🧮 algebra

1. Problem 4a: Write a system of linear inequalities for the theater ticket sales. Let $x$ be the number of adult tickets and $y$ be the number of youth tickets.

1. **Problem Statement:** Given two functions $f(x) = 7x + 1$ and $g(x) = 5x + 8$, find the composite functions $(f \circ g)(x)$ and $(g \circ f)(x)$. 2. **Formula and Explanation:

1. **Problem 1:** Complete the sequence where each term is of the form $\text{number} \times 8 + \text{digit}$. 2. **Observation:** The pattern shows that multiplying the number fo

1. Problem 17: Given the operation $a \otimes b = \frac{a^2}{b}$ for all nonzero numbers, find $$[(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)].$$ 2. Use the definition of t

1. **تحليل العبارات الجبرية:** - العبارة الأولى: $E=5a-10$

1. Let's clarify the problem: you mentioned "the equation above," but no specific equation was provided in this message. 2. Please provide the exact equation or problem statement y

1. Let's clarify the problem: You mentioned that the equation is "the other way round," meaning the denominator becomes the numerator and vice versa. 2. Suppose the original equati

1. **State the problem:** Given the equation $\frac{x}{y} = 2.5$, find the values of $x$ and $y$. 2. **Understand the equation:** The equation $\frac{x}{y} = 2.5$ means that $x$ is

1. **Problem Statement:** We are exploring the discriminant (Δ) of a quadratic equation and its implications on the roots and graph of the equation. 2. **Definition and Formula:**

1. **Problem Statement:** Solve each system of linear equations using the matrix method, i.e., express as $AX = B$ and find $X = A^{-1}B$ if $A$ is invertible. 2. **Matrix Method F

1. **Problem statement:** (a) A squash club has 27 members. 19 have black hair, 14 have brown eyes, and some have both black hair and brown eyes.

1. **Problem:** Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin? 2. **Problem:** Which of these numb

1. **State the problem:** A gardening service charges a base fee of 45 plus 16 for each hour of work. The total cost is 253. We need to find the number of hours $h$ worked. 2. **Wr

1. The problem asks us to find the number of hours, denoted as $$h$$, that the gardener works on the job. 2. To solve this, we need a relationship or equation involving the number

1. **State the problem:** A taxi charges a flat rate of $10$ plus $2$ for each kilometre driven. The total cost of the ride was $100$. We need to find the number of kilometres, $k$

1. **Problem Statement:** A rectangular lawn measures 12 m by 10 m and is surrounded by a uniform walkway of width $x$ meters on all sides. The total area of the lawn plus the walk

1. **State the problem:** Solve the equation $2(x + 19) = 78$ for $x$. 2. **Recall the distributive property:** $a(b + c) = ab + ac$. This helps us expand expressions.

1. Problem 32(a): An arithmetic progression (AP) has $n$ terms with the $n$th term $a_n = 4$ and common difference $d = 2$. The sum of $n$ terms $S_n = -14$. Find $n$ and the sum o

1. **State the problem:** Factorize the expression $$a^4 + 64b^4$$. 2. **Recall the formula:** This is a sum of two fourth powers. We can use the sum of squares and difference of s

1. **State the problem:** The product of 5 and an unknown number $u$ is 40. 2. **Write the equation:** Using $u$ as the unknown number, the word statement translates to the equatio

1. The problem states: The product of 5 and an unknown number is 40. 2. Let the unknown number be $u$.