# Grade - examples - page 74

1. Decomposition
Make decomposition using prime numbers of number 155. Result write as prime factors (all, even multiple)
2. Rhombus
ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
3. Lie/do not lie
The function is given by the rule f(x) = 8x+16. Determine whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for the your answer.
4. Two wine
In 2:1 mix wine solution cost 4.1 USD. In 1:2 mix wine solution cost 4.5 USD. How much cost liter of each wine?
5. Three digits number
From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there?
In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
7. Exponential equation
Solve exponential equation (in real numbers): 98x-2=9
8. Traffic collision
When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village.
9. Right triangle
Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
10. Coordinate
Determine missing coordinate of the point M [x, 120] of the graph of the function f bv rule: y = 5x
11. Mrak - cloud
It is given segment AB of length 12 cm, where one side of the square MRAK laid on it. MRAK's side length 2 cm shown. MRAK gradually flips along the line segment AB the point R leaves a paper trail. Draw the whole track of point R until square can do the.
12. Tons of coal
Coal hopper has a capacity of 285 liters. How many tons is it? The bulk density of coal is 916 kg/m3.
13. Diamond
Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.
14. Cellar
Cellar for storing fruit has a rectangular base with sides 14 m and 7 meters. You should paint sidewall to 2 m. How m2 surface must be painted?
Once upon a time, we learned in school that the Russians have "wider" tracks than our, because they have less tolerable ground. In truth, decide olny area of sleepers, no track gauge. Calculate how many millimeters, our track 1435 mm different from the R
16. Circle chord
Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.
17. Rabbits
Michael breeding rabbits. His 7 rabbits will eat 98 feed rations for 7 days. How many equal portions of feed should be eat 5 rabbits in 6 days?
18. Powers
Is true for any number a,b,c equality:? ?
19. Similarity
The area of the regular 10-gon is 563 cm2. The area of similar 10-gon is 606 dm2. What is the coefficient of similarity.
20. Tent
Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.

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