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math_4159 | <image>
As shown in the figure, in the right triangle $$\text{Rt} \triangle ABC$$, points $$D$$ and $$E$$ are on the hypotenuse $$AB$$, and $$BD=BC$$, $$AE=AC$$. What is the measure of $$\angle DCE$$ in degrees? | 45 | 8 | false |
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math_6586 | <image>
As shown in the figure, the parabola $$y=x^{2}-2x-3$$ intersects the $$x$$-axis at points $$A(-1,0)$$ and $$B(3,0)$$, and intersects the $$y$$-axis at point $$C(0,-3)$$. $$M$$ is the vertex of the parabola. If the parabola is translated upwards by 3 units parallel to the $$y$$-axis, then the area swept by the curve $$CMB$$ during the translation is ___ (area units). | 9 | 4 | false |
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math_6455 | <image>
If in the system of equations , x is twice y, then a = ______. | -6 | 16 | false |
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math_6808 | <image>
Represent the irrational numbers $\sqrt{11}$, $\sqrt{5}$, and $-\sqrt{3}$ on a number line. Among these three irrational numbers, which one is covered by the ink (as shown in the figure)? | \sqrt{11} | 16 | false |
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math_6049 | <image>
As shown in the figure, Xiaoming walked 5 meters forward from under a street lamp and found that the length of his shadow DE on the ground is 2 meters. If Xiaoming's height is 1.6 meters, then the height of the street lamp from the ground AB is meters. | 5.6 | 1 | false |
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math_1335 | <image>
Run the flowchart shown in the figure. If the input value of $$m$$ is $$2$$, then the output value of $$i$$ is ___. | 4 | 5 | false |
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math_8070 | <image>
The histogram below shows the frequency distribution of scores for 48 students in a math test (scores are integers only). The height ratio of the rectangles from left to right is 1:3:6:4:2. According to the graph, the number of students with scores in the range of 70.5 to 80.5 is . | 18 | 16 | false |
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math_5364 | <image>
As shown in the figure: To measure the height of the flagpole AB on the opposite bank of the river, the angle of elevation from point C to the top A is measured to be 30°. Moving 20m in the direction of CB to point D, the angle of elevation to the top A of the flagpole is measured to be 45°. What is the height of the flagpole AB in meters? (Round to 0.1m) | 27.3 | 12 | false |
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math_1114 | <image>
In the figure, $AB \parallel GH \parallel CD$, point $H$ is on $BC$, and $AC$ intersects $BD$ at point $G$. Given $AB=2$ and $CD=3$, find the length of $GH$. | 1.2 | 8 | false |
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math_2620 | <image>
Place a set of triangular rulers as shown in the figure, then the obtuse angle formed by the two hypotenuses $$\alpha =$$___ degrees. | 165 | 0 | false |
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math_374 | <image>
As shown in the figure, the linear functions $$y=-\dfrac {2}{3}x+b$$ and $$y=ax-2$$ intersect at point $$P\left(-1,2\right)$$. Based on the graph, the solution set of the inequality $$-\dfrac {2}{3}x+b>ax-2$$ is ___. | x>-1 | 16 | false |
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math_5519 | <image>
In a shooting training session, the scores of a group are shown in the table below. It is known that the average score of the group is $$8$$ points. Therefore, the number of people who scored $$9$$ points is ___. | 3 | 16 | false |
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math_5570 | <image>
A rectangular piece of white paper, 25cm in length and 10cm in width, is glued together as shown in the figure below. The width of the glued part is 2cm. Let the total length of y cm be obtained after gluing x pieces of white paper. The functional relationship between y and x is. | y=23x+2 | 5 | false |
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math_870 | <image>
As shown in the figure, right triangle ABC is rotated 40° counterclockwise around point C to obtain triangle EDC, with point D now on AB. What is the measure of ∠BAC in degrees? | 20 | 0 | false |
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math_3470 | <image>
As shown in the figure, in the right triangle $$\text{Rt}\triangle ABP$$, $$\angle ABP=90^{\circ}$$, $$BC \perp AP$$, with the foot of the perpendicular at point $$C$$, and given that $$AB=2\sqrt{6}$$, $$AC=4$$, then $$PB=$$ ___. | 2 \sqrt{3} | 1 | false |
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math_4871 | <image>
In the figure, in $$△ABC$$, $$AB=10$$, $$AC=7$$, $$AD$$ is the angle bisector, $$CM⊥AD$$ at $$M$$, and $$N$$ is the midpoint of $$BC$$. Then, $$MN=$$______． | 1.5 | 5 | false |
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math_5796 | <image>
The population consists of 30 individuals numbered $$01$$, $$02$$, $$\cdots$$, $$29$$, $$30$$. Using the random number table below, select 5 individuals. The selection method starts from the 3rd and 4th columns of the 1st row and selects two digits at a time from left to right. The number of the 5th selected individual is ______. | 29 | 2 | false |
