🧮 algebra

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

1. Let's start by understanding the problem you want to solve. Since you didn't specify, I'll explain how to solve a simple algebra problem step-by-step, like an 8th grader would.