🧮 algebra

1. **State the problem:** Simplify the expression $6 - 6 \times 6 + 6 \div 6$. 2. **Recall the order of operations (PEMDAS/BODMAS):**

1. **State the problem:** Given the equation $(2x - 1) - p(x^2 + 2) = 0$, where $p$ is a constant, we need to show that $2p^2 + p - 1 \leq 0$ for the equation to have real roots, a

1. The problem is to subtract the mixed number $-3 \frac{1}{6}$ from $-4 \frac{3}{4}$ and express the answer in fraction form. 2. First, convert the mixed numbers to improper fract

1. **Problem Statement:** Given the function $f(x) = 3x + 3$, find: (a) the $x$-intercept and $y$-intercept,

1. The problem is to subtract the mixed number $-2 \frac{1}{4}$ from $3 \frac{2}{5}$.\n\n2. First, convert the mixed numbers to improper fractions.\n\nFor $3 \frac{2}{5}$: $$3 \fra

1. **Problem Statement:** Express the given ratios as percentages. 2. **Formula:** To convert a ratio $a:b$ to a percentage, use the formula:

1. **State the problem:** We are given a point $P = \left(x, \frac{2}{3}\right)$ that lies on the unit circle centered at the origin. We need to find the value of $x$ in simplest f

1. **Problem:** Find the determinant of the matrix \(\begin{bmatrix} l & o \\ v & e \end{bmatrix}\). 2. **Formula:** The determinant of a 2x2 matrix \(\begin{bmatrix} a & b \\ c &

1. Diketahui barisan aritmetika dengan jumlah 8 suku pertama $S_8 = 260$ dan suku pertama $a_1 = 5$. 2. Rumus jumlah $n$ suku pertama barisan aritmetika adalah $$S_n = \frac{n}{2}

1. **State the problem:** Tina can till a piece of land in 6 hours, and Tony can do the same in 10 hours. We need to find how long they will take if they work together. 2. **Formul

1. Diketahui barisan aritmetika dengan suku ketiga $a_3 = 10$ dan suku ketujuh $a_7 = 26$. 2. Rumus suku ke-$n$ barisan aritmetika adalah $$a_n = a_1 + (n-1)d$$ di mana $a_1$ adala

1. **State the problem:** Simplify the expression $$(a+1)(a-2)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Determine if the system of equations $$\begin{cases} x + 2y = 8 \\ x - y = 4 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{18x - 200x^3}{40xy^2 - 12y^2}$$. 2. **Identify the formula and rules:** To simplify a fraction, factor numerator and denom

1. The problem is to solve the equation $$6x - 48x^2 = 0$$ and understand how $$x = 2$$ is a solution. 2. Start by factoring the equation:

1. **Problem statement:** Find the turning point and its nature, and the intersection points with the axes for the quadratic function $$y = x^2 - 4x + 3$$.

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations on both sides of the equation.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations to both sides of the equation.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations to both sides of the equation.

1. Diketahui jumlah 10 suku pertama barisan aritmetika $S_{10} = 220$ dan suku pertama $a_1 = 7$. 2. Rumus jumlah $n$ suku pertama barisan aritmetika adalah $$S_n = \frac{n}{2} (2a

1. The problem is to prove the formula for the sum of the arithmetic sequence: $$1 + 5 + 9 + 13 + \dots + (4n - 3) = \frac{n(4n - 2)}{2}$$ 2. This sequence is arithmetic with the f