🧮 algebra

1. **Nêu bài toán:** Cho hàm số $$y = \frac{ax^2 + bx + c}{x}$$ với điều kiện $$ac \neq 0$$.

1. **Problem Statement:** (i) Sketch the graph of the rational function $$y = \frac{-8}{x^2 - 4}$$ and find vertical and horizontal asymptotes, domain, and range.

1. **State the problem:** Solve the system of equations:

1. **State the problem:** Solve the equation $$25^x \times 5^{x+1} = \frac{1}{5^2}$$ for $x$. 2. **Rewrite the bases:** Note that $25 = 5^2$, so rewrite $25^x$ as $\left(5^2\right)

1. **State the problem:** Simplify the expression $$\frac{mk-2k}{3k} \div \frac{m^2 - 4}{6}$$. 2. **Recall the division of fractions rule:** Dividing by a fraction is the same as m

1. **Problem:** Factor $x^2 + 36x$ completely. 2. **Formula:** For factoring expressions like $ax^2 + bx$, factor out the greatest common factor (GCF).

1. **State the problem:** A student starts with $100$ savings and adds $50$ every week. We want to find how much money the student will have after several weeks. 2. **Write the lin

1. **State the problem:** Mr Jashim needs to repair a $2$ km road in $30$ days with an initial budget of $200000$. He hired $20$ workers. After $12$ days, work stopped for $4$ days

1. Problem: Find the selling price, cost price, and markup for the given cases. Formula: Selling Price (SP) = Cost Price (CP) + Markup (M)

1. **State the problem:** Solve the equation $$8 \cdot 13 = -2(3 - 4) + 3y$$ for $$y$$. 2. **Rewrite the equation:** The original equation is $$8 \cdot 13 = -2(3 - 4) + 3y$$.

1. **State the problem:** Evaluate the expression $$- \left(-\frac{2}{3}\right)^2 + \left(\frac{1}{2}\right)^3 \cdot (-1) - \frac{2}{5} \cdot (-2)^3 + \frac{11}{2} - \left(\frac{1}

1. **State the problem:** We want to find the value of the summation $$\sum_{n=1}^5 n$$ which means adding all integers from 1 to 5. 2. **Formula used:** The sum of the first $k$ n

1. The problem is to simplify the fraction $\frac{30}{4000000}$. 2. The formula for simplifying fractions is to divide the numerator and denominator by their greatest common diviso

1. **State the problem:** We want to express the polynomial $X^2+2x-1$ in terms of the given expression involving $A$, $B$, and $C$:

1. **State the problem:** We need to find constants $A$, $B$, and $C$ such that $$x^2 + 2x - 1 = A(x-1)(x+2) + B(x-1)(x+2) + C(x-1)^2(x+2).$$ 2. **Combine like terms on the right s

1. **State the problem:** Factor the quadratic expression $$x^2 + \frac{5}{4}x + \frac{3}{8}$$ completely. 2. **Rewrite the expression to clear fractions:** Multiply the entire exp

1. **State the problem:** Solve the equation $$2 (x + 5) + 4x = x + 25$$ for $$x$$. 2. **Use the distributive property:** Expand $$2 (x + 5)$$ to get $$2x + 10$$.

1. **State the problem:** Solve the equation $$9x + 16 = 6x + 1$$ for $$x$$. 2. **Write the formula and rules:** To solve linear equations, we isolate the variable $$x$$ by perform

1. **State the problem:** Heather needs to find the total feet of lumber required for a ladder with 2 stilts and 12 rungs. Each stilt requires $13$ feet and each rung requires $2$

1. **State the problem:** Justin is using the formula $$\frac{x+y+5}{2}$$ to estimate his adult height, where $x$ and $y$ are his parents' heights. 2. **Given values:** Mom's heigh

1. **State the problem:** We want to find in which situations the information about Tyler can be represented by the expression $$r+3$$, where $$r$$ represents information about Ray