🧮 algebra

1. **Problem Statement:** We have a point $M$ on the parabola given by the equation $$y = \frac{1}{2}x^2 - 2x + 3.$$ We draw perpendiculars from $M$ to the $x$-axis and $y$-axis, f

1. نعتبر الدالة $f(x) = ax + \beta$ حيث $a$ و $\beta$ أعداد حقيقية. 2. لحساب المتبوع عند النقطة $(0,1)$ نعوض $x=0$ في الدالة:

1. We are given the function $F(x) = \frac{1}{\sqrt{3x^3}}$. Our goal is to simplify and understand this function. 2. Rewrite the square root in the denominator as an exponent: $$F

1. The problem is to understand and work with the linear equation $x + 2y = 14$. 2. This is a linear equation in two variables, $x$ and $y$, representing a straight line.

1. The problem statement is not provided clearly, so I will assume you want a generic algebraic equation solved. 2. To solve an equation such as $ax^2 + bx + c = 0$, use the quadra

1. Stating the problem: Solve the equation $x + 2y = 14$ for $x$ in terms of $y$. 2. Isolate $x$ on one side of the equation by subtracting $2y$ from both sides:

1. The problem asks to graph three different functions and determine several properties: x-intercepts, y-intercepts, domain, range, maxima or minima, and the number of solutions. 2

1. The problem asks to graph three different functions and analyze each for intercepts, domain, range, extrema, and number of solutions. 2. Since no specific functions were given,

1. **State the problem:** Simplify the expressions $6 \sqrt{48}$ and $3 \sqrt{36}$ without leaving remainders. 2. **Simplify $6 \sqrt{48}$:**

1. Simplify $\frac{36}{60}$: Find the gcd of 36 and 60, which is 12.

1. The problem is to understand how to teach conic sections effectively. 2. Conic sections are the curves obtained by intersecting a plane with a double-napped cone.

1. We are asked to solve the equation \( f(x) = 0 \). 2. To find \( x \) such that \( f(x) = 0 \), we set the function equal to zero and solve for \( x \).

1. We are given a polynomial defined by its roots: $1 - 7i$, $1 + 7i$, $4i\sqrt{3}$, and $-4i\sqrt{3}$. We want to find the explicit form of the polynomial $f(x)$. 2. Recall that i

1. State the problem: We need to estimate the value of $\sqrt{4.92} + 2.18 \times 7.31$. 2. Estimate $\sqrt{4.92}$: Since $\sqrt{4.92}$ is close to $\sqrt{4.9}$, and $\sqrt{4.9}$ i

1. The problem is to find the slope-intercept form of a line given the slope and the y-intercept. 2. The slope-intercept form of a line is given by: $$y = mx + b$$ where $m$ is the

1. **State the problem:** Identify the slope-intercept form $y = mx + b$ of a line passing through the points (0, 2), (1, 3), and (2, 4). 2. **Find the y-intercept ($b$):** From th

1. The problem gives a polynomial $$f(x) = x^4 - 2x^3 + 48x^2 + 4x - 100$$ and states that $$1 - 7i$$ is a zero. 2. Since the polynomial has real coefficients, its complex conjugat

1. The problem asks to write the equation of a line in slope-intercept form, which is $$y = mx + b$$

1. The problem is to evaluate the expression $\sqrt{4.92} + 2.18 \times 7.31$.\n\n2. First, calculate the square root: $\sqrt{4.92}$. Using a calculator or estimation, $\sqrt{4.92}

1. The problem asks to find the slope-intercept form of a line given the slope $m=4$ and a point $(2,10)$ on the line. 2. Recall the slope-intercept form of a line is given by: $$y

1. Problème : Expliquons la transition entre $$\frac{10(4 - 3x - x^3)^4 (x^2 + 2x - 1)^4 (x + 1) + 12(x^2 + 2x - 1)^5 (4 - 3x - x^3)^3 (x^2 + 1)}{(4 - 3x - x^3)^8}$$