在平面直角坐标系中,点 A 的坐标是 (3, 4),点 B 的坐标是 (3, -2),则线段 AB 的长度是 ___。
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气温上升用正数表示,下降则用负数表示。题目中气温下降了2℃,应记作-2℃,因此正确答案是B。
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[{"id":2147,"content":"某学生在解方程时,将方程 2x + 3 = 7 的两边同时减去3,得到 2x = 4,然后两边同时除以2,得到 x = 2。这一过程主要运用了等式的哪一条基本性质?","type":"选择题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"简单","answer":"D","explanation":"该学生在解题过程中,先两边同时减去3(运用了等式性质1:两边同时减去同一个数,等式仍成立),再两边同时除以2(运用了等式性质2:两边同时除以同一个不为零的数,等式仍成立)。因此,整个过程中综合运用了等式的基本性质,选项D最全面准确。","options":[{"id":"A","content":"等式两边同时加上同一个数,等式仍然成立"},{"id":"B","content":"等式两边同时减去同一个数,等式仍然成立"},{"id":"C","content":"等式两边同时乘或除以同一个不为零的数,等式仍然成立"},{"id":"D","content":"以上三条性质都运用了"}]},{"id":313,"content":"某班级为了了解学生最喜欢的课外活动,随机抽取了50名学生进行调查,并将数据整理成如下统计表。已知喜欢阅读的学生人数是喜欢绘画的2倍,且喜欢运动的人数比喜欢绘画的多10人。如果喜欢音乐的学生有8人,那么喜欢绘画的学生有多少人?","type":"选择题","subject":"数学","grade":"初一","stage":"初中","difficulty":"简单","answer":"B","explanation":"设喜欢绘画的学生人数为x人。根据题意,喜欢阅读的人数是2x人,喜欢运动的人数是x + 10人,喜欢音乐的有8人。总人数为50人,因此可以列出方程:x(绘画) + 2x(阅读) + (x + 10)(运动) + 8(音乐) = 50。合并同类项得:4x + 18 = 50。解这个一元一次方程:4x = 32,x = 8。所以喜欢绘画的学生有8人。","options":[{"id":"A","content":"6人"},{"id":"B","content":"8人"},{"id":"C","content":"10人"},{"id":"D","content":"12人"}]},{"id":1931,"content":"某学生在整理班级同学每日运动时间数据时,发现若将数据按从小到大的顺序排列,第8个和第9个数据分别为25分钟和27分钟。已知这组数据共有15个,且唯一众数为20分钟,出现4次。若去掉一个最大值和一个最小值后,剩余13个数据的平均数恰好比原平均数多1分钟,则原数据中的最大值是____分钟。","type":"填空题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"困难","answer":"40","explanation":"中位数为(25+27)\/2=26。设原平均数为x,则新平均数为x+1。总和关系:15x - (最小值+最大值) = 13(x+1),化简得最大值+最小值=2x-13。结合众数、中位数和整数约束,推得最大值为40。","options":[]},{"id":435,"content":"90","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":1917,"content":"某班级进行了一次数学测验,成绩分布如下表所示。若将成绩分为“优秀”(90分及以上)、“良好”(75~89分)、“及格”(60~74分)和“不及格”(60分以下)四个等级,则成绩为“良好”的学生人数占总人数的百分比是多少?\n\n| 分数段 | 人数 |\n|--------------|------|\n| 90~100 | 8 |\n| 75~89 | 12 |\n| 60~74 | 6 |\n| 60以下 | 4 |","type":"选择题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"简单","answer":"B","explanation":"首先计算总人数:8 + 12 + 6 + 4 = 30(人)。成绩为“良好”(75~89分)的学生有12人。因此,“良好”等级所占百分比为:(12 ÷ 30) × 100% = 40%。故正确答案为B。","options":[{"id":"A","content":"30%"},{"id":"B","content":"40%"},{"id":"C","content":"50%"},{"id":"D","content":"60%"}]},{"id":201,"content":"某学生用一根长为20厘米的铁丝围成一个正方形,这个正方形的边长是_空白处_厘米。","type":"填空题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"5","explanation":"正方形的周长等于四条边长之和。已知铁丝总长为20厘米,即正方形的周长为20厘米。设边长为x厘米,则有4x = 20。解这个方程得x = 20 ÷ 4 = 5。因此,正方形的边长是5厘米。","options":[]},{"id":219,"content":"某学生在计算一个数减去5时,误将减号看成了加号,结果得到12。那么正确的计算结果应该是____。","type":"填空题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"2","explanation":"该学生误将减法当作加法计算,即把原式中的“减去5”算成了“加上5”,得到12。设原数为x,则根据错误运算有:x + 5 = 12,解得x = 7。因此正确的计算应为7 - 5 = 2。","options":[]},{"id":2515,"content":"一个圆形花坛的半径为6米,现要在花坛边缘均匀种植一圈月季花,相邻两株月季花之间的弧长为π米。问一共需要种植多少株月季花?","type":"选择题","subject":"数学","grade":"九年级","stage":"初中","difficulty":"简单","answer":"B","explanation":"首先计算圆形花坛的周长。已知半径r = 6米,根据圆的周长公式C = 2πr,得C = 2 × π × 6 = 12π米。题目中说明相邻两株花之间的弧长为π米,因此所需株数等于总周长除以每段弧长,即12π ÷ π = 12。因为是沿着圆周均匀种植一圈,首尾相连,所以不需要额外加1。因此,一共需要种植12株月季花。","options":[{"id":"A","content":"6"},{"id":"B","content":"12"},{"id":"C","content":"18"},{"id":"D","content":"24"}]},{"id":2461,"content":"某校八年级学生参加数学竞赛,成绩分布如下表所示。若将成绩按从小到大的顺序排列,则第15个数据是85分,第16个数据是88分,那么这次竞赛成绩的中位数是____分。","type":"填空题","subject":"数学","grade":"八年级","stage":"初中","difficulty":"中等","answer":"86.5","explanation":"中位数是数据排序后中间两个数的平均数。第15和第16个数据分别为85和88,中位数为(85 + 88) ÷ 2 = 86.5。","options":[]},{"id":320,"content":"在一次班级数学测验中,某学生记录了5名同学的数学成绩(单位:分)分别为:78、85、90、82、85。这组成绩的中位数和众数分别是多少?","type":"选择题","subject":"数学","grade":"初一","stage":"初中","difficulty":"简单","answer":"A","explanation":"首先将5个成绩从小到大排列:78、82、85、85、90。中位数是中间的那个数,即第3个数,为85。众数是出现次数最多的数,其中85出现了两次,其余数各出现一次,因此众数是85。所以正确答案是A。","options":[{"id":"A","content":"中位数是85,众数是85"},{"id":"B","content":"中位数是82,众数是85"},{"id":"C","content":"中位数是85,众数是90"},{"id":"D","content":"中位数是84,众数是82"}]}]