某学生在数轴上标记了三个有理数:点A表示的数比-3大2,点B表示的数是点A的相反数,点C表示的数比点B小5。那么点C表示的有理数是多少?
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点 A 和点 B 的横坐标相同,都是 3,说明它们位于同一条竖直线上。两点之间的距离等于它们纵坐标之差的绝对值。计算:|4 - (-2)| = |4 + 2| = |6| = 6。因此,两点之间的距离是 6。
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[{"id":1893,"content":"某学生在平面直角坐标系中绘制了一个四边形ABCD,其中A(0, 0),B(4, 0),C(5, 3),D(1, 3)。该学生声称这个四边形是平行四边形,并试图通过计算对边长度和斜率来验证。若该四边形确实是平行四边形,则其对角线AC和BD的交点坐标应为多少?若该学生计算后发现交点不在两条对角线的中点,则说明该四边形不是平行四边形。请问该四边形的对角线交点坐标是?","type":"选择题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"困难","answer":"A","explanation":"要判断四边形ABCD是否为平行四边形,可先验证其对边是否平行且相等。但本题直接要求计算对角线AC和BD的交点坐标。在平面直角坐标系中,若四边形是平行四边形,则对角线互相平分,即交点为两条对角线的中点。因此,只需计算对角线AC和BD的中点,若两者重合,则该点即为交点。\n\n点A(0, 0),C(5, 3),则AC中点坐标为:((0+5)\/2, (0+3)\/2) = (2.5, 1.5)\n\n点B(4, 0),D(1, 3),则BD中点坐标为:((4+1)\/2, (0+3)\/2) = (2.5, 1.5)\n\n两条对角线中点相同,说明对角线互相平分,因此四边形ABCD是平行四边形,其对角线交点为(2.5, 1.5)。\n\n故正确答案为A。","options":[{"id":"A","content":"(2.5, 1.5)"},{"id":"B","content":"(2, 1.5)"},{"id":"C","content":"(2.5, 2)"},{"id":"D","content":"(3, 1.8)"}]},{"id":591,"content":"6件","type":"选择题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"待完善","explanation":"解析待完善","options":[]},{"id":322,"content":"某学生在整理班级同学最喜欢的课外活动调查数据时,制作了如下频数分布表。已知喜欢阅读的人数是喜欢绘画人数的2倍,且总人数为30人。如果喜欢绘画的有x人,那么根据题意列出的方程是:","type":"选择题","subject":"数学","grade":"初一","stage":"初中","difficulty":"简单","answer":"A","explanation":"题目中说明喜欢绘画的有x人,喜欢阅读的人数是绘画的2倍,即2x人。总人数为30人,且只涉及这两类活动(隐含在简单题设中),因此可列出方程:x + 2x = 30。选项A正确。选项B错误地将倍数关系理解为加2;选项C表示的是人数差,不符合总人数条件;选项D凭空多出一个常数5,题干未提及,属于干扰项。","options":[{"id":"A","content":"x + 2x = 30"},{"id":"B","content":"x + 2 = 30"},{"id":"C","content":"2x - x = 30"},{"id":"D","content":"x + 2x + 5 = 30"}]},{"id":2459,"content":"某学生在研究一组数据时发现,这组数据的平均数是12,若将每个数据都乘以2后再减去3,得到的新数据组的平均数是___。","type":"填空题","subject":"数学","grade":"八年级","stage":"初中","difficulty":"中等","answer":"21","explanation":"原平均数为12,每个数据乘以2后平均数变为24,再减去3,新平均数为24 - 3 = 21。数据线性变换后平均数按相同规律变化。","options":[]},{"id":500,"content":"某学生调查了班级同学每天使用手机的时间(单位:分钟),并将数据整理如下:15,20,25,30,35,40,45,50,55,60。如果去掉一个最大值和一个最小值后,剩余数据的平均数是多少?","type":"选择题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"A","explanation":"首先确定原始数据中的最大值是60,最小值是15。去掉这两个值后,剩余的数据为:20,25,30,35,40,45,50,55,共8个数。计算这些数的和:20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 = 300。然后用总和除以数据个数:300 ÷ 8 = 37.5。因此,剩余数据的平均数是37.5,正确答案是A。","options":[{"id":"A","content":"37.5"},{"id":"B","content":"40"},{"id":"C","content":"42.5"},{"id":"D","content":"45"}]},{"id":2382,"content":"在一次校园绿化活动中,学校计划在一块直角三角形的空地上铺设草皮。已知该直角三角形的两条直角边长度分别为√12米和√27米。为了计算所需草皮的面积,一名学生需要先化简边长并应用勾股定理求出斜边长度,再计算面积。请问该直角三角形的面积是多少平方米?","type":"选择题","subject":"数学","grade":"八年级","stage":"初中","difficulty":"中等","answer":"A","explanation":"首先化简两条直角边:√12 = √(4×3) = 2√3,√27 = √(9×3) = 3√3。直角三角形的面积公式为(1\/2)×直角边1×直角边2,因此面积为(1\/2)×2√3×3√3 = (1\/2)×6×3 = (1\/2)×18 = 9(平方米)。注意题目仅要求面积,无需计算斜边。选项A正确。","options":[{"id":"A","content":"9"},{"id":"B","content":"6√3"},{"id":"C","content":"18"},{"id":"D","content":"9√3"}]},{"id":2197,"content":"某学生在练习本上记录了一周内每天的温度变化情况,规定比前一天升高记为正,降低记为负。已知周一到周二的温度变化为 -3℃,周三到周四的温度变化为 +5℃,周五到周六的温度变化为 -2℃。如果周一的起始温度为 10℃,那么周六的温度是多少?","type":"选择题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"简单","answer":"B","explanation":"从周一的 10℃ 开始,周二变化 -3℃,温度为 10 - 3 = 7℃;周三到周四变化 +5℃,即温度上升 5℃,变为 7 + 5 = 12℃;周五到周六变化 -2℃,即下降 2℃,变为 12 - 2 = 10℃。因此周六的温度是 10℃,正确答案是 B。","options":[{"id":"A","content":"8℃"},{"id":"B","content":"10℃"},{"id":"C","content":"12℃"},{"id":"D","content":"14℃"}]},{"id":533,"content":"某学生在整理班级同学的课外阅读情况时,随机抽取了20名学生,记录了他们每周课外阅读的时间(单位:小时),数据如下:3, 5, 4, 6, 3, 7, 5, 4, 5, 6, 4, 3, 5, 6, 7, 4, 5, 6, 5, 4。为了分析这些数据,该学生制作了频数分布表。请问阅读时间为5小时的学生人数是多少?","type":"选择题","subject":"数学","grade":"初一","stage":"初中","difficulty":"简单","answer":"C","explanation":"题目考查的是数据的收集、整理与描述中的频数统计。我们需要从给出的20个数据中,统计出数值为5的个数。原始数据为:3, 5, 4, 6, 3, 7, 5, 4, 5, 6, 4, 3, 5, 6, 7, 4, 5, 6, 5, 4。逐个数出5出现的次数:第2个是5,第7个是5,第9个是5,第13个是5,第17个是5,第19个是5,共出现6次。因此,阅读时间为5小时的学生有6人,正确答案是C。","options":[{"id":"A","content":"4人"},{"id":"B","content":"5人"},{"id":"C","content":"6人"},{"id":"D","content":"7人"}]},{"id":600,"content":"在一次环保主题活动中,某学校七年级学生收集了可回收垃圾的重量数据(单位:千克),并整理成如下表格:\n\n| 班级 | 收集重量 |\n|------|----------|\n| 七(1)班 | 12.5 |\n| 七(2)班 | 比七(1)班多3.2千克 |\n| 七(3)班 | 比七(2)班少1.8千克 |\n| 七(4)班 | 是七(3)班的2倍 |\n\n请问七(4)班收集的可回收垃圾重量是多少千克?","type":"选择题","subject":"数学","grade":"初一","stage":"初中","difficulty":"简单","answer":"A","explanation":"首先根据表格信息逐步计算各班收集的重量:\n\n1. 七(1)班:12.5 千克;\n2. 七(2)班比七(1)班多3.2千克,即 12.5 + 3.2 = 15.7 千克;\n3. 七(3)班比七(2)班少1.8千克,即 15.7 - 1.8 = 13.9 千克;\n4. 七(4)班是七(3)班的2倍,即 13.9 × 2 = 27.8 千克。\n\n因此,七(4)班收集的可回收垃圾重量为27.8千克,正确答案是A。\n\n本题考查学生对小数的加减乘除运算在实际情境中的应用,属于‘数据的收集、整理与描述’知识点,并结合有理数的运算,难度适中,贴近生活。","options":[{"id":"A","content":"27.8"},{"id":"B","content":"28.8"},{"id":"C","content":"29.8"},{"id":"D","content":"30.8"}]},{"id":617,"content":"第一天","type":"选择题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"待完善","explanation":"解析待完善","options":[]}]