🧮 algebra

1. Problem: Solve the equation $$|x+4| + |3x+3| = |x| + 10$$ and verify the solution. 2. Identify critical points where expressions inside absolute values change sign:

1. Bài toán yêu cầu tính giá trị của định thức $$\Delta=\begin{vmatrix}0 & 2 & 0 \\ m & 0 & -1 \\ 0 & m+1 & 2 \\ 3 & -m & -2 \\ -m & m+1 & 1 \\ m & -1 & 0\end{vmatrix}$$ với tham s

1. **State the problem:** Solve the equation $x + 2 = 6$ for $x$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation. This uses the subtraction pr

1. **State the problem:** Simplify the expression $x + 2(8 + 2)$. 2. **Apply the order of operations:** First, solve inside the parentheses.

1. **Problem:** Fully factorise the quadratic expression $2x^2 + 12x + 18$. 2. **Formula and rules:** To factorise a quadratic expression of the form $ax^2 + bx + c$, first look fo

1. Muammo: Berilgan arifmetik progressiya hadlari $\{a_n\}$ va geometrik progressiya hadlari $\{b_n\}$ uchun shartlar berilgan: $b_1 + b_2 + b_3 = 65$, $b_6 > b_5$, $b_1 - a_1 = 1$

1. **Problem statement:** We have two sequences: an arithmetic progression $\{a_n\}$ and a geometric progression $\{b_n\}$. Given: - $b_1 + b_2 + b_3 = 65$

1. **State the problem:** Find the 5th term of the sequence defined by $T_n = 3n - 2$. 2. **Formula:** The general term of the sequence is given by $T_n = 3n - 2$.

1. **State the problem:** Solve the equation $\frac{26991.5}{x} = 0.025$ for $x$. 2. **Formula and rules:** To solve for $x$ when it is in the denominator, multiply both sides of t

1. **State the problem:** Solve for $x$ in the equation $\frac{25991.5}{x} = 0.025$. 2. **Formula and rules:** To solve for $x$ when it is in the denominator, multiply both sides b

1. **பிரச்சினை:** பொதுஉறுப்பு $T_n = 3n - 2$ எனில், அதன் 5 ஆம் உறுப்பை காண்க. 2. **பொருள்:** பொதுஉறுப்பின் சூத்திரம் $T_n = 3n - 2$.

1. **Nyatakan masalah:** Selesaikan persamaan $$2(k - 1) = -\frac{5}{2}$$. 2. **Gunakan formula dan peraturan:** Kita akan gunakan sifat pengagihan dan operasi algebra asas untuk m

1. **State the problem:** Solve the equation $$-4(p + 5) = 20$$. 2. **Use the distributive property:** Multiply $$-4$$ by each term inside the parentheses.

1. **State the problem:** We are given a polynomial $$P(x) = x^5 + x^2 + ax + b$$ and it is divided by $$x^2 - 1$$. The remainder is $$2x + 3$$. We need to find the values of $$a$$

1. The problem is to understand and apply the Law of Indices (also called the Laws of Exponents). 2. The Law of Indices states rules for simplifying expressions involving powers of

1. The problem asks for the coefficient of $y$ in the expression $5y + 8$. 2. The coefficient of a variable is the numerical factor that multiplies the variable.

1. The problem is to simplify the expression $3x + 4x$. 2. We use the rule that like terms can be added by adding their coefficients. Here, both terms have the variable $x$.

1. Muammo: Berilgan tenglamani yeching. 2. Tenglama va qo'llaniladigan qoidalar: Tenglama ko'rsatilmagan, iltimos, aniq tenglamani taqdim eting.

1. **State the problem:** We have a rectangular garden PQRS with sides QR = 80 m and SR = (5x + 8) m. The garden has grassy areas WSV and TQU, and the rest is a cemented area PTURV

1. The problem asks to graphically represent the functions $f(x) = e^x$ and $f(x) = 2x + 4$ and find the coordinates of their intersection if the second function is a straight line

1. The problem asks to graphically represent the functions $f(x) = e^x$ and $f(x) = 2x + 4$ and find the coordinates of their intersection if the second function is a straight line