🧮 algebra

1. **Problem statement:** We have a line segment joining points $P_1(-5, -4)$ and $P_2(3, 4)$, divided into four equal parts. We need to find the point of division nearest to $P_2$

1. **State the problem:** You pay 28.94 each month for your cell phone for two years. We need to find the total cost over these two years. 2. **Formula:** Total cost = monthly paym

1. Masalah: Diberikan barisan bilangan 2, 6, 12, 20, 30, …, kita diminta mencari nilai suku ke-10. 2. Perhatikan pola barisan: suku ke-1 adalah 2, ke-2 adalah 6, ke-3 adalah 12, ke

1. Masalah: Diketahui bilangan $X$ yang mengalami operasi sebagai berikut: dikali 2, ditambah 10, dibagi 2, lalu dikurangi 5, hasil akhirnya adalah 13. Tentukan nilai $X$. 2. Tulis

1. The problem is to find the value of $A$ in the equation $4 + 8 : 2 \times 3 = 10 : 2 \times A + 1$. 2. We use the order of operations (PEMDAS/BODMAS): division and multiplicatio

1. Masalah: Diberikan deretan persegi panjang dengan pola panjang dan lebar sebagai berikut: Panjang: 2, 3, 5, ...

1. The problem is to find the next two terms in the sequence: 4, 8, 8, 6, 12, 4, …, … 2. Let's analyze the sequence step-by-step to identify a pattern.

1. **State the problem:** Solve the system of linear equations: $$10x + 4y = 15$$

1. We are given the system of linear equations: $$8x - 5y = 66$$

1. **Express the following as partial fractions:** $$\frac{9x^2 + 20x - 10}{(x + 2)(3x - 1)}$$

1. Masalah: Diberikan barisan 2, 3, 5, 8, 13, …, tentukan suku ke-10. 2. Perhatikan pola barisan: 2, 3, 5, 8, 13, …

1. **Problem:** Simplify the expression $$\frac{6^3 \times 9^6 \times 3^4}{18^3}$$. 2. **Recall the rules:**

1. **مسئله:** حاصل عبارت $$\frac{3^4 \times 3^3 \times 6^4 \times 6^3}{18^3}$$ را بیابید. 2. **فرمول‌ها و قوانین مهم:**

1. **State the problem:** Evaluate the expression $3 + 3 \times 3 - 3 \div 3 - 2$. 2. **Recall the order of operations (PEMDAS/BODMAS):**

1. **Problem Statement:** Calculate the new price of an item after a 15% increase in the first month, a 20% increase in the second month, and an 8% decrease in the third month, giv

1. **State the problem:** Arrange the ratios 1:2, 3:4, and 4:5 in ascending order. 2. **Convert ratios to fractions:** Ratios can be expressed as fractions for easier comparison.

1. The problem is to understand the inequality $y > -(x-2)^2 + 3$ and describe the region it represents. 2. This inequality involves a quadratic function in vertex form: $y = a(x-h

1. **Problem Statement:** We want to understand how to solve systems of quadratic equations, which are sets of two or more equations where at least one equation is quadratic (degre

1. **State the problem:** Solve the inequality $$(x+4)^2 - 4 < 0$$. 2. **Rewrite the inequality:** Add 4 to both sides to isolate the square term:

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

1. **State the problem:** Factor the expression $3a^4 - 18a^2 b^2 + 3b^4$. 2. **Identify common factors:** Notice each term has a factor of 3, so factor out 3: