# Examples for 9th grade - page 82

- Inscribed circle

The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c. - Diagonals

A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal. - Magic number

The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend. - Iron collecting

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? - Mother and daughter

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? - Storm

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. - How far

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? - Embankment

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. - Cross section

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. - Big number

hat is the remainder when dividing number 10 to 47 - 111 by number 9? - 6 terms

Find the first six terms of the sequence. a1 = 7, an = an-1 + 6 - Remainder

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 ? - Points on line 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. - Photocopier

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? - Modulo

Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 . - Mushrooms

Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them? - Percentages 5

$5.25 is 7 1/2% of what number? - Scale factor

A prism with a volume of 1458 mm^{3}is scaled down to a volume of 16mm^{3.}What is the scale factor in fraction form? - Rhombus construction

Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides... - Equation with abs

Solve this equation with absolute value member: ?

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