# Examples for 9th grade - page 32

1. Two workers
Two workers carry will do certain work for 12 days. After 8 days of working was one removed, and then the other finished the job alone in 10 days. For how many days would do this work alone each worker?
2. ISO trapezoid v2
bases of Isosceles trapezoid measured 12 cm and 5 cm and its perimeter is 21 cm. What is the are of a trapezoid?
3. Diagonal
Diagonal of the rectangle has length 46.4 cm. Angle between diagonal and londer sife of rectangle is 22°. Calculate area of the rectangle.
4. 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?
5. Invitations
For every 5 minutes writes Dana 10 invitations, while Anna 14 invitations. How long will write together 120 invitations?
6. 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?
7. TV diagonal
Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?
8. Resistors
Two resistors connected in series give the resulting resistance 216Ω and 48Ω in parallel. Determine the resistance of this resistors.
9. 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?
10. 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
11. 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
12. Raffle
How many raffle tickets must be purchased by Peter in raffle with issued 200 tickets if he wants to be sure win at least 3 price? In the raffle draws 30 prices.
13. Sales off
If a sweater sells for \$ 19 after a 5% markdown, what was its original price?
14. Simple interest 2
Find the simple interest if 13905 USD at 4.5% for 6 months.
15. 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.
16. 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 =.
17. 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?
18. Squaring the Circle
Calculating side of the square with the same area as the circle of radius 18.
19. 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.
20. Lathe
Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.

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