# The most difficult examples

- Parabola 3

Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ? - Straight lines

Draw two lines c, d so that c || d. On line c mark points A, B, from point A start perpendicular to line c, from point B perpendicular to line c. - Regular octagon

Draw the regular octagon ABCDEFGH inscribed with the circle k (S; r = 2.5 cm). Select point S' so that |SS'| = 4.5 cm. Draw S (S '): ABCDEFGH - A'B'C'D'E'F'G'H'. - Draw a trapezoid

Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task. - Box and whisker plot

Construct a box and whisker plot for the given data. 56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43 - Right triangle

Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC. - 10 pieces

How to divide the circle into 10 parts (geometrically)? - Three points

Mark three points E, F and G in the plane not lie on one line. a) Draw a line segment FG b) Construct halfline (ray) EG c) Draw a line EF - The sum graphically

Draw a graphically sum of the all sides of 4-gon ABCD. - Draw it!

Draw two lines c, d that c || d. On line c mark the points A, B. By point A lead perpendicular line to c. By point B lead perpendicular line to c. - Square ABCD

Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4]. - Equation with abs

Solve this equation with absolute value member: ? - Parcel 4

To send a parcel by messenger within city limits costs 60 cents for the first pound and 48 cents for each additional pound. What is the cost, in cents, of sending a parcel weighing p=6 pounds? - Modulo

Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 . - Square area

Complete the table and then draw each square. Provide exact lengths. Describe any problems you have. Side Length Area . - Ratio iso triangle

The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure. - Photo enlarge

Mark wants to enlarge a 4-inch by 6-inch photo so that it has a height of 15inches. Use a ratio table to determine the new width of the photo. - Plot

The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the rectan - Four circles

1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm. - Volume and area

What is the volume of a cube which has area of 361 cm^{2}?

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