🧮 algebra

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

1. Problem: Mamy funkcję $f(x)$ i chcemy zrozumieć, co się dzieje z wykresem funkcji, gdy mamy wyrażenie $f(x+1) - 2$. 2. Reguły przesunięć wykresu funkcji:

1. **Problem:** The length of a rectangle is twice the width. The perimeter is 20 cm. Find the width. 2. **Formula:** The perimeter $P$ of a rectangle is given by $$P = 2(\text{len

1. **Problem Statement:** Evaluate the following matrix expressions and find the values of variables $x$, $y$, and $z$ given matrices $M$, $A$, and $B$.

1. **Problem:** Given the point (1, 2) lies on the graph of $y=2^x$, find the corresponding point on the graph of $y=3x^2 - 7x + 18$. 2. **Formula:** To find the corresponding poin

1. **State the problem:** We have revenue function $R(x) = 110x$ and cost function $C(x) = 60x + 7500$, where $x$ is the quantity sold.

1. **State the problem:** Joshua covers a floor of area 45 m² with tiles. He buys one box of tiles for every 1.5 m², each box costs 64, and he buys 5 bags of adhesive at 12 each. H

1. **State the problem:** We want to find an approximate root of the equation $$\sin(x) = x^2 - 1$$ using Newton's method. 2. **Rewrite the equation:** Define a function $$f(x) = \

1. Problem: If the point (3,4) lies on the graph of the equation $3y = ax - 7$, find the value of $a$. 2. Substitute $x=3$ and $y=4$ into the equation:

1. **State the problem:** Solve the equation $$\frac{5 - 2x}{6} = 3x - 4$$ for $x$. 2. **Multiply both sides by 6** to eliminate the denominator: