answer:Simple Explanation: A simple sentence contains one independent clause and no dependent clauses. In this sentence, "I watered the plants" is the independent clause, and there are no dependent clauses. Therefore, the sentence is a simple sentence.

answer:A neuron is a specialized cell in the nervous system that comprises several key parts. These include: 1. Dendrites: These are the branched extensions that receive signals from other neurons. 2. Soma (Cell Body): The central part of the neuron that contains the nucleus and other organelles necessary for cellular functions. 3. Axon: A long, slender projection that transmits signals from the neuron to other cells. Together, these components enable neurons to communicate effectively within the nervous system.

answer:To parametrize the curve, we will create equations for each segment. For the line segment from (-2, -14) to (0, -12): The slope is (y2 - y1) / (x2 - x1) = (-12 - (-14)) / (0 - (-2)) = 1. Thus, the equation of the line is y = x - 12. To convert this to parametric form, let x = t: x = t y = t - 12 So, the parametric equations for the line segment are: {eq}boxed{mathbf{r}_1(t) = langle t, t - 12 rangle, text{ for } -2 leq t leq 0}. {/eq} For the parabolic segment from (0, -12) to (2, 0): The given parabolic equation is y = -12 + 3x^2. To find the parametric equations, let x = t: x = t y = -12 + 3t^2 So, the parametric equations for the parabolic segment are: {eq}boxed{mathbf{r}_2(t) = langle t, -12 + 3t^2 rangle, text{ for } 0 leq t leq 2}. {/eq} The complete curve, with the positive orientation as t increases, is shown in the graph below: [Insert image of the graph, with the curve starting from (-2, -14), following the line segment to (0, -12), and then continuing along the parabolic segment to (2, 0), indicating the positive orientation.]

answer:The original centroid, E, can be calculated as: [ E(frac{-2+3+5}{3}, frac{3+2-6}{3}) = E(frac{6}{3}, frac{-1}{3}) = E(2, -0.33) ] After dilation by a factor of 2 about (1, -8), the new vertices are: [ A'(-5, 14) ] [ B'(5, 12) ] [ C'(9, -4) ] The dilated centroid, F, is then calculated as: [ F(frac{-5+5+9}{3}, frac{14+12-4}{3}) = F(frac{9}{3}, frac{22}{3}) = F(3, 7.33) ] The distance, d, between the original centroid E and the dilated centroid F is: [ d = sqrt{(3-2)^2 + (7.33+0.33)^2} ] [ d = sqrt{1 + (7.66)^2} ] [ d = sqrt{1 + 58.68} ] [ d = sqrt{59.68} ] [ d approx 7.73 ] Therefore, the centroid moves approximately 7.73 units.