images
images listlengths 1
1
| problem
stringlengths 14
1.27k
| answer
stringlengths 1
93
| id
stringlengths 6
9
|
|---|---|---|---|
<image>
As shown in the figure, line segment AB = 24 cm, C is any point on line segment AB, M and N are the midpoints of AC and BC, respectively. The length of MN is cm.
|
12
|
math_1257
|
|
<image>
Count the number of triangles in the figure.
|
3
|
math_7437
|
|
<image>
To monitor the water quality of a river, 6 water quality tests were conducted, and a line graph of the ammonia nitrogen content was drawn as shown in the figure. If the average ammonia nitrogen content of these 6 water quality tests is 1.5 mg/L, then the ammonia nitrogen content of the 3rd test is ___ mg/L.
|
1
|
math_4440
|
|
<image>
In the right triangle ABC, CD is the median on the hypotenuse AB, given that CD = 2, AC = 3, then cosB =?
|
\frac{\sqrt{7}}{4}
|
math_1270
|
|
<image>
As shown in the figure, quadrilateral $ABCD$ is a spatial quadrilateral. $E$, $F$, $G$, and $H$ are points on the sides of the quadrilateral, and they are coplanar. $AC$ is parallel to plane $EFGH$, and $BD$ is parallel to plane $EFGH$. Given $AC = m$ and $BD = n$, what is the ratio $AE:EB$ when quadrilateral $EFGH$ is a rhombus?
|
m:n
|
math_3463
|
|
<image>
As shown in the figure, $OA$ is a radius of $\odot O$, $AB$ is tangent to $\odot O$, and $BO$ intersects $\odot O$ at point $C$. If $\angle BAC=30{}^\circ $, then $\angle AOC=$ degrees.
|
60
|
math_608
|
|
<image>
In the 'Belt and Road' (English: The Belt and Road, abbreviated as B&R) Knowledge Competition, the stem-and-leaf plot of the scores of the seven contestants from the 'Jiangsu' team is shown in the figure. After removing the highest and the lowest scores, the variance of the remaining data is.
|
\frac{8}{5}
|
math_4258
|
|
<image>
Using 4 congruent regular octagons to connect, such that two adjacent octagons share one common side, they form a circle with a square in the middle, as shown in Figure 1. Using n congruent regular hexagons to connect in the same way, as shown in Figure 2, if they form a regular polygon in the middle when connected in a circle, then the value of n is ___.
|
6
|
math_6553
|
|
<image>
As shown in the figure, $$\triangle ABC$$ is inscribed in $$\odot O$$, $$D$$ is a point on the minor arc $$AB$$, $$E$$ is a point on the extension of $$BC$$, and $$AE$$ intersects $$\odot O$$ at $$F$$. To make $$\triangle ADB \sim \triangle ACE$$, an additional condition that should be added is ___.
|
\angle DAB = \angle CAE
|
math_3132
|
|
<image>
As shown in the figure, in parallelogram ABCD, AB=4, BC=6, and the height from A to BC, AE=2. Then the length of the height from A to DC, AF, is ___.
|
3
|
math_2183
|
|
<image>
As shown in the figure, for the hyperbola $$\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$$ ($$a$$, $$b>0$$), the two vertices are $$A_{1}$$, $$A_{2}$$, the endpoints of the imaginary axis are $$B_{1}$$, $$B_{2}$$, and the two foci are $$F_{1}$$, $$F_{2}$$. If the circle with $$A_{1}A_{2}$$ as its diameter is inscribed in the rhombus $$F_{1}B_{1}F_{2}B_{2}$$, touching the sides at points $$A$$, $$B$$, $$C$$, $$D$$, then the eccentricity of the hyperbola $$e=$$ ___.
|
\dfrac{\sqrt{5}+1}{2}
|
math_5331
|
|
<image>
In the figure, in $$\triangle ABC$$, $$AB=4$$, $$BC=6$$, $$\angle B=60^{\circ}$$, if $$\triangle ABC$$ is translated 2 units in the direction of the ray $$BC$$, resulting in $$\triangle A'B'C'$$, and $$A'C$$ is connected, then the perimeter of $$\triangle A'B'C$$ is ___.
|
12
|
math_7719
|
|
<image>
As shown in the figure, in the Cartesian coordinate system xOy, A(1, 1), B(2, 2). The line $y=kx+3$ intersects the line segment AB. The range of values for $k$ is:
|
-2\le k\le -\frac{1}{2}
|
math_1258
|
|
<image>
As shown in the figure, △OAB is an equilateral triangle, and OA coincides with the x-axis. Point B is a point on the graph of the inverse proportion function y = -\frac{4\sqrt{3}}{x}. What is the perimeter of △OAB?
