🧮 algebra

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

1. The problem is to evaluate the function $y = 3 \cdot 5^x$ for $x = 0$. 2. The formula given is $y = 3 \cdot 5^x$. Here, $5^x$ means 5 raised to the power of $x$.

1. Bài toán yêu cầu tìm các giá trị thực của tham số $k$ để phương trình $$x^2 + (k - 1)x + k^2 - 5k + 6 = 0$$ là phương trình bậc hai. 2. Phương trình bậc hai có dạng chung $$ax^2

1. **State the problem:** We need to evaluate the function $$y = 5 \cdot 2^x$$ for $$x = 3$$. 2. **Formula used:** The function is given by $$y = 5 \cdot 2^x$$.

1. **State the problem:** We have two lines, $D_1$ and $D_2$. We know $D_1$ cuts the y-axis at $(0, -5)$ and is parallel to $D_2$ given by $x - 2y - 1 = 0$. We also know $D_1$ cuts

1. **Тодорхойлолт:** Моторт завь A зогсоолоос B зогсоол руу явахдаа хоёр өөр хурдтай явсан үед цагийн зөрүү гарчээ. 2. **Өгөгдөл:**

1. **State the problem:** We need to find the width of a rectangle given its area and length. 2. **Given:**

1. The problem is to divide the fraction $\frac{7}{9}$ by the whole number 3. 2. Recall the rule for dividing fractions: dividing by a number is the same as multiplying by its reci

1. The problem is to solve for $h$ using a different method than previously used. 2. Suppose the original equation is $A = \frac{1}{2}bh$ (area of a triangle), and we want to solve

1. **State the problem:** You are rooting for the Warriors in a 10-game series against the Lakers.