# The most difficult problems - last page

- Reciprocal equation 2

Solve this equation: x + 5/x - 6 = 4/11 - Isosceles

Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area. - Concentric 6751

A circle K with radius r = 8 cm is given. How big a radius must a smaller concentric circle that divides a circle K into two parts with the same area? - Rectangles

How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm? (a rectangle with sides of 50cm and 450cm is considered to be the same as a rectangle with sides of 450cm and 50cm) - Thousand 6741

The museum sold seven thousand tickets in 3 days. We know that the second day sold 20% more tickets than the first day, and Day 3 sold 10% less than Day 2. How many tickets were sold on each day? - Square into three rectangles

Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible. - Merchant 6730

A merchant sells a blend of tea. Kilogram for 450 CZK. Another species for 900 CZK. Cheaper for 369 CZK. How much tea must buy per 5 kg of the mix? - Sandbox

Sandbox has area of 32 sq ft and length of 4 1/2 ft. What is width of sandbox. - Digits

Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z. - Geometric progression 4

8,4√2,4,2√2 - Algebra

If x+y=5, find xy (find the product of x and y if x+y = 5) - Simplify 3

Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution. - Adding mixed numerals

3 3/4 + 2 3/5 + 5 1/2 Show your solution. - Calculate 6706

Given a triangle KLM points K [-3.2] L [7, -3] M [8.5]. Calculate the side lengths and perimeter. - Calculate: 6686

We know the right angle γ, side b = 14 cm, and height vc = 8.8 cm in the right triangle ABC. Calculate: angle α = angle β = page a = page c = - Lampshade

The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm² of material will we need when we 10% is waste? - Complete 6639

Complete the number series with another number, which is 150 on average: 43 69 87 125 197 211 298 - Determine 6621

1) The function f is given: y = I 2-x I + 2. Determine the values of the function in points, ie F (-2), f (0), f (1), f (4,8). - 15 teachers

15 teachers teach for a combined amount of 128 days over a period of 64 days. What is this expressed as a percentage? - Accommodated 6614

Sixteen students on the brigade will be accommodated in one 8-bed and two 4-bed rooms. How many ways can they do that?

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