🧮 algebra

1. **State the problem:** Simplify the expression $$7 - 2n + 3 + n$$ and then evaluate it at $$n = -2$$. 2. **Combine like terms:** Group the constants and the terms with $$n$$:

1. **Problem:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula:** Use the factorization method or quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ wher

1. Let's start by understanding what a function is. A function is a relation where each input has exactly one output. 2. The general form of a function is $f(x)$, where $x$ is the

1. **Nyatakan masalah:** Diberi jumlah n sebutan pertama bagi janjang geometri $$S_n = \frac{7}{2} (3^n - 1).$$ Cari sebutan pertama $$a$$ dan nisbah sepunya $$r$$. 2. **Formula ju

1. **State the problem:** Simplify the expression $$3y^2 \times (yz)^3$$. 2. **Recall the exponent rules:** When raising a product to a power, apply the exponent to each factor: $$

1. نبدأ بكتابة المعادلة المعطاة: $$\frac{1}{y} = \frac{16}{36}$$ 2. الهدف هو إيجاد قيمة $y$. نستخدم قاعدة التساوي بين الكسرين: إذا كان $$\frac{a}{b} = \frac{c}{d}$$ فإن $ad = bc$.

1. **State the problem:** Calculate the value of the expression $$4^2 \times 2^3 \times 8^2$$. 2. **Recall the base and exponent values:**

1. **State the problem:** You have a car that runs $8$ km per litre of petrol. On a trip, you used $18$ litres. You want to find how much petrol you would have saved if you had dri

1. **State the problem:** We are given two equations representing the prices of reams of A4 and A3 paper: $$3x + 2y = 42$$

1. **Stating the problem:** Solve the system of linear equations: $$x - 5y = -8$$

1. **State the problem:** Divide the polynomial $$5x^3 + x^2 + 18x$$ by $$x + 3$$ using long division.

1. **State the problem:** Find the slope of the line passing through the points $(-2,0)$ and $(-3,-3)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1)$ and $

1. **State the problem:** Find the slope of the line passing through the points $(-2,0)$ and $(-3,-3)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1)$ and $

1. The problem asks to find the square of $17$ raised to the power $t$, which can be written as $(17)^t$ squared. 2. The formula for squaring a power is $\left(a^b\right)^2 = a^{2b

1. **State the problem:** We are given the linear equation $$y=\frac{2}{3}x-4$$ and two points $(0,-4)$ and $(3,-2)$ that lie on the graph. We want to understand the graph and veri

1. **State the problem:** We need to graph the linear function $$y=\frac{2}{3}x-4$$. 2. **Formula and rules:** This is a linear equation in slope-intercept form $$y=mx+b$$ where $$

1. $$2 \times 10^3 - 2 \times 10^3 = 0$$ 2. $$\frac{5^{13}}{2^3 \times 3^5} = \frac{5^{13}}{2^3 \times 3^5}$$

1. **Nyatakan masalah:** Sederhanakan ekspresi eksponen berikut:

1. **State the problem:** We need to graph the linear equation $$y = -x - 6$$. 2. **Formula and rules:** This is a linear equation in slope-intercept form $$y = mx + b$$ where $$m$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 14x + 5y = 31 \\ 2x - 3y = -29 \end{cases}$$

1. **State the problem:** We need to subtract the polynomial $$4f^2 - 12f + 9$$ from $$f^3 - 5f + 25$$.