🧮 algebra

1. The problem is to graph the function $g(x) = \frac{1}{4}x^2$ and understand its shape. 2. The formula for a quadratic function is $g(x) = ax^2 + bx + c$. Here, $a = \frac{1}{4}$

1. **State the problem:** The sum of 9 and a certain number is one and a half times the original number. We need to find the number. 2. **Define the variable:** Let the certain num

1. **State the problem:** We have a wall that is a 10 feet by 10 feet square, so its total area is $10 \times 10 = 100$ square feet. 2. A square window with side length $x$ feet is

1. **State the problem:** We are given the area of a rectangular parking lot as $\alpha^2 - 25$ and told the length is longer than the width. We need to factor the area expression

1. **State the problem:** We need to graph the two linear equations $y = 4x - 1$ and $y = -x + 4$. 2. **Recall the slope-intercept form:** The general form of a linear equation is

1. **State the problem:** We need to graph the two linear equations: $$y = -2x - 3$$ and $$y = \frac{3}{2}x + 4$$ on the coordinate plane. 2. **Recall the slope-intercept form:** T

1. The problem is to create 15 similar questions based on a given math topic or problem type. 2. Since no specific topic was provided, I will generate 15 algebraic equation problem

1. **Stating the problem:** We are given several algebraic expressions and equations involving $x$ and $y$, and we want to find the value of $x$ and check the correctness of the st

1. **State the problem:** Solve a quadratic equation by factorization method. 2. **General form:** A quadratic equation is written as $$ax^2 + bx + c = 0$$ where $a \neq 0$.

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$.

1. **Problem statement:** Find the equation of the tangent to the circle $x^2 + y^2 + 2x - 3y + 13 = 0$ at the point $(1, -2)$. 2. **Formula and rules:** The equation of the tangen

1. Problem (a): Simplify $32x^8 \div 8x^{32}$. 2. Use the division rule for exponents: $\frac{a^m}{a^n} = a^{m-n}$.

1. The problem is to understand and work with indices (exponents) in algebra. 2. The basic rule of indices is that for any base $a$ and integers $m$ and $n$:

1. **State the problem:** Simplify the expression $$\left(\frac{27}{8}\right) \times \left(-\frac{4}{3}\right)$$. 2. **Recall the rule for multiplying fractions:** Multiply the num

1. **Stating the problem:** Solve the inequality $$2^{2x+2} < 6^x + 2 \cdot 3^{2x+2}$$. 2. **Rewrite terms with common bases:** Note that $$6^x = (2 \cdot 3)^x = 2^x \cdot 3^x$$ an

1. Vamos analisar o problema: Determinar os valores de $k$ para que a função $f(x) = x^2 + 2x - 3 + k$ tenha dois zeros. 2. A função é um polinômio do segundo grau, e o número de z

1. **State the problem:** Solve the inequality $4x \geq -9$ for $x$. 2. **Recall the rule for inequalities:** When dividing or multiplying both sides of an inequality by a positive

1. **State the problem:** Solve the inequality $$4x \geq -9$$ and graph the solution. 2. **Formula and rules:** To solve inequalities, we isolate the variable by performing inverse

1. **State the problem:** We need to find the Least Common Multiple (LCM) of two numbers given that their product is 2112 and their Highest Common Factor (HCF) is 4. 2. **Recall th

1. **State the problem:** Find the value of $\sqrt{287}$. 2. **Recall the definition:** The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Calculate the value of the expression $(8+2) \times 3 - 8 \times 2 \div 4$. 2. **Recall the order of operations:** Use PEMDAS/BODMAS rules: Parentheses, E