🧮 algebra

1. **Stating the problem:** We are given the objective function $$Z = 18x + 10y$$ with a value of $$Z = 134$$ and several points and constraints:

1. **State the problem:** We are given two functions $f(x) = x + 3$ and $g(x) = x - 1$. We need to find the composite function $(fg)(x)$, which means $f(g(x))$. 2. **Formula and ex

1. **State the problem:** We are given two functions $f(x) = x + 3$ and $g(x) = x - 1$. We need to find the product of these functions, denoted as $(f \cdot g)(x)$, and simplify th

1. **State the problem:** We are given two functions $f(x) = x + 3$ and $g(x) = x - 1$. We need to find the function $(f - g)(x)$ and simplify it. 2. **Formula used:** The differen

1. **Énoncé du problème :** Soit $x$ un nombre réel tel que $x < 3$. Montrer que $2x + 3 > -5$ et $\sqrt{x + 13} < 4$.

1. **State the problem:** We are given three expressions involving exponents and asked to find values of $m$ and $n$, and to simplify an expression.

1. **Problem:** Simplify the expression $x^5 \times x^7$ and find the value of $m$ such that $x^5 \times x^7 = x^m$. 2. **Formula:** When multiplying powers with the same base, add

1. The problem is to evaluate the expression $14 - 2 \times 4 + 12$. 2. According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition and subtra

1. **State the problem:** We have a rectangular garden with an area of 40 m². The length and width are whole numbers, and we want to find the smallest possible perimeter. 2. **Form

1. **State the problem:** Find the value of $f(0)$ and find $x$ such that $f(x) = -5$ for the function $f : x \to \frac{1}{2}x - 1$.

1. **Stating the problem:** George takes out a loan with compound interest. We have the loan values at the start, after 1 year, and after 2 years. We need to find: a) The annual in

1. **Stating the problem:** George takes out a loan of £7500 that gathers compound interest. We are given the loan values after 1 and 2 years and need to find:

1. **Problem statement:** There are 1225 students arranged in rows such that the number of rows equals the number of students in each row. We need to find how many students are in

1. **State the problem:** Prove the inequality $$(a+1)(a+2)(a+3)(a+6) > 96a^2.$$\n\n2. **Rewrite the inequality:** We want to show that the product of these four linear terms is gr

1. **Problem statement:** There are 125 students arranged in rows such that the number of rows equals the number of students in each row. We need to find how many students are in e

1. **Problem statement:** There are 125 students arranged in rows such that the number of rows equals the number of students in each row. We need to find how many students are in e

1. **State the problem:** We are given the quadratic equation $$25x^2 + 9 = 30x$$ and asked to compute its discriminant and identify the type of solutions. 2. **Rewrite the equatio

1. **State the problem:** Mr. Chang bought 8 volleyballs and 2 nets for 1460.

1. **Problem Statement:** Evaluate each logarithm expression given. 2. **Formula and Rules:** Recall that $\log_a b = c$ means $a^c = b$.

1. **Problem 1: For the function $f(x) = 2x + 5$** 1. a) The domain of $f(x)$ is all real numbers because there are no restrictions on $x$ in a linear function.

1. **State the problem:** A photograph originally measures 16 cm by 11 cm. It is cropped by removing the same width $x$ cm from the top and left side. The area is reduced by 72 cm²