# Line + reason - math problems

#### Number of problems found: 26

- Divide an isosceles triangle

How to divide an isosceles triangle into two parts with equal contents perpendicular to the axis of symmetry (into a trapezoid and a triangle)? - Double-track line

A 160 m long passenger train runs on a double-track line in one direction at a constant speed of 54 km/h, and a 240 m long express train in the opposite direction. a) How fast is the express train if passing the passenger train driver for 6 s? b) How long - Points in space

There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - Dodecagon

Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - Three parallels

The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - Three lines

At 6 am, three bus lines are departing from the station. The first line has an interval of 24 minutes. The second line has an interval of 15 minutes. The third line runs at regular intervals of more than 1 minute. The third line runs at the same time as t - Hexagon

Divide a regular hexagon into lines into nine completely identical parts; none of them must be in a mirror image (individual parts can only be rotated arbitrarily). - Set of coordinates

Consider the following ordered pairs that represent a relation. {(–4, –7), (0, 6), (5, –3), (5, 2)} What can be concluded of the domain and range for this relation? - Find the

Find the image A´ of point A [1,2] in axial symmetry with the axis p: x = -1 + 3t, y = -2 + t (t = are real number) - The publisher

The publisher prepares the release of the dictionary. Print preparation costs no matter the number of printed copies of 150000 CZK. The printer charges 80 CZK for one print. A) What are the costs of one dictionary if 5000 copies printed? B) For what numbe - Prove

Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Lines

How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line? - Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side. The segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - 2d shape

Calculate the content of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of the segment AB is 5 cm. - Points in plane

The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points? - Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE is divided into a triangle and parallelogram, as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE, and the area of the triangle CDE is 3 cm^{2}. Determine the area of the trape - Z9-I-4

Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row, she wrote a sum of this number and its one nines. Fina - Hexagon rotation

A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - Right triangles

How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality). - Salat

Grandmother planted salad. In each row, he planted 13 seedlings. After a morning frost, many seedlings died. In the first row, five seedlings died. In the second row, two seedlings died more than 1st row. In the third row, three seedlings died less than 1

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