🧮 algebra

1. **State the problem:** Solve the quadratic equation $zx^2 + 10z - 24 = 0$ for $x$. 2. **Identify the coefficients:** Here, the quadratic is in terms of $x$, so $a = z$, $b = 0$,

1. **Stating the problem:** We have two functions $f(x) = 2x^2 - x - 1$ and $g(x) = x^2 - 3x + 7$ intersecting at two points $K(a,b)$ and $L(c,d)$. A line $m$ passes through these

1. **State the problem:** Solve the system of equations: $$y = 3x + 2$$

1. The problem asks to list variables and constants in each expression. 2. Variables are symbols that can change values; constants are fixed values.

1. **State the problem:** Find the sum of the first five terms of a geometric series where the first term $a=3$ and the common ratio $r=2$. 2. **Formula used:** The sum of the firs

1. **State the problem:** We are given an arithmetic progression (AP) with first term $a = 28$, common difference $d = -4$, and number of terms $n = 7$. We need to find the $n$th t

1. **State the problem:** Simplify the expression $$\frac{(x-8)^3 (x+8)^4}{(x+8)^5 (x-8)^2}$$. 2. **Recall the rule for dividing powers with the same base:** $$\frac{a^m}{a^n} = a^

1. **State the problem:** Simplify or expand the expression $$(x-8)^3 (x+8)^4$$. 2. **Recall the binomial expansion formula:**

1. The problem asks to find the value that makes an expression undefined. 2. Typically, expressions become undefined when there is division by zero or taking the square root of a n

1. **State the problem:** Simplify the expression $\frac{x - 3}{x(x + 2)}$. 2. **Understand the expression:** The numerator is $x - 3$ and the denominator is $x(x + 2)$.

1. **State the problem:** Find the value of $a^2$ when $a=4$. 2. **Formula used:** The square of a number $a$ is given by $a^2 = a \times a$.

1. Masalah: Tentukan akar-akar dari persamaan kuadrat $x^2 - 5x + 6 = 0$. 2. Rumus yang digunakan adalah rumus kuadrat: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ di mana $a$, $b$,

1. **State the problem:** We need to find the first four terms of an arithmetic progression (AP) where the first term $a=2$ and the common difference $d=4$. 2. **Formula for the $n

1. Diberikan fungsi $f$ dengan sifat $f(x + y) = x + f(y)$ dan nilai $f(0) = 2$. Kita diminta mencari nilai $f(2019)$.\n\n2. Substitusikan $y = 0$ ke dalam persamaan fungsi:\n$$f(x

1. Problem: Find the value of $q$ in the quadratic equation $$x^2 - 8x + q = 0$$ given that the difference between its roots is 2. 2. Formula: For a quadratic equation $$ax^2 + bx

1. The problem is to find the solution and answer for the division $\frac{7}{3.5}$.\n\n2. The formula for division is $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denomi

1. The problem asks to find the reciprocal of 17. 2. The reciprocal of a number $a$ is given by the formula $$\text{reciprocal} = \frac{1}{a}$$

1. **State the problem:** Simplify the expression $k^{10mn} \cdot k^{4} - k^{8} \cdot mn^{\text{power}}$ (assuming the last term is $mn$ to some power, but since it's unclear, we f

1. Stating the problem: We need to find the numbers to fill the boxes in the equation $$\square \times (x + 3) + 7x (2x + 1) = 5x (\square \times x + 5)$$

1. **State the problem:** Simplify the expression $1 \frac{7}{8} \times 2v$. 2. **Convert the mixed number to an improper fraction:**

1. The problem is to solve the equation or expression given before, but now we will explain it in simple words. 2. First, we use the formula or rule that helps us solve this kind o