🧮 algebra

1. **State the problem:** Simplify and understand the expression for $J$ given by $$J=\frac{-(d - m_2) \pm \sqrt{(d - m_2)^2 - 4 \left(\frac{1}{k}\right) \left(b \times \frac{y m_3

1. **State the problem:** We need to verify if $x=\frac{1}{2}$ is a root of the polynomial $$P(x) = 3x + 2x + 5 = 0.$$\n\n2. **Simplify the polynomial by combining like terms:** $$

1. **State the problem:** We have three functions: $$ f(x) = \frac{4x+5}{1-2x}, \quad g(x) = 3x + 5, \quad h(x) = px^2 + q - 1 $$

1. The problem is to verify if $x=\frac{1}{2}$ is a root of the polynomial $P(x) = 3x + 2x + 5 = 0$.\n\n2. First, simplify the polynomial by combining like terms: $$P(x) = 3x + 2x

1. Stated problem: Solve the equation $4x - 7 = 9 - x$ for $x$. 2. Add $x$ to both sides to collect the $x$ terms on the left: $$4x + x - 7 = 9$$ which simplifies to $$5x - 7 = 9$$

1. Simplifica el siguiente cociente de potencias y expresiones: $$\frac{(8x^{3} y^{-2})^{\frac{2}{3}}}{(2x^{-1} y)^{2}}$$

1. **State the problem:** We are given the polynomial $4x^3 - 6x + ax + 3$ and told that when it is divided by $2x - 1$, the remainder is 7.

1. El problema plantea que un fabricante debe producir 300 pares de zapatos en 5 días. 2. Nos dan que para hacer 150 pares se necesitan 3 operarios trabajando 6 horas al día.

1. The problem is to verify if $x=\frac{2}{3}$ is a solution to the equation $p(x) = 2x + 3x + 4 = 0$. 2. First, simplify the expression for $p(x)$ by combining like terms:

1. The problem states the polynomial equation $p(x) = 2x + 3x + 4 = 0$ and suggests checking if $x=\frac{2}{3}$ is a solution. 2. First, simplify the polynomial expression: $2x + 3

4. **Stating the problem:** Find the maximum and minimum values of \(P=3x+2y\) subject to the inequalities \(x \geq 2.5\), \(y \geq 3.5\), and \(y \leq -4x + 11.5\).

1. Let's start with what simplifying means in math. Simplifying an expression means making it as straightforward and easy to understand as possible by combining like terms, reducin

1. Stating the problem: We need to simplify the expression $$\frac{y - 7 (x - 5)(x + 5)}{xy - 3}$$ given the equation $0 = 1$ which is likely a mistake or unrelated. 2. Simplify th

1. We are given a pyramid of numbers and need to find the values of $a$, $b$, $c$, and $d$. 2. The pyramid is structured so that each number above is the sum of the two numbers dir

1. **Problem 1:** Given inequalities: $x \geq 2.5$, $y \geq 3.5$, and $y \leq -4x + 11.5$. Find max and min of $P = 3x + 2y$.

1. Stating the problem: We want to find the remainder when the cubic polynomial $$f(x) = 2x^3 - x^2 + 2x - 16$$ is divided by $$x + 5$$. 2. According to the Remainder Theorem, the

1. El problema parece referirse a determinar si una función es impar. 2. Recordemos que una función $f(x)$ es impar si cumple la condición $f(-x) = -f(x)$ para todo $x$ en el domin

1. The problem is to find the unknown number represented by "?" in the equation 12 + 5 - ? + 4 = 8. 2. First, combine the known numbers on the left side: 12 + 5 + 4 = 21.

1. **State the problem:** Solve the equation $$\sqrt{39 - x} + \sqrt{7 - x} = 8$$ for $$x$$. 2. **Isolate one square root:** Let $$a = \sqrt{39 - x}$$ and $$b = \sqrt{7 - x}$$, so

**Problem 7:** Evaluate function values at given points. Since the exact function is not given for problem 7, I assume it corresponds to problem 15: $f(x) = 2x^2 - 7x - 30$ (based

1. **State the problem:** We need to find how much total damage the gun deals in 6 seconds. Given data: damage per magazine = 10576, damage per shot = 5288, reload speed = 1.5 seco