answer:The equation of a plane in 3D space can be written as Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane and can be found using the cross product of two vectors formed by the given points. Let's first find the vectors: Vector overrightarrow{P_1P_2} = langle 0 - 5, -4 - (-5), -3 - (-3) rangle = langle -5, 1, 0 rangle Vector overrightarrow{P_1P_3} = langle -1 - 5, 1 - (-5), -1 - (-3) rangle = langle -6, 6, 2 rangle Now, we calculate the cross product to find the normal vector (A, B, C): N = overrightarrow{P_1P_2} times overrightarrow{P_1P_3} = begin{vmatrix} mathbf{i} & mathbf{j} & mathbf{k} -5 & 1 & 0 -6 & 6 & 2 end{vmatrix} = mathbf{i}(1 cdot 2 - 6 cdot 0) - mathbf{j}(-5 cdot 2 - 6 cdot 0) + mathbf{k}(-5 cdot 6 - 1 cdot (-6)) = mathbf{i}(2) - mathbf{j}(0) + mathbf{k}(-24) N = langle 2, 0, -24 rangle Now, we need to find D such that the plane passes through point {P_1}(5,-5,-3): 2(5) + 0(-5) - 24(-3) + D = 0 10 + 72 + D = 0 D = -82 So, the equation of the plane is 2x - 24z - 82 = 0, which can be simplified to x + 12z + 41 = 0.

answer:Six months. Explanation: In many jurisdictions, drivers under the age of 21 are subject to stricter DUI laws than older drivers. A BAC of .02 or greater is considered a DUI offense for underage drivers, and the penalty typically includes a six-month suspension of driving privileges.

answer:We can use the trigonometric ratio sine to find the measure of angle A. begin{align} sin A &=frac{text{opposite}}{text{hypotenuse}}[0.3cm] sin A &=frac{12 text{ cm}}{23text{ cm}}[0.3cm] sin A &=frac{12 }{23}[0.3cm] A &=sin^{-1}left ( frac{12 }{23}right )[0.3cm] A &=31.44^{circ} end{align} Therefore, the measure of angle A is {eq}displaystyle{boxed{color{magenta}{ 31.44^{circ} }}} {/eq}.

answer:Research suggests that synaptic pruning, a process where the brain and synapses work together to focus on essential thoughts, plays a crucial role in enhancing clear thinking. This process involves eliminating unnecessary connections and strengthening important ones, allowing for more efficient and focused thought processes.