# Quadratic equation - problems - page 8

1. RT perimeter
The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
2. A mast
A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?
3. Rectangle
Calculate area of the rectangle if its length is 12 cm longer than its width and length is equal to the square of its width.
Which of the points belong function f:y= 2x2- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
5. Time gone
Square of Richard age equals the age of his mother. When he will bw two times older then his mom will be 7/2 times older than he. How old is Richard and his mom?
6. Geometric seq
Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
7. The gardener
The gardener bought trees for 960 CZK. If every tree was cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
8. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
9. 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?
10. Variation equation
Solve combinatorics equation: V(2, x+8)=72
11. 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?
12. Solve equation
solve equation: ?
13. Combinations
How many elements can form six times more combinations fourth class than combination of the second class?
14. MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
15. Right triangle from axes
A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ?
16. 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.
If 5x + x² > 100, then x is not
18. Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
19. A bridge
A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
20. 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?

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