🧮 algebra

1. **Problem statement:** A manufacturer wants to minimize the cost of producing a cylindrical can with volume 340 cm³.

1. **State the problem:** Find the equation of an ellipse given the center $(1,3)$, one focus $(1,0)$, and one vertex $(1,-1)$. 2. **Recall the standard form of an ellipse equation

1. The problem is to find the equation of the line passing through the points given in the link (assuming points are (2,3) and (4,7) for demonstration). 2. The formula for the slop

1. نبدأ بكتابة المعادلة المعطاة: $$3س^2 + كس + 5 = 0$$ 2. هذه معادلة تربيعية على الشكل العام $$أس^2 + بس + ج = 0$$ حيث $$أ = 3$$ و $$ب = ك$$ و $$ج = 5$$.

1. **State the problem:** We need to determine which fraction is greater: $-\frac{55}{33}$ or $-\frac{24}{33}$. 2. **Understand the fractions:** Both fractions have the same denomi

1. **State the problem:** Find the prime factors of 27. 2. **Recall the definition:** Prime factors are the prime numbers that multiply together to give the original number.

1. **State the problem:** We want to find if there is any other three-digit number where the sum of its digits is 15, the tens digit is 3 more than the ones digit, and the hundreds

1. **State the problem:** We need to find a three-digit number where the sum of its digits is 15, the tens digit is 3 more than the ones digit, and the hundreds digit is 2 less tha

1. **State the problem:** We need to solve the equation:

1. The problem states: Both A and B are 8 times. We need to understand what "8 times" means in this context. 2. If it means A is 8 times some value and B is also 8 times some value

1. Bài toán yêu cầu giải phương trình bậc hai: $$x^2 - 5x + 6 = 0$$. 2. Công thức nghiệm của phương trình bậc hai $$ax^2 + bx + c = 0$$ là $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

1. **State the problem:** Simplify the expression $$\frac{x^{7} \cdot \left(y^{-6} \cdot z^{5}\right)^{2}}{x^{8} \cdot y^{-3} \cdot z^{4}}$$ and write the answer with positive expo

1. **Problem statement:** Find equivalent fractions and simplify fractions using the properties given: Property 1: $-\frac{a}{b} = \frac{-a}{b}$ for $b > 0$.

1. **Problem:** Express $3 - 12x - 2x^2$ in the form $ax^2 + bx + c$ and find the turning point of the curve $y = 3 - 12x - 2x^2$. 2. **Rewrite the quadratic:** The standard form o

1. **State the problem:** We need to simplify and solve the equation:

1. **State the problem:** Multiply and simplify the expression $$(5x - 3\sqrt{3})(5x + 3\sqrt{3})$$. 2. **Recall the formula:** This is a product of conjugates, which follows the d

1. **Problem:** Given the algebraic expression $$4x^2 - 3x + 2x^2 - 7x - 5$$ 2. **Step 1: Identify the terms (Suku-suku) in the expression.**

1. **State the problem:** Find the values of $a$ and $b$ for the cubic polynomial $f(x) = 3x^3 + ax^2 + x + b$ given that $x + 1$ is a factor of $f(x)$ and when $f(x)$ is divided b

1. Solve the system \(y = 3x - 5\) and \(5x + 4y = -3\). Substitute \(y\) from the first equation into the second:

1. **State the problem:** Determine the relationship between the lines given by the equations: $y = 3x - 5$

1. **State the problem:** Solve the first system of linear equations: $$y = 3x - 5$$