Álgebra preguntas y respuestas

Write the following in simplified radical form. \[ \sqrt[5]{w^{14}} \] Assume that the variable represents a positive real number.

Use the properties of complex numbers to simplify \( (9+\sqrt{-4})+(-9-\sqrt{-16}) \). (1 point) \( 18-2 i \) \( 6 i \) \( 18-\sqrt{-20} \) \( -2 i \)

Solve \( (x-3)^{2}-50=0 \), where \( x \) is a real number. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( x=\pi \) sol... Nolution

Part 2 of 2 A town's population is 52,800 . About 100 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 56,100 . It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.

Simplify. \[ \frac{12 x y^{2}}{20 x^{4} y} \]

Ejercicio 5. Sistemas de Ecuaciones con infinitas soluciones. Cada uno de los siguientes sistemas de ecuaciones lineales homogéneo ( \( 2 \times 3 \) ), tiene infinitas soluciones. Para cada sistema, realiza lo siguiente: - Determine el conjunto solución. - Identifique un sistema fundamental de soluciones, es decir, una base que genere conjunto solución obtenido en el ítem anterior. - Describa la naturaleza geométrica de la solución obtenida en el ítem anterior (si corresponde a una recta o un plano en el espacio). Puede utilizar GeoGebra para realizar una verificación geométrica visual de la solución. C. \( \left\{\begin{array}{c}4 x+y+z=0 \\ 8 x-5 y+2 z=0\end{array}\right\} \)

Uma loja está com uma promoção de \( 40 \% \) de desconto em fones de ouvido. Com este desconto, o preço de um par de fones é \( \$ 36 \). Qual é o preço original do par de fones de ouvido?

Rewrite using a single positive \[ \frac{5^{-2}}{5^{-6}} \]

Write the following as a radical expression \( 10^{\frac{5}{7}} \)

Writing the equations of vertical and horizontal lines through a given point horizontal line: \( \square \) vertical line: \( \square \) vertical lines passing through the point \( (1,7) \).