🧮 algebra

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

1. **State the problem:** Solve the system of inequalities by graphing: $$y \leq \frac{1}{10}x + 6$$

1. **Stating the problem:** We want to find the sum $S_5 = b_1 + b_2 + b_3 + b_4 + b_5$ where the terms are given as $b_k = (-3)^{k-1}$ for $k=1$ to $5$. 2. **Formula used:** This

1. **Problem statement:** Find the general term formula $b_n$ of a geometric progression satisfying the condition $b_4 + b_2 = 20$. 2. **Recall the general term of a geometric prog

1. **Problem statement:** Factor the following expressions from problems 7 to 11, parts а to к. ---

1. Зөвхөн 7-11 дугаар бодлогуудыг товч аргаар бодох болно. 2. 7. а) $x^5 - x^3 + x^2 - 1$

1. Бодлого: 7-11 хүртэлх бодлогуудыг долоон томёогийн аргаар бодно. 2. Томёо 1: Тэгшитгэлийг тэгшитгэлийн дүрмээр задлах, жишээ нь: $a^2 - b^2 = (a-b)(a+b)$.

1. The problem is to understand the value of $\alpha$ given as $30$.\n\n2. Here, $\alpha$ is a variable, often used to represent an angle in degrees or radians.\n\n3. Since $\alpha

1. The problem is to factor and simplify the given polynomial expressions from problems 2 to 10. 2. We use common factoring techniques such as:

1. Тодорхойлолт: 6 дугаар бодлогын а)–ж) хэсгүүдийг долоон томёогийн аргаар хялбаршуулна. 2. Томёо:

1. The problem asks for the expected total value of donations when the charity received 60 donations, based on the given graph. 2. From the graph, the expected value of donations i

1. **Тодорхойлолт:** 6 дугаар бодлогын а), в), д), ж), з), б), г), е) томёогийн аргаар бодно. 2. **Томёо ба дүрэм:** Томёогийн аргаар бодохдоо дараах томёог ашиглана:

1. The problem is to solve the equation $$\frac{2x+3}{x-1} = 4.$$\n\n2. We use the property that if $$\frac{a}{b} = c,$$ then $$a = bc,$$ provided $$b \neq 0.$$\n\n3. Multiply both