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If 11 + 3x is 29, what is 2x?

In ΔABC the length of AB is 15 and the length of side AC is 5. What is the least possible integer length of side BC?

"The Cell Cycle" by Joseph Ritchie (2014) The process by which cells divide and multiply is known as the cell cycle. This cycle consists of two main phases: interphase and mitosis. Each phase consists of a series of clearly defined and observable steps. At the conclusion of the cycle, each parent cell produces two genetically identical daughter cells that may also replicate by proceeding through the cell cycle. Roughly ninety percent of the cell cycle is spent in interphase. Interphase is comprised of three main steps: the first gap phase, the synthesis phase (also called "S phase"), and the second gap phase. The initial gap phase is a period of cellular preparation in which the cell increases in size and readies itself for DNA synthesis. In the synthesis phase, or S phase, DNA replication occurs, so that when the cell divides, each daughter cell will have the DNA necessary to function properly. In the second gap phase, the cell grows in size and prepares for cellular division in the mitotic phase. At the end of each gap phase, the cell has to pass a regulatory checkpoint to ensure that nothing is going wrong. If anything has gone wrong, the checkpoints stop the cell from proceeding through the cell cycle any further. The next part of the cell cycle is mitosis. Mitosis is a form of cell division and is broken down into five distinct phases. During prophase, the genetic material contained in the cell’s chromatin condenses into distinct chromosomes. Prometaphase is marked by the breakdown of the cell’s nuclear envelope and the formation of centrosomes at the poles of the cell. During metaphase, the cell’s chromosomes are moved to the center of the cell. A checkpoint ensures that the chromosomes are properly aligned on the center and halts the cell cycle if any errors have occurred. In anaphase, chromosomes break apart at their center, or centromere, and sister chromatids move to opposite ends of the cell. Lastly, telophase and cytokinesis occur as nuclear membranes form to physically divide the cell into two new daughter cells. Chromosomes also unwind into loose chromatin during this part of mitosis. Cytokinesis is defined as the division of the each cell’s cytoplasm and organelles. At the conclusion of the cell cycle, two genetically identical daughter cells have formed. The cell cycle operates by a series of checkpoints and external cues. This system of checks enables the cell to enter a state of dormancy known as the gap zero phase when conditions or other factors inhibit the cell cycle. Conversely, unregulated and uncontrolled cellular division can occur under certain circumstances. A cell in a state of uncontrolled division is known to be cancerous. Lastly, cells have the ability to mediate their own death by way of apoptosis if certain genetic or physical abnormalities exist. The cell cycle is a complex process that enables cells to replicate and proliferate under a stringent set of checks and balances that produce healthy and viable daughter cells that are each able to perform the process in the future. About how much time does a cell spend undergoing mitosis in the cell cycle?

If one side of a square is 5 units, what is the area of the square? 

Adapted from “Humming-Birds: As Illustrating the Luxuriance of Tropical Nature” in Tropical Nature, and Other Essays by Alfred Russel Wallace (1878) The food of hummingbirds has been a matter of much controversy. All the early writers down to Buffon believed that they lived solely on the nectar of flowers, but since that time, every close observer of their habits maintains that they feed largely, and in some cases wholly, on insects. Azara observed them on the La Plata in winter taking insects out of the webs of spiders at a time and place where there were no flowers. Bullock, in Mexico, declares that he saw them catch small butterflies, and that he found many kinds of insects in their stomachs. Waterton made a similar statement. Hundreds and perhaps thousands of specimens have since been dissected by collecting naturalists, and in almost every instance their stomachs have been found full of insects, sometimes, but not generally, mixed with a proportion of honey. Many of them in fact may be seen catching gnats and other small insects just like fly-catchers, sitting on a dead twig over water, darting off for a time in the air, and then returning to the twig. Others come out just at dusk, and remain on the wing, now stationary, now darting about with the greatest rapidity, imitating in a limited space the evolutions of the goatsuckers, and evidently for the same end and purpose. Mr. Gosse also remarks, “All the hummingbirds have more or less the habit, when in flight, of pausing in the air and throwing the body and tail into rapid and odd contortions. This is most observable in the Polytmus, from the effect that such motions have on the long feathers of the tail. That the object of these quick turns is the capture of insects, I am sure, having watched one thus engaged pretty close to me.” Based on the way the term is used in passage, what is “the Polytmus”?