|
12
|
math_4045
|
|
<image>
In triangle ABC, points E and F are on sides AB and AC, respectively, and EF is parallel to BC. If $\frac{EB}{AB}=\frac{4}{5}$, then $\frac{AC}{FC}$ =.
|
\frac{5}{4}
|
math_3248
|
|
<image>
The graph shows the statistics of donations made by the 7th, 8th, and 9th grades of a middle school to children in poor mountainous areas. It is known that the school has a total of 2000 students in the 7th, 8th, and 9th grades. Please estimate the total donations made by the 7th, 8th, and 9th grades based on the statistical graph.
|
25180
|
math_7874
|
|
<image>
As shown in the figure, quadrilateral $$ABCD$$ is an inscribed quadrilateral in circle $$\odot O$$, and $$\angle B=148^{\circ}24'$$. What is the measure of $$\angle AOC$$ in degrees?
|
63
|
math_6186
|
|
<image>
In the right-angled triangle ABC, ∠C = 90°, ∠A = 30°, and AB = 8 cm. Therefore, BC = ______ cm.
|
4
|
math_21
|
|
<image>
As shown in the figure, $$AB=CD$$, $$AC$$ and $$BD$$ intersect at point $$O$$. To prove that $$\triangle ABC \cong \triangle DCB$$, one possible additional condition is ___ (write one only).
|
\angle ABC=\angle DCB
|
math_501
|
|
<image>
As shown in the figure, in the cube $$ABCD - {A_1}{B_1}{C_1}{D_1}$$, point $$P$$ is a moving point on the upper base $${A_1}{B_1}{C_1}{D_1}$$. The ratio of the area of the front view to the area of the left view of the tetrahedron $$P-ABC$$ is ______.
|
1
|
math_5355
|
|
<image>
As shown in the figure, in tetrahedron $$D-ABC$$, if $$AB=BC$$, $$AD=CD$$, and point $$E$$ is the midpoint of $$AC$$, then the correct sequence number(s) of the following propositions is/are ___. 1. Plane $$ABC \perp$$ plane $$ABD$$; 2. Plane $$ABD \perp$$ plane $$BDC$$; 3. Plane $$ABC \perp$$ plane $$BDE$$, and plane $$ADC \perp$$ plane $$BDE$$; 4. Plane $$ABC \perp$$ plane $$ADC$$, and plane $$ADC \perp$$ plane $$BDE$$.
|
3
|
math_6429
|
|
<image>
The figure below is a flowchart of an algorithm. The output value of $$x$$ is ___.
|
23
|
math_3384
|
|
<image>
Given that $a$, $b$, and $c$ are positioned on the number line as shown in the figure, then $\left| 2a-b \right|+5(c-a)-4\left| b-c \right|=$.
|
-7a+5b+c
|
math_6274
|
|
<image>
In triangle ABC, ∠BAC = 90°, AB = 5 cm, AC = 2 cm. Triangle ABC is rotated 45° clockwise around vertex C to the position of triangle A₁B₁C. The area of the region swept by segment AB (the shaded part in the figure) is ___ cm².
|
\frac{\text{25}\pi }{\text{8}}
|
math_4034
|
|
<image>
As shown in the figure, $$\angle C=\angle E=90^{\circ}$$, $$AC=3$$, $$BC=4$$, $$AE=2$$, then $$AD=$$ ___.
|
\dfrac{10}{3}
|
math_2838
|
|
<image>
As shown in the figure, a container is 5.9 meters long, 2.3 meters wide, and 2.3 meters high. It needs to be filled with cubic wooden boxes with an edge length of 0.7 meters. The maximum number of wooden boxes that can be accommodated is ______.
|
72
|
math_6427
|
|
<image>
Execute the program flowchart shown in the figure, then the output value of $S$ is.
|
2550
|
math_967
|
|
<image>
As shown in the figure, the graph of the inverse proportion function $$y=\dfrac{2}{x}$$ passes through the midpoint $$D$$ of side $$AB$$ of rectangle $$OABC$$. The area of rectangle $$OABC$$ is ___.
|
4
|
math_6999
|
|
<image>
Xiao Ming made a kite as shown in the figure, where $$ \angle EDH = \angle FDH$$, $$ED = FD = a$$, $$EH = b$$, then the perimeter of the quadrilateral kite is ___.
