# Equation - high school - examples - page 14

1. Difference AP 4 Calculate the difference of the AP if a1 = 0.5, a2 + a3 = -1.1
2. Combinations If the number of elements increase by 3, it increases the number of combinations of the second class of these elements 5 times. How many are the elements?
3. Elements If the number of elements is decreased by two the number of permutations is decreased 30 times. How many elements are?
4. Variation equation Solve combinatorics equation: V(2, x+8)=72
5. Parabola 3 Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ?
6. Wagons and cranes Several of the same cranes unloaded 96 wagons. If there were 2 more cranes there would be less 8 wagons for each crane. How many cranes were here?
7. Solve equation solve equation: ?
8. Trapezium internal angles A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.
9. Modulo Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
10. Equation of circle 2 Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
11. Lighthouse The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lightho If 5x + x² > 100, then x is not
13. Children The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
14. Digit sum The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
15. Ratio of sides The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
16. Clouds Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
17. Prove Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
18. Equation with abs Solve this equation with absolute value member: ?
19. Sphere equation Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
20. Flying The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?

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