The blacksmith Jones worked hard in his shop. The son of Mr. White, ______ rich neighbor, came to see him everyday. “Young man, why not learn to make shoe tacks (钉)?” said Jones. “It may be useful to you
day.” After a little practice, the boy found he could make some of the finest tacks. Old Mr. White died and because of the war the son lost all his goods. He ____
___(force) to leave home and live in another country. It happened __
___ in this village many shoemakers spent a lot of money ___
___ (buy) tacks for their shoes and sometimes they were not able to buy them _____
____ there was a high demand for soldiers’ shoes. Young Mr. White, who was finding ____
___difficult to earn his ___
___ (day) bread, told the shoemakers that he would make the tacks if they would help to get him ___
___ (settle) in his workshop. The shoemakers were only too glad of the offer. Soon Mr. Smith found that he was making the finest tacks in the village. “How funny,” he said, “Even making tacks can bring a fortune. My trade is ___
___ (much) useful to me than all my former riches.”
因式分解 ______.
如图,已知点 ,直线 经过点 .试探究:直线与线段 有交点时 的变化情况,猜想 的取值范围是________.
古希腊的毕达哥拉斯学派对整数进行了深入的研究,尤其注意形与数的关系,“多边形数”也称为“形数”,就是形与数的结合物.用点排成的图形如下:
其中:图①的点数叫做三角形数,从上至下第一个三角形数是 ,第二个三角形数是 ,第三个三角形数是 ,……
图②的点数叫做正方形数,从上至下第一个正方形数是 ,第二个正方形数是 ,第三个正方形数是 ,……
……
由此类推,图④中第五个正六边形数是____.
如图,直角三角形 纸片中, ,点 是 边上的中点,连结 ,将 沿 折叠,点 落在点 处,此时恰好有 .若 ,那么 ____.
已知 , ,则 ____.