to eliminate the fractions:

1. **Problem Statement:** Find the smallest term of the expression $$\frac{2^2}{n^2}$$ where $n$ is a variable. 2. **Rewrite the expression:** The expression simplifies as $$\frac{

1. The problem involves simplifying or evaluating the expression for "3 multiple (-2 -1)", which can be interpreted as multiplying 3 by the sum of -2 and -1. 2. Calculate the sum i