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math_2032 | <image>
As shown in the figure, points A, B, and C are all on circle O. If ∠AOB = 80°, then ∠ACB = °. | 40 | 16 | false |
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math_1824 | <image>
As shown in the figure, the perimeters of $$ABCD$$ and $$DCFE$$ are equal, and $$∠BAD=60^{\circ}$$, $$∠F=110^{\circ}$$, then the measure of $$∠DAE$$ is ___ degrees. | 25 | 1 | false |
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math_7002 | <image>
As shown in the figure, in $\vartriangle ABC$, $AB=AC=10cm$, $BC=8cm$. Point D is the midpoint of AB, and point P moves from point B to point C on segment BC at a speed of $3cm/s$. At the same time, point Q moves from point C to point A on segment CA. If the speed of point Q is the same as that of point P, after how many seconds will $\vartriangle BPD \cong \vartriangle CQP$? | 1 | 13 | false |
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math_1149 | <image>
As shown in the figure, Xiao Liang starts from point A, moves forward 10 meters, turns right 15 degrees, then moves forward another 10 meters, turns right 15 degrees again, and so on. He continues this pattern until he returns to the starting point A for the first time. How many meters has he walked in total? | 240 | 16 | false |
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math_5098 | <image>
The Forbidden City in Beijing was the imperial palace of the Ming and Qing dynasties in China, also known as the 'Purple Forbidden City.' It is located at the center of Beijing's central axis. The Forbidden City is 750 meters wide from east to west and 960 meters long from north to south, covering an area of 720,000 square meters. 300 students from Ape School are going to visit the Forbidden City. There are two types of buses available for rent: large buses and minibuses. Please first write down the most cost-effective rental plan, and then calculate the total cost of ______ yuan. | 6100 | 0 | false |
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math_7694 | <image>
The voltage of a certain type of battery is a constant value. When using this power source, the function relationship between current Ι(A) and variable resistance R(Ω) is shown in the figure. When the current of the electrical appliance is 10A, the variable resistance of the electrical appliance is ______ Ω. | 6Ω | 0 | false |
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math_532 | <image>
In the figure, in $$\triangle ABC$$, $$D$$ and $$E$$ are the midpoints of $$AB$$ and $$AC$$, respectively. The ratio of the area of $$\triangle ADE$$ to the area of $$\triangle ABC$$ is ___. | 1:4 | 16 | false |
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math_8009 | <image>
Execute the algorithm flowchart shown in the figure, then the value of the output $$S$$ is ___. | -5 | 0 | false |
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math_2691 | <image>
As shown in the figure, quadrilateral $$ABCD$$ is an inscribed square in circle $$⊙O$$. If the area of the square is $$4$$, then the area of circle $$⊙O$$ is ___. | 2\pi | 16 | false |
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math_7849 | <image>
As shown in the figure, to measure the height of the Eiffel Tower in France, a baseline $$AB$$ is selected on the ground, where $$AB = 324\sqrt{4-\sqrt{3}}\ \unit{m}$$. At point $$A$$, the angle of elevation to the top of the tower $$P$$ is $$\angle OAP = 30^{\circ}$$, and at point $$B$$, the angle of elevation to the top of the tower $$P$$ is $$\angle OBP = 45^{\circ}$$. It is also measured that $$\angle AOB = 60^{\circ}$$. What is the height of the tower in meters? | 324 | 4 | false |
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math_2741 | <image>
The flowchart of a program is shown in the figure. If the output is $$S = 10$$, then the natural number $$a =$$ ______. | 4 | 16 | false |
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math_4690 | <image>
The partial graph of the function $f(x)=A\sin (\omega x+\varphi )$ $(A > 0, 0 \le \varphi < 2\pi )$ is shown in the figure. What is the value of $f(2019)$? | -1 | 2 | false |
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math_3331 | <image>
Execute the program flowchart shown below. If the input value of n is 6, then the output value of S is. | 15 | 16 | false |
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math_941 | <image>
As shown in the figure, lines $$AD$$ and $$BC$$ intersect at point $$O$$, and $$AB \parallel CD \parallel EF$$. If $$CE=2$$, $$EB=4$$, and $$FD=1.5$$, then $$AD=$$ ___. | 4.5 | 2 | false |
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math_3693 | <image>
"The 'Domino Effect' tells us: a minimal force may cause only an imperceptible gradual change, but what it triggers could be a dramatic transformation, with each subsequent energy release being greater than the last$$\cdots \cdots $$ The diagram shows the designer placing identically sized dominos, arranged parallel to each other, with their length, width, and height (units: $$\unit{cm}$$) as shown. If the first domino must fall and touch the second domino at the $$\dfrac{3}{5}$$ height (from the bottom up) when it falls, then the distance between the two dominos is ___ cm. | 8 | 0 | false |
