🧮 algebra

1. **State the problem:** Simplify the expression and solve the equation: $$m - 1 + 2\sqrt{m} + 4 + m - 1 = 1$$

1. **State the problem:** Solve the equation $$\sqrt{5}^{2x-1} = \sqrt{5}^{-1}$$ for $x$. 2. **Recall the property of exponents:** If $a^m = a^n$ and $a > 0$, $a \neq 1$, then $m =

1. **State the problem:** We have a supply function $$S(p) = 0.08p^3 + 2p^2 + 10p + 11$$ and need to find the change in the number of units supplied when the price changes from $$p

1. The problem is to understand the value of $x$ given as $0,11$. 2. In many countries, the comma is used as a decimal separator instead of a period.

1. The problem is to solve the quartic equation $$y^4 + p y^2 + q y + r = 0$$ by reducing it to a cubic equation in $s$. 2. We start by rewriting the quartic as $$\left(y^2 + \frac

1. **Problem Statement:** We are given a quartic equation in $x$:

1. The problem involves solving and simplifying a system of polynomial equations with variables $p$, $q$, $r$, $s$, $t$, and $a$, focusing on cubic equations and their relationship

1. The problem is to verify the transformation and simplification of the quartic equation $$x^4 + b x^3 + c x^2 + d x + e = 0$$ into the depressed quartic form $$y^4 + p y^2 + q y

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x_1 + x_2 + 2x_3 = -1 \\ 2x_1 - x_2 + 2x_3 = -4 \\ 4x_1 + x_2 + 4x_3 = -2 \end{cases}$$

1. **Stating the problem:** We have a polynomial function $f(x) = 5x^5 + bx^4 + cx^3 + dx^2 - 5$ and we know that $x=\frac{1}{2}$ is a root of this polynomial. We want to find the

1. **State the problem:** We have the polynomial function $$F(x) = 5x^5 + 6x^4 + cx^3 + dx - 5$$ and we know that $$x=1$$ is a root of this polynomial. 2. **Use the root condition:

1. مسئلہ: مساوات $[5x - 3] - 2 = 3$ کو حل کریں جہاں $x \in W$ یعنی قدرتی اعداد یا صفر میں سے ہو۔ 2. مساوات کو آسان کریں:

1. The problem asks us to complete the table for the equation $y = 3x$. 2. The formula given is $y = 3x$, which means for each value of $x$, multiply it by 3 to find $y$.

1. **State the problem:** We need to complete the table for the equation $y = x + 3$ by finding the values of $y$ for given $x$ values. 2. **Formula:** The equation is $y = x + 3$.

1. The problem is to evaluate an expression without using a mathematical table. 2. Since the exact expression to evaluate is not provided, I cannot proceed with specific calculatio

1. **Problem a:** Find the equation of the line with slope $m=2$ and y-intercept $b=5$. The general form of a line is $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept.

1. **State the problem:** Solve the equation $x^2 - 5x + 6 = 0$. 2. **Formula used:** For quadratic equations of the form $ax^2 + bx + c = 0$, the solutions are given by the quadra

1. **Énoncé du problème :** Calculer les valeurs des expressions $A = 9 \cdot (7 - x)$ et $B = 4x - 7\frac{3}{2}3\frac{3}{3}$ pour $x = 2$, $x = 0$ et $x = -5$. 2. **Formules et rè

1. The problem is to understand how the values $n=10$ and $n=12$ were calculated. 2. Typically, $n$ represents a number of terms, objects, or elements in a sequence or set.

1. **State the problem:** Solve the system of equations: $$\begin{cases} w+x+y+z=2 \\ 2w - x - y + 2z = 7 \\ 2w + 3x + 2y - z = -2 \\ 3w - 2x - y - 3z = -2 \end{cases}$$

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. The formula we use here is to isolate $x$ by performing inverse operations. Important r