🧮 algebra

1. **State the problem:** We are given a parabola with vertex at $(-4,-2)$ and a point on the parabola at $(-1,4)$. The parabola opens to the right. We want to find the equation of

1. **State the problem:** We are given two temperature expressions: the temperature at noon is $18 - 2h$ °C and the temperature in the early morning is $12 - h$ °C. We need to find

1. The problem asks to solve an equation using the "labieniez technique." However, there is no problem stated above to apply this technique. 2. To proceed, please provide the speci

1. **Stating the problem:** We are given a parabola with vertex at $ (3, -2) $ and a point on the parabola at $ (-5, -4) $. The parabola opens downward and is symmetric about the v

1. **State the problem:** We are given a linear function $F(x) = 5x + 4$ and two points $x_0 = 3$ and $x_1 = 7$. We want to find the values of the function at these points. 2. **Fo

1. **State the problem:** Subtract the polynomial expressions \((7x+3)-(2x+1)\). 2. **Formula and rules:** When subtracting polynomials, subtract the coefficients of like terms (te

1. **Problem Statement:** Given a hyperbola centered at the origin with equation $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ where $$a^2=9$$ and $$b^2=4$$, find the key points includ

1. **State the problem:** We need to find the value of $k$ such that the quadratic equation $$x^2 - (k + 3)x + 2k = 0$$ has two equal roots. 2. **Recall the condition for equal roo

1. The problem is to solve the equation $$\frac{2x+3}{x-1} = 4.$$\n\n2. We use the property of equations that if $$\frac{A}{B} = C,$$ then $$A = B \times C,$$ provided $$B \neq 0.$

1. **State the problem:** We are given a system of inequalities and points to check, and then asked to graph inequalities and describe graph shapes. 2. **Check points for inequalit

1. **Problem:** Determine if the ordered pair (2, 3) is a solution to the inequality $x + y < 7$. 2. **Formula:** Substitute $x=2$ and $y=3$ into the inequality.

1. **State the problem:** Simplify the expression $x - \frac{1}{x} - \frac{1}{x} + \frac{1}{x} + \frac{1}{x}$ and solve for $x$ if possible. 2. **Simplify the expression:** Combine

1. The first question asks: What do the green dots on the parabola represent? 2. The graph is a red parabola opening upward with vertex below the x-axis and crossing the x-axis at

1. The problem is to solve the equation represented by the red circled math expression. 2. Since the user did not provide the explicit equation, I will assume a common example: sol

1. **State the problem:** Given the function

1. **Problem:** Calculate $-18 \div 3$. 2. **Formula:** Division of integers follows the rule: dividing a negative by a positive gives a negative result, dividing two negatives giv

1. **State the problem:** Rushdi's father is currently five times as old as Rushdi. In three years, the father's age will be four times Rushdi's age. We need to find Rushdi's curre

1. **State the problem:** We need to complete the table for the equation $$y = -x + 1$$ by finding the corresponding $$y$$ values for $$x = -2, 0, 1$$. 2. **Formula used:** The equ

1. **State the problem:** We are given the equation of a line $$y = -x + 1$$ and a table with some values of $$x$$ and corresponding $$y$$ values. We need to complete the table and

1. **State the problem:** We want to understand the graph of the function $h(x) = \frac{2}{x+3} + 5$ and compare it to the original function $f(x) = -\frac{1}{x}$.\n\n2. **Recall t

1. **State the problem:** Solve for $v$ in the equation $$\sqrt{v + 11} - 5 = 2.$$\n\n2. **Isolate the square root term:** Add 5 to both sides to get $$\sqrt{v + 11} = 7.$$\n\n3. *