# Examples for 9th grade - page 32

1. Trapezoid IV In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
2. Vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
3. TV diagonal Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?
4. Invitations For every 5 minutes writes Dana 10 invitations, while Anna 14 invitations. How long will write together 120 invitations?
5. Sales off If a sweater sells for \$ 19 after a 5% markdown, what was its original price?
6. Summerjob Albert, Beny, Cyril and Dan worked on summerjob. From the total revenue Albert received 2/5, Beny 1/6 , 3/10 Cyril and Dan the rest which is 324 euros. How many euros earned every one of them?
7. Chalet The children were on a school trip to the mountain . One third of the journey went by the train and continue by bus. When you get off the bus, they remained a third of the distance they traveled by bus. What part of journey children went by the bus (wrote
8. 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
9. Simple interest 2 Find the simple interest if 13905 USD at 4.5% for 6 months.
10. Flowerbed Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =.
11. Train from Brno First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.
12. Mushrooms from the forest Magda and Tereza goes to pick mushrooms. Total found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms found Magda?
13. 3sides prism The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
14. Squaring the Circle Calculating side of the square with the same area as the circle of radius 18.
15. Lathe Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.
16. The professor's birthday Professor of mathematics had 57 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the direc
17. Skier At this point, the first skier lead 20 km before the second skier and travels at a constant speed 19 km/h. The second skier rides at 24 km/h. How long take him to catch up the first?
18. Cube wall Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
19. ISO Triangle V2 Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
20. Triangle Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.

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