|
2a+2b
|
math_2883
|
|
<image>
As shown in the figure, a ship sails due north. At point A, it observes a lighthouse S at a bearing of 30° east of north. After sailing 12 nautical miles to point B, it observes the lighthouse S at a bearing of 60° east of north. During the ship's continued journey due north, the closest distance to the lighthouse S is ___ nautical miles? (Do not approximate the calculation)
|
6 \sqrt{3}
|
math_2890
|
|
<image>
As shown in the figure, line $$PA$$ is perpendicular to the plane containing $$\odot O$$, $$\triangle ABC$$ is inscribed in $$\odot O$$, and $$AB$$ is the diameter of $$\odot O$$. Point $$M$$ is the midpoint of line segment $$PB$$. The following conclusions are given: (1) $$BC \perp PC$$; (2) $$OM \parallel$$ plane $$APC$$; (3) The distance from point $$B$$ to plane $$PAC$$ is equal to the length of line segment $$BC$$. Which of the following are correct? (Fill in the sequence numbers).
|
(1)(2)(3)
|
math_746
|
|
<image>
As shown in the figure, the 'Zhao Shuang Xian Tu' is composed of four congruent right-angled triangles and a square, forming a larger square. Let the longer leg of the right-angled triangle be $a$, and the shorter leg be $b$. If $ab=6$, and the area of the larger square is 25, then the side length of the smaller square is ___.
|
\sqrt{13}
|
math_162
|
|
<image>
An office has 6 people who are going on a trip in a minibus. The minibus has 6 seats arranged as shown in the figure. Among them, person A and person B have a close relationship and must sit in the same row and next to each other. How many different seating arrangements are there?
|
144
|
math_1717
|
|
<image>
Given the linear function $$y=ax+b$$ ($$a$$, $$b$$ are constants, and $$a≠0$$), the partial corresponding values of $$x$$ and $$y$$ are shown in the table: Then the solution to the equation $$ax+b=0$$ is ___.
|
x=1
|
math_1206
|
|
<image>
As shown in the figure, vector $\overrightarrow{OA} \bot \overrightarrow{OB}$, $|\overrightarrow{OA}|=2$, $|\overrightarrow{OB}|=1$, and $P$ is a moving point on the arc $\overset\frown{AC}$ of a circle centered at $O$ with radius $|\overrightarrow{OA}|$. If $\overrightarrow{OP}=m\overrightarrow{OA}+n\overrightarrow{OB}$, then the maximum value of $mn$ is.
|
1
|
math_915
|
|
<image>
As shown in the figure, $AB$ is the diameter of circle $\odot O$. Points $C$ and $D$ are points on $\odot O$ located on opposite sides of the diameter $AB$. Connect $AC$, $AD$, $BD$, and $CD$. If the radius of $\odot O$ is $5$ and $BD=8$, then the value of $\sin \angle ACD$ is.
|
\frac{3}{5}
|
math_1897
|
|
<image>
As shown in the figure, there are ___ different ways to go from $$A \rightarrow C$$ (assuming it is not possible to go from $$B$$ to $$A$$).
|
6
|
math_6938
|
|
<image>
The three views of a rectangular prism (unit: $$\unit{cm}$$) are shown in the figure. According to the data in the figure, calculate the volume of this rectangular prism, which is ___$$\unit{cm^{3}}$$.
|
24
|
math_6870
|
|
<image>
Xiaoming drew a statistical graph showing the age distribution of a basketball team as shown in the figure. The basketball team has ___ members.
|
12
|
math_4007
|
|
<image>
As shown in the figure, $$OA$$ is a radius of $$\odot O$$, $$AB$$ is a chord, $$\angle OAB=45^{\circ}$$, and $$OA=8$$. Then, $$AB=$$ ___.
|
8 \sqrt{2}
|
math_4622
|
|
<image>
As shown in the figure, the cross-section of the channel is an isosceles trapezoid. The channel wall AB is √5 meters, and the slope is 1:0.5. Then the depth of the channel AC is meters.
|
2
|
math_5700
|
|
<image>
As shown in the figure, in $$\triangle ABC$$, $$D$$ and $$E$$ are points on $$AB$$ and $$AC$$ respectively. $$AF$$ bisects $$\angle BAC$$, intersecting $$DE$$ at point $$G$$ and $$BC$$ at point $$F$$. If $$\angle AED = \angle B$$, and $$AG:GF = 2:1$$, then $$DE:BC =$$ ___.
|
2:3
|
math_3100
|
|
<image>
As shown in the figure, in $\vartriangle ABC$, points D and E are on AB and BC, respectively, and $DE\parallel AC$. AE and CD intersect at point F. If the ratio of the areas ${{S}_{\vartriangle BDE}}:{{S}_{\vartriangle DEC}}=1:3$, then the ratio ${{S}_{\vartriangle DEF}}:{{S}_{\vartriangle AFC}}$ is .