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math_4660 | <image>
According to the program shown in the figure, if the initial input value is x=5, then the final output result is. | 120 | 15 | false |
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math_4932 | <image>
The table below shows the water consumption (in units: hundred tons) of a factory from January to April: From the scatter plot, it can be seen that there is a good linear correlation between water consumption $$y$$ and month $$x$$. The linear regression equation is $$y=-0.7x+a$$. What is the value of $$a$$? | 5.25 | 16 | false |
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math_7674 | <image>
As shown in the figure, in the spatial quadrilateral $$ABCD$$, $$E$$, $$F$$, $$G$$, and $$H$$ are points on $$AB$$, $$BC$$, $$CD$$, and $$DA$$ respectively, and quadrilateral $$EFGH$$ is a rhombus. If $$AC \parallel$$ plane $$EFGH$$, $$BD \parallel$$ plane $$EFGH$$, $$AC = m$$, and $$BD = n$$, then what is the ratio of $$AE$$ to $$EB$$? | m:n | 13 | false |
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math_5291 | <image>
In triangles $$\triangle ABC$$ and $$\triangle AEF$$, $$B$$ is the midpoint of $$EF$$, $$AB=EF=1$$, $$CA=CB=2$$. If $$\overrightarrow{AB} \cdot \overrightarrow{AE} + \overrightarrow{AC} \cdot \overrightarrow{AF} = 2$$, then the angle between $$\overrightarrow{EF}$$ and $$\overrightarrow{BC}$$ is ___. | \dfrac{\pi}{3} | 2 | false |
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math_6239 | <image>
The chart shows the visitor index statistics for the Palace Museum in Beijing during the National Day holiday in 2018 (the visitor index is the ratio of the daily visitor count to the visitor count on October 1, 2018). According to the information in the chart, without considering other factors, if Xiaoyu wants to visit the Palace Museum with fewer visitors during this year's National Day, it is best to visit on October __. | 7 | 15 | false |
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math_3639 | <image>
As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at point O. If AB = 3 and OC = 2.5, then the length of BC is. | 4 | 16 | false |
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math_5582 | <image>
As shown in the figure, in the cube $$ABCD-A_{1}B_{1}C_{1}D_{1}$$, what is the cosine of the angle formed by the diagonal $$B_{1}D$$ and the plane $$A_{1}D$$? | \dfrac{\sqrt{6}}{3} | 0 | false |
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math_7111 | <image>
As shown in the figure, an activity area consists of a right-angled triangle and a square. The two legs of the triangle are $$10\ \unit{m}$$ and $$24\ \unit{m}$$, respectively. What is the area of this venue in square meters? | 796 | 7 | false |
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math_7736 | <image>
Given the graph of the quadratic function y=2x^2 as shown in the figure, if the x-axis is shifted 2 units up along the y-axis, it intersects the parabola at points A and B. The area of triangle AOB is. | 2 | 5 | false |
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math_2926 | <image>
Any polygon can be divided into several triangles using the method shown in Figure (1). According to the method in Figure (1), the dodecagon in Figure (2) can be divided into ______ triangles. | 10 | 16 | false |
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math_2652 | <image>
As shown in the figure, there are the graphs of the inverse proportion functions $y=\frac{1}{x}$ and $y=-\frac{1}{x}$, and a circle centered at the origin with a radius of $2$. Then, ${{S}_{shaded}}=$． | 2\pi | 2 | false |
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math_6208 | <image>
Read the following flowchart. If the input $$x=3$$, then the output $$y$$ is ___. | 40 | 16 | false |
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math_2429 | <image>
The pseudocode of an algorithm is shown in the figure. If the input value of $x$ is $32$, then the output value of $y$ is. | 5 | 16 | false |
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math_1508 | <image>
In the cube $ABCD-{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}$ with an edge length of 6, $F$ is the midpoint of edge $AD$, and $E$ is a point on the line segment $C{{C}_{1}}$. The volume of the tetrahedron $E-FD{{D}_{1}}$ is. | 18 | 15 | false |
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math_4127 | <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 | 0 | false |
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math_6188 | <image>
Using the rectangular sheet shown in the figure with a length of $$\quantity{31.4}{cm}$$ and a width of $$\quantity{6.28}{cm}$$, form a cylinder. The area of the base circle is ___ $$\unit{cm^{2}}$$ ($$ \pi $$ is taken as $$3.14$$) | 78.5 | 9 | false |
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