🧮 algebra

1. **Stating the problem:** We have two arithmetic sequences representing daily targets for two projects over 15 days.

1. **State the problem:** Find the value of $x$ in the equation $$\frac{6^{16} \times 6^{2}}{6^{9} \times 6^{4}} = 6^{x}$$.

1. **Stating the problem:** Simplify the expression $$\frac{12p^4 \times 3q^{-3}}{\frac{18p}{q^5}}$$. 2. **Write the expression clearly:**

1. The problem asks to find the result of the expression: $$\frac{5}{81} \times \frac{3}{8} \times \frac{5}{64} \times \frac{5}{94} \div \frac{1}{27} \times \frac{1}{1}$$

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Simplify and understand the function $f(x) = (x \cdot x^2 + 3x - 1)^3$. 2. **Rewrite the expression inside the parentheses:** Note that $x \cdot x^2 = x^{

1. **Énoncé du problème :** Calculer la valeur de $A = \frac{15}{7} \times \frac{2}{3} \times \frac{11}{5}$ et écrire le résultat sous forme de fraction irréductible. 2. **Formule

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 $y = x + 3$.