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山西思而行 2023-2024学年高二年级期中联考(4月)数学.考卷答案试卷答案
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上期参考答案B1-B4版第二节1-5BAACC6-10ACBBA11-15CABCBOnepossibleversion:16-20CACAB21-25CCABD26-30BCCBAJustthen,thehomelessmanrushedtowardsthe31-35BADAD36-40FAGEB41-45BADDCwoman.Aftergettingtoher,hehelpedherpickupwhatshe46-50BABCC51-55BCADA56.difficulthadbought.Whiledoingit,hekeptcomfortingthewoman.57.saw58.theSecondslater,everythingreturnedtohercart.Then,heoffered59.which/thattohelppushthecarttohercar.Howthoughtfulhewas!The60.wasprovided61.toask62.seriouslywomanthankedhimalot.IlookeddownatScarlett,finding63.organisation64.years65.with/byshewasviewingitwithhermouthwideopen.Andsuddenly第一节sheopenedherwalletandpulledouthermoney.Onepossibleversion:"Mom,Iwantedtogivemymoneytohim,"shesaid.Myfavoriteteacherlookingupatme.Surprised,Iopenedthecardoor.ScarlettMr.Wang,whoteachesushistory,ismyfavoriteteacher.rantothehomelessman.JuneandIfollowed.AftergettingHeismorethanfiftyyearsoldandhehastheabilitytohim,Scarletthandedouthermoneyandsaid,"Sir,Iwanttomakeasubjectthatmanystudentsfindincrediblyboringtohelpyou."Surprisedandtouched,hesaid,"Really?"cometolifethroughhisenthusiasmforhistoryandhisloveScarlettnoddedhappily.Knowingwhatwasgoingon,theyoungwomanalsogavehimmoney.Themanwassoofbeingateacher.Inhislessons,historyissomethingthatthankful.Whenreturningtoourcar,Scarlettsaid,"Itfeelswecansee,hearandfeel,andwecanmakeitalivethroughgoodtohelpsomeone!"Weallsmiled.dressingupandactingoutscenes.Heisanamazingteacher.Ilovehimverymuch.本版主编张资清责编代瑞芝
分析作出平面区域，结合向量的知识和点到直线的距离公式可得．
解答解：不等式组$\left\{\begin{array}{l}{x≥0}\\{y≥0}\\{x+y≥4}\end{array}\right.$表示的区域如图阴影，
当M、N分别在图中的位置时，|$\overrightarrow{OM}$+$\overrightarrow{ON}$|取最小值，
由点到直线的距离公式可得|OM|=$\frac{4}{\sqrt{{1}^{2}+{1}^{2}}}$=2$\sqrt{2}$，
∴|$\overrightarrow{OM}$+$\overrightarrow{ON}$|的最小值为2$\sqrt{2}$-1，
故答案为：2$\sqrt{2}$-1．
点评本题考查简单线性规划，涉及向量的模长公式和点到直线的距离公式，准确作图并转化是解决问题的关键，属中档题．