|
1:16
|
math_222
|
|
<image>
In the figure, in the right triangle $$\text{Rt}\triangle ABC$$, $$AC=12$$, $$BC=5$$. The length of the altitude $$CD$$ on the hypotenuse is ___.
|
\dfrac {60}{13}
|
math_5116
|
|
<image>
Grandma Zhang bought a batch of pomelos and sold them at a retail market. It is known that the relationship between the weight of pomelos sold $$x$$ (kg) and the selling price $$y$$ (yuan) is as follows: According to the data in the table, if 10 kg of pomelos are sold, the selling price would be ______ yuan.
|
12.1
|
math_6927
|
|
<image>
As shown in the figure, in circle $$\odot O$$, $$\angle OAB=45\degree$$, and the distance from the center $$O$$ to the chord $$AB$$ is $$OE=2cm$$. What is the length of the chord $$AB$$? ______ $$cm$$.
|
4
|
math_516
|
|
<image>
A new media outlet conducted a survey on the public's welcome towards the early commercial use of '5G mobile communication technology' in our country. A total of 1000 people participated in the survey, with the number of people holding various attitudes as shown in the table: . To further understand the specific thoughts of the respondents, the media plans to select 50 people for a more detailed survey. The number of people who should be selected from those who hold a 'very welcome' attitude is.
|
36
|
math_5509
|
|
<image>
It is known that the base of a pyramid is a parallelogram, and the three views of the pyramid are shown in the figure (unit: m). What is the volume of the pyramid in m$^{3}$?
|
2
|
math_1794
|
|
<image>
A certain forage planting base planted 50 acres of three types of forage, A, B, and C, in 2019, with the planting ratio as shown in the figure. The base plans to expand the planting areas of varieties A and C in 2020, while keeping the planting area of variety B unchanged, which will reduce the planting area ratio of variety B to 10%. If the planting area ratio of variety C remains unchanged, what will be the planting area of variety C in 2020?
|
15
|
math_7743
|
|
<image>
As shown in the figure, trapezoid $$A_{1}B_{1}C_{1}D_{1}$$ is the perspective drawing of plane figure $$ABCD$$ (the perspective drawing is made using the oblique projection method). If $$A_{1}D_{1}\parallel O'y'$$, $$D_{1}C_{1}$$ is on $$O'x'$$, $$A_{1}B_{1}\parallel O'x'$$, and $$A_{1}D_{1}=1$$, $$A_{1}B_{1}=2$$, $$C_{1}D_{1}=3$$, then the area of plane figure $$ABCD$$ is ___.
|
5
|
math_4923
|
|
<image>
As shown in the figure, it is a numerical conversion machine. If the input value of $x$ is 2, then the output result is:
|
-2
|
math_450
|
|
<image>
The figure shows the three views of a geometric solid. If the volume of this solid is $$36$$, then its surface area is ___.
|
72
|
math_5623
|
|
<image>
Given the flowchart of a program as shown, if the values of $$x$$ input are $$0$$, $$1$$, $$2$$, and the program outputs the values of $$y$$ as $$a$$, $$b$$, $$c$$ respectively, then $$a+b+c=$$ ___.
|
6
|
math_4532
|
|
<image>
The flowchart of the program is shown in the figure. Its output result is ___.
|
127
|
math_7511
|
|
<image>
As shown in the figure, in the right triangle $$ABC$$, $$\angle ACB=90^{\circ}$$, $$\angle A < \angle B$$. The triangle $$ABC$$ is folded along the median $$OC$$, so that point $$A$$ lands on point $$D$$. If $$CD$$ is exactly perpendicular to $$MB$$, then what is the value of $$\tan A$$?
|
\dfrac{\sqrt{3}}{3}
|
math_3045
|
|
<image>
As shown in the figure, there are the following 3 conditions: 1. AC = AB, 2. AB ∥ CD, 3. ∠1 = ∠2. Select any 2 of these 3 conditions as premises, and the remaining 1 as the conclusion. The probability that the resulting proposition is a true statement is ___.
|
1
|
math_4127
|
|
<image>
As shown in the figure, in the right trapezoid $$ABCD$$, $$DC \parallel AB$$, $$CB \perp AB$$, $$AB=AD=a$$, $$CD=\dfrac{a}{2}$$, points $$E$$ and $$F$$ are the midpoints of segments $$AB$$ and $$AD$$, respectively. Then $$EF=$$ ___.
|
\dfrac{a}{2}
|
math_59
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.