Examples for 9th grade - page 82

  1. Inscribed circle
    vpisana The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
  2. Diagonals
    rhombus_3 A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
  3. Magic number
    prof_einstein_1 The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend.
  4. Iron collecting
    paper_1 Class 7A collected 3.2 tonnes of iron more than class 7B. Together they collected 6.4 tonnes of iron to the secondary raw material collection. How much did each class collect?
  5. Mother and daughter
    family_20 The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?
  6. Storm
    storm-012 So far, a storm has traveled 35 miles in 1/2 hour in direction straight to observer. If it is currently 5:00 p. m. and the storm is 105 miles away from you, at what time will the storm reach you? Explain how you solved the problem.
  7. How far
    lighthouse_1 From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
  8. Embankment
    sss Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
  9. Cross section
    trapezium_right The cross section ABCD of a swimming pool is a trapezium. Its width AB=14 metres, depth at the shallow end is 1.5 metres and at the deep end is 8 metre. Find the area of the cross section.
  10. Big number
    modulo_1 hat is the remainder when dividing number 10 to 47 - 111 by number 9?
  11. 6 terms
    arithmet_seq Find the first six terms of the sequence. a1 = 7, an = an-1 + 6
  12. Remainder
    numbers2_35 A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
  13. Points on line segment
    segment Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
  14. Photocopier
    picture A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
  15. Modulo
    modulo Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
  16. Mushrooms
    huby_2 Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
  17. Percentages 5
    usd_1 $5.25 is 7 1/2% of what number?
  18. Scale factor
    cuboid_7 A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
  19. Rhombus construction
    rhombus_7 Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...
  20. Equation with abs
    abs Solve this equation with absolute value member: ?

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