🧮 algebra

1. El problema es resolver el primer ejercicio de los que tienes, pero como no especificaste cuál, resolveré un ejemplo típico de álgebra: resolver la ecuación lineal $2x + 3 = 7$.

1. Problema: Reduce a una sola potencia la expresión $[(-6)^6 \cdot (-6)^7] : (-6)^2$. 2. Fórmula usada: Para potencias con la misma base, se suman los exponentes al multiplicar y

1. **Planteamiento del problema:** Hallar el valor de $m$ para que el módulo del vector $\vec{u}=\left(\frac{3}{5},m\right)$ sea 1.

1. Problem: Solve the equation $x^2 - 5x + 6 = 0$. 2. Formula: To solve a quadratic equation $ax^2 + bx + c = 0$, use the quadratic formula:

1. Das Problem lautet: Wandle die Potenz $3^{-3}$ in einen Stammbruch ohne Potenz um. 2. Die Regel für negative Exponenten besagt: $a^{-n} = \frac{1}{a^n}$, wobei $a \neq 0$ und $n

1. **State the problem:** Solve the equation $$\frac{6 + 2}{x} \times 3 = \frac{8}{x}$$ for $x$. 2. **Simplify the numerator:** Calculate $6 + 2$.

1. The problem is to create a system of 3 equations. 2. A system of equations consists of multiple equations with multiple variables that we solve simultaneously.

1. The problem is to understand and simplify the expression $7^{-5}$. 2. The rule for negative exponents states that $a^{-n} = \frac{1}{a^n}$ where $a$ is a nonzero number and $n$

1. **State the problem:** Solve the equation $$\frac{1}{x} + \frac{2}{x^2} = 3$$ for $x$. 2. **Identify the common denominator:** The denominators are $x$ and $x^2$. The least comm

1. **State the problem:** Find the number $x$ such that 1% of $x$ is 7. 2. **Formula used:** The percent proportion formula is $\frac{\text{part}}{\text{whole}} = \frac{\text{perce

1. The problem asks: What percent is 4 of 50? 2. To find the percent, we use the proportion formula:

1. **Stating the problem:** Simplify the expression $8x + 2 \cdot 7 \cdot 8x + N2 + 2$. 2. **Understanding the expression:** The expression contains terms with $x$ and constants. W

1. **State the problem:** Solve the quadratic equation $$x^2 - x - 42 = 0$$ by factoring. 2. **Recall the factoring method:** To factor a quadratic equation of the form $$ax^2 + bx

1. **State the problem:** Expand the expression $ (5x + 6y)^2 $. 2. **Formula used:** The square of a binomial is given by the formula $$ (a + b)^2 = a^2 + 2ab + b^2 $$ where $a =

1. The problem is to simplify the complex fraction $$\frac{2 + 7i}{4 - 2i}$$. 2. To simplify a complex fraction, multiply the numerator and denominator by the conjugate of the deno

1. **Stating the problem:** Determine the lines parallel to the x-axis that cut a segment on the ellipse $$\frac{x^2}{4} + \frac{y^2}{16} = 1$$ whose length equals the semi-focal d

1. **State the problem:** Simplify the expression $2 - 3(3 - x)$. 2. **Apply the distributive property:** Multiply $-3$ by each term inside the parentheses:

1. The original expression to simplify is $48 - x + 26 - x + x + 5$. 2. Combine the constant terms: $48 + 26 + 5 = 79$.

1. **State the problem:** Simplify the expression $\frac{2}{2x^2}$.\n\n2. **Write the expression:** $\frac{2}{2x^2}$.\n\n3. **Simplify the fraction by canceling common factors:** B

1. **State the problem:** Simplify the expression $\frac{3}{5x^2}$. 2. **Understand the expression:** This is a fraction where the numerator is 3 and the denominator is $5x^2$.

1. **Problem statement:** Find an expression in $x$ for $T$, the total time in hours, that it will take Jacob to kayak from $S$ to $B$ and then run from $B$ to $F$.