🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{6x^2+23x+20}{8x^2+20x} \div \frac{3x^2-23x-36}{x^2-18x+81}$$ 2. **Rewrite division as multiplication:**

1. **State the problem:** Simplify or analyze the quadratic expression $x^2 + 42x + 13$. 2. **Formula and rules:** To factor a quadratic expression of the form $ax^2 + bx + c$, we

1. **Problem 2:** Simplify $$\frac{15x + 3}{x(x - 4y) + 4y^2} \cdot \frac{3x - 6y}{5x + 1}$$ 2. **Step 1:** Factor all expressions where possible.

1. **State the problem:** We need to find the quadratic function with x-intercepts at $-2$ and $3$, and y-intercept at $-12$. 2. **Recall the form of a quadratic function given roo

1. **Nyatakan masalah:** Kita diminta mencari koefisien $a$ dan $b$ dari persamaan $$(x^2+1)(x+a) - 12 = (x-1)(x-2)(x-3) + 10x^2 - 10x - 2$$

1. The problem states that the value of $A$ is given as $2$. 2. Since the value is directly provided, no further calculation is needed.

1. **State the problem:** Find all factors of the number $36$. 2. **Recall the definition:** Factors of a number are integers that divide the number exactly without leaving a remai

1. **State the problem:** We are given the equation $$X + X = 24$$ and need to find the value of $X$. 2. **Write the equation:** $$X + X = 24$$

1. The problem is to solve or analyze the expression or equation involving $B$. 2. Since the user only mentioned $B$ without additional context, we assume $B$ is a variable or part

1. **State the problem:** We want to show that by substituting $p = 2^x$, the equation

1. **State the problem:** We need to find the sum of the fractions $\frac{5}{14}$ and $\frac{6}{9}$. 2. **Formula and rules:** To add fractions, they must have a common denominator

1. **State the problem:** We need to graph the parabola given by the equation $$y = \frac{1}{4} x^2$$ and plot five points: the vertex, two points to the left, and two points to th

1. **Problem:** You save $2000$ in week one and increase your deposit by $400$ each week. Find the total saved after $20$ weeks. 2. **Formula:** This is an arithmetic series where

1. **Solve the equation** $11y - 2 = 10y + 4$. 2. Start by isolating $y$ on one side.

1. **Planteamiento del problema:** Resolver una función cuadrática significa encontrar los valores de $x$ que satisfacen la ecuación cuadrática general $$ax^2 + bx + c = 0$$ donde

1. **State the problem:** We are given an arithmetic sequence with some missing terms: $$\square, -33, -19, \square, \square, ...$$ 2. **Recall the formula for an arithmetic sequen

1. **State the problem:** Find the equation of line H in the form $y = mx + c$. 2. **Identify given information:** The line crosses the y-axis at $10$, so $c = 10$.

1. The user is asking if there is another equation similar to a given one, but no specific equation was provided. 2. To help, we need an example equation or context to suggest alte

1. **State the problem:** We have a farm with chickens and cows. The total number of animals is $23$, and the total number of legs is $56$. We want to find how many chickens and co

1. Diberikan lingkaran dengan persamaan $$x^2 + y^2 + 2x - 8y + 9 = 0$$ dan titik singgung $$ (1, 2) $$. 2. Kita ingin mencari persamaan garis singgung lingkaran di titik tersebut.

1. **State the problem:** We want to model Miguel's savings taken from a piggy bank containing two types of coins: ₱10-coins and ₱20-coins.