# Grade - examples - page 86

- Trapezoid thirds

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

Calculate the absolute value of complex number -15-29i. - Rectangles - sides

One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm^{2}. What are the dimensions of the original rectangle? - Diplomas

Suzanne helped write out diplomas. Issuance its first took 3 minutes, each next 2.3 minutes. How much time it will take to write out n=16 diplomas (including the first), write out this pace? - Quadratic equation

Determine the numbers b, c that the numbers x_{1}= -1 and x_{2}= 3 were roots of quadratic equation: ? - Truck PRG-BA

Truck driving on highway from Prague to Bratislava at average speed of 72 km/h. At the moment when the truck passes 54 kilometer from Prague passenger car departs from Prague which travel to Bratislava at speed 90 km/h. When and where (at waht highway ki - Right triangle trigonometrics

Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Area of RT 2

Calculate the area of right triangle whose legs have a length 5.8 cm and 5.8 cm. - Cylinder

The cylinder-shaped container has 80 liters of water. The water reaches 45 cm height. How many liters of water will be in a container if water level extend to a height 72 cm? Write the result in liters, write down only as a whole or decimal number. - Cyclist

Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target? - Equilateral triangle v2

Equilateral triangle has a perimeter 36 dm. What is its area? - Workshop

In the workshop have to be produced for 5 days 2000 components. How many components must be produced in the workshop every day and how much per hour, if shift is 8 hours. - The store

The store received the same number of cans of peas and corn. The first day sold 10 cans of peas and 166 cans ofcorn so that left 5 times more peas than corn cans. How many cans of each kind were in the store? - Hexa prism

Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm. - Dices throws

What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once - Two numbers

The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number. - UV radiation

The glass of 1 mm thickness absorb 4% of UV radiation passing through. How many percent of UV rays absorb glass with a thickness 1.1 cm, made from 1 mm thick those glasses? - Catheti

The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs. - Cottages

The summer camp is 41 cottages. Rooms are for three and for four in them. How many of the 140 campers lives of three?

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