De las siguientes opciones, la que describe correctamente la dimensión del kernel de la transformación lineal \( T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3} \) definida por: \[ T\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{c}x+3 y-2 z \\ 2 x-4 y+z \\ -x+y+4 z\end{array}\right] \] es:

2. Expand and simplify \( \begin{array}{ll}\text { a. } 2(x+3) & \text { b. } \quad x\left(x^{2}-3 x\right) \\ \text { c. } \quad(x+7)(x-5) & \text { d. } \quad(x-3)^{2}\end{array} \)

Greg drove at a constant speed in a rainstorm for 280 miles. He took a break, and the rain stopped He then drove 264 miles at a speed that was 9 miles per hour faster than his previous speed. If he drove for 14 hours, find the car's speed for each part of the trip. The rate of the car in the rain was

Solve for \( M \). Assume that all other variables are nonzero. \( Q=\frac{2 \text { twM }^{2}}{3 c} \) \( M=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.

The number of incarcerated adults N (measured in thousands) in a certain country can be approximated by the equation \( \mathrm{N}=-2.8 \mathrm{x}^{2}+72.4 \mathrm{x}+1914 \), where x is the number of years since 2000. In 2012 , the number of incarcerated adults peaked. How many adults were incarcerated in that year? There were \( \square \) incarcerated adults in 2012.

Given the quadratic \( y=-2(x+1)^{2}-7 \) write the equation in standard form.