🧮 algebra

1. **State the problem:** Solve the quadratic equation $x^2 - 4x + 8 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by

1. **State the problem:** Simplify or analyze the quadratic expression $x^2 - 4x + 8$. 2. **Recall the quadratic form:** A quadratic expression is generally written as $ax^2 + bx +

1. **Problem Statement:** Find the value of $a$ if $a^{\sqrt{a}} = (a \sqrt{a})^{a}$. 2. **Formula and Rules:** We use properties of exponents:

1. **Problem statement:** b) Determine which company Mrs. Hanim is likely to hire if she wants the work done within 2 weeks, assuming 7 working days per week and 8 working hours pe

1. **Problem Statement:** Mrs. Hanim wants to find the equations for the total cost $y$ based on the number of hours $x$ for two contractors, A and B.

1. **Problem Statement:** Solve the quadratic equation by middle term breaking. 2. **General Formula:** A quadratic equation is of the form $$ax^2 + bx + c = 0$$.

1. We are given the quadratic expression $16x^2 - 24x + 10$ and want to express it in the form $(4x + a)^2 + b$. 2. Recall the formula for expanding a binomial square: $$(4x + a)^2

1. **State the problem:** Calculate the expression $$(3a+3b+3c)(27a+27b+27c) \div (9bc+9ca+9ab).$$ 2. **Rewrite the expression:** Factor out common terms:

1. **State the problem:** Calculate the expression $$\frac{(3a+3b+3c)(27a+27b+27c)}{9bc+9ca+9ab}$$. 2. **Rewrite the expression:** Factor out constants from each term:

1. **State the problem:** Ben buys 10 books. The first book costs 3. Each subsequent book doubles in price. After the 6th book, each additional book gets a 15% discount. 2. **Defin

1. **Problem:** Find the equation of the line passing through points $A=(1,3)$ and $B=(-2,-3)$. 2. **Formula:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ i

1. The problem is to evaluate the expression given, which appears to be a long, complex, and unclear sequence of numbers and operations. 2. However, the expression contains many sy

1. **Problem Statement:** Determine if the function $f(x)$ described by the plot is one-to-one and onto. Also, find the domain and range of $f(x)$. 2. **One-to-One Function:** A fu

1. **State the problem:** Find the intersection point of the lines given by the equations $$4x - 18 = -3y$$ and $$5x - 2y = 11$$. 2. **Rewrite the equations in standard form:**

1. **Énoncé du problème :** Justifier graphiquement que, pour tout $x \in ]0,+\infty[$, on a $g(x) - h(x) > 0$ avec $g(x) = x^2$ et $h(x) = 2 \ln x - (\ln x)^2$.

1. **State the problem:** Hashim bought maize for 70000 and spent 20500 to convert it into maize flour. He obtained 3 bags of maize flour, each weighing 25 kg. We need to find the

1. **State the problem:** We are given that a number $N$ decreased by 12% equals 132. We need to find the original number $N$. 2. **Write the expression for 12% decrease:** A 12% d

1. The problem is to find the set of values for $x$ such that $x \in \{1, 2\}$ and $x \geq -1$. 2. The set $\{1, 2\}$ means $x$ can only be 1 or 2.

1. נניח כי יש לנו את הטענה: $$\sum_{k=1}^n \frac{k+2}{k(k+1)2^k} = 1 - \frac{1}{(n+1)2^n}$$

1. **Problem statement:** We need to find a whole number $n$ such that the product $n \times (n + 42)$ is a prime number. 2. **Recall the definition of a prime number:** A prime nu

1. **Stating the problem:** We need to sketch the graph of the equation $$2X - y - 3 = 0$$.