🧮 algebra

1. Let's start by understanding what fractions are. A fraction represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator (top number) and $b$ is the d

1. The problem asks us to plot the point $(-5.5, 2.5)$ on a Cartesian coordinate grid. 2. An ordered pair $(x, y)$ represents a point where $x$ is the horizontal coordinate and $y$

1. The problem asks us to plot the point $(-5.5, 2.5)$ on a coordinate plane. 2. Recall that an ordered pair $(x, y)$ represents a point where $x$ is the horizontal coordinate and

1. **Problem Statement:** In a college, 120 students have access to three software packages P, Q, and R. Given data: - 25 students used none of the packages.

1. **Problem Statement:** We need to determine whether the given expressions are surds by simplifying them fully.

1. مسئله: معادله $$0 = 15 - 9x + 3x^2 - 3x^3$$ داده شده است و یکی از ریشه‌های آن $$x=17$$ است. باید ریشه‌های دیگر معادله را پیدا کنیم. 2. ابتدا معادله را مرتب می‌کنیم به صورت استان

1. **State the problem:** Solve the equation $$\frac{12x + 28}{4} - \frac{8}{13} = r(x - 8)$$ for $r$ given the line passes through points $(0,7)$ and $(8,0)$.\n\n2. **Understand t

1. **State the problem:** Solve for $x$ in the equation given or implied. 2. **Identify the equation:** Since no specific equation is provided, let's consider a general linear equa

1. **State the problem:** Simplify the expression $$\frac{12x + 28}{4} - \frac{8}{13} = r(x - 8)$$ and solve for $r$ if possible. 2. **Rewrite the expression:** The left side has t

1. **State the problem:** Solve for $s$ in an equation involving $s$ (the exact equation is not provided, so we will demonstrate a general approach). 2. **General formula and rules

1. **Problem Statement:** Determine whether the slope of each line is positive, negative, zero, or undefined based on the given descriptions. 2. **Recall the slope formula:** The s

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x}{\sqrt{3x - x}}$$. 2. **Simplify the expression inside the square root:**

1. **Problem Statement:** In a college, 120 students have access to three software packages P, Q, and R. 25 students used none of the packages. 14 used only P, 22 used only Q, 11 u

1. **Problem Statement:** Solve for $k$ or $t$ in each given exponential equation. 2. **Key Formula:** For equations of the form $e^{ax} = b$, take the natural logarithm on both si

1. Problem 49: Solve for $y$ given $\ln y = 2t + 4$. 2. Recall that if $\ln y = A$, then $y = e^A$.

1. **State the problem:** Find the vertex, focus, and directrix of the parabola given by the equation $$y^2 - 4y - 16x + 52 = 0.$$\n\n2. **Rewrite the equation and complete the squ

1. **State the problem:** We have two algebraic expressions:

1. **Express logarithms in terms of $\ln 2$ and $\ln 3$** Recall the properties of logarithms:

1. **Énoncé :** Soit $P(X) = 3X^3 - 2$, $Q(X) = X^2 + X - 1$, $R(X) = aX + b$. Calculer $P + Q$, $P \times Q$, $(P + Q) \times R$ et $P \times Q \times R$. Trouver $a$ et $b$ pour

1. **State the problem:** Solve the equation $6^a - 6^b = 1260$ for $a$ and $b$. 2. **Recall the properties of exponents:** For any real numbers $x$, $y$, and base $c > 0$, $c^x -

1. **State the problem:** Solve the equation $$16^x + 16^x = 4^x$$ for $x$. 2. **Rewrite the bases as powers of 2:**