# Examples for 9th grade - page 83

- Quotient

Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4. - Three friends

Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor. - Coach

Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach? - Trees

Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples? - Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Equilateral triangle ABC

In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta - Three granaries

Three granaries hold 7,800 metric cent (q) of grain. In the first, 70 tonnes of grain was more than the second and in the third it was 120 tonnes less than in the second. How many grain were in each granary? - Two lands

The common area of the two neighboring lands is 964 m^{2}. The second land is 77 m^{2}smaller than twice the size of the first land. Find the areas of each land. - Years

Susan is 3 years and as she will be old as Teodor now him will be 11. How old is Teodor today? - Drying apples

By drying, apples lose 85% of their weight. How many kgs of dried apples do we get from 820 kilograms of fresh? - Forces on earth directions

A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object? - Hexagon area

The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area. - Chord

It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB. - Q of GP

Calculate quotient of geometric progression if a1=5 a a1+a2=12. - Sum of members

What is the sum of the first two members of the aritmetic progression if d = -4.3 and a3 = 7.5? - Cancer

Of the 80 people 50 people ill cancer. What percentage of people isn't ill? - Trapezium ABCD

In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60 - 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? - Shots

Determine the percentage rate of keeper interventions if from 32 shots doesn't caught four shots. - Coefficient

Determine the coefficient of this sequence: 7.2; 2.4; 0.8

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