🧮 algebra

1. সমস্যা: একটি সরল রৈখিক সমীকরণ সমাধান করুন, যেমন $2x + 3 = 7$। 2. সূত্র: সরল রৈখিক সমীকরণের সাধারণ রূপ হল $ax + b = c$, যেখানে $a$, $b$, এবং $c$ ধ্রুবক। সমাধানের জন্য, $x$ কে একপ

1. Diberikan matriks-matriks berikut dan persamaan: $$\begin{bmatrix} a - 1 & b \\ 1 & 1 \end{bmatrix} \begin{bmatrix} a & b \\ 2 & 2 \end{bmatrix} = \begin{bmatrix} 2 & c \\ d & 3

1. **Problem:** Determine if $g(x) = \frac{x^2 + 6x + 8}{x + 4}$ is continuous at $x = -4$. 2. **Formula and rules:** A function is continuous at $x = a$ if:

1. **Problem statement:** We have two amounts with interest over 5 years: 28000 and 40000. We need to find:

1. **State the problem:** Simplify the expression $6 - \frac{4^2}{6} + 4^2$. 2. **Recall order of operations:** We must evaluate exponents first, then division and multiplication f

1. **Problem:** Suppose you have two quantities, A and B, and their ratio is given as 3:4. If the total of A and B is 56, find the values of A and B. 2. **Formula and Rules:** The

1. Montrons que pour tout $x \in \mathbb{R}^-_*$, on a $x + \frac{1}{x} \leq -2$. 2. Soit $x < 0$. Posons $x = -t$ avec $t > 0$. Alors

1. **Problem statement:** In the binomial expansion of $ (1 + kx)^6 $, the coefficient of $ x^3 $ is twice the coefficient of $ x^2 $. Find $ k $. 2. **Formula:** The general term

1. **State the problem:** We need to find the value of the expression $$-1 \cdot f(-8) - 4 \cdot g(4)$$ given the graphs of functions $f(x)$ and $g(x)$.\n\n2. **Find $f(-8)$:** Loc

1. **State the problem:** Simplify or factor the quadratic expression $12m^2 + m - 90$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two number

1. **State the problem:** Solve the inequality $5x + 3 > 2x - 7$. 2. **Recall the rule:** To solve inequalities, we isolate the variable on one side. When adding or subtracting ter

1. The problem is to simplify or analyze the expression $x^2 - 4x + 24$. 2. This is a quadratic expression in the form $ax^2 + bx + c$ where $a=1$, $b=-4$, and $c=24$.

1. **State the problem:** Solve the inequality $\frac{1}{2}x - 1 < 3$. 2. **Formula and rules:** To solve inequalities, we isolate the variable on one side. Remember, when multiply

1. **State the problem:** Solve the linear inequality $$-2x + 6 \ge 2$$. 2. **Recall the rule:** When solving inequalities, if you multiply or divide both sides by a negative numbe

1. **State the problem:** Factor the quadratic expression $x^2 - 24x + 63$ into the form $(x - a)(x - b)$. 2. **Recall the factoring formula:** For a quadratic $x^2 + bx + c$, the

1. **State the problem:** Factor the quadratic expression $x^2 - 24x - 63$ into the form $(x - a)(x - b)$. 2. **Recall the factoring formula:** For a quadratic $x^2 + bx + c$, fact

1. **State the problem:** Factor the quadratic expression $$x^2 - 24x = 63$$ into the form $$(x - a)(x - b)$$. 2. **Rewrite the equation:** Move all terms to one side to set the eq

1. **State the problem:** We are given the function $h(x) = 4x$ and asked to find $h(3)$. 2. **Formula used:** The function $h(x)$ means for any input $x$, the output is $4$ times

1. **State the problem:** We are given the function $f(x) = 2x - 3$ and asked to find $f(0)$. 2. **Recall the function evaluation rule:** To find $f(a)$ for some value $a$, substit

1. **State the problem:** We are given the function $g(x) = x^2 - 3x$ and asked to find $g(2)$. 2. **Formula and explanation:** To find $g(2)$, substitute $x = 2$ into the function

1. **State the problem:** Solve the equation $2x - 10 = 3(x - 10)$. 2. **Write down the formula and rules:** We will use the distributive property and properties of equality to iso