# Algebra - problems - page 61

- Pyramid Z8–I–6

Each brick of pyramid contains one number. Whenever possible, the number in each brick is lowest common multiple of two numbers of bricks lying directly above it. That number may be in the lowest brick? Determine all possibilities. - Tree

Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree? - Tickets

On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)? - Ruler

How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm. - Primes 2

For what primes p,q,r is true: p^{2}-(q+r)^{2}=647 - Cuboid edges in ratio

Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm^{3.} - Cuboid easy

The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid. - Infirmary

Two thirds of children from the infirmary went on a trip seventh went to bathe and 40 children remained in the gym. How many children were treated in the infirmary? - Land - isosceles trapezoid

Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m. - VCP equation

Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0 - Hello adding

Fill letters instead of digits so the indicated sum (equal letters represent equal digits). What number is hidden under the