Expression of a variable from formula - problems

  1. Isosceles
    rr_lichobeznik_1 Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
  2. Cube into sphere
    sphere_in_cylinder_1 The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
  3. Digits
    seq_5 Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z.
  4. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  5. Cube edges
    cube_shield_3 The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.
  6. Ellipse
    elipsa Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
  7. Area of iso-trap
    diagons-of-an-isosceles-trapezoid Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other.
  8. Simplify 2
    expr Simplify expression: 5ab-7+3ba-9
  9. Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  10. A square
    rhombus3_3 A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
  11. Rectangles
    rectangle_15 The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
  12. Book reading
    books_30 If we read the book at a speed of 15 pages a day, we read it 3 days before we read it at a speed of 10 pages per day. If I read at 6 pages per day, how many days will I read the book?
  13. The tank
    nadrz_15 The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank?
  14. The sum 2
    seq_4 The sum of five consecutive even integers is 150. Find the largest of the five integers. A.28 B.30 C.34 D.54 Show your solution and explain your answer.
  15. Right Δ
    ruler Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
  16. Tereza
    cube The cube has area of base 225 mm2. Calculate the edge length, volume and area of its surface.
  17. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  18. IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
  19. Theater
    SND The theater has in each row with 10 seats. Ticket to the first 5 rows is for 21 USD. In next rows is for 13 USD. The theater was completely sold out. Revenue was 3520 USD. How many rows are in the theater?
  20. Floating barrel
    floating_barrel Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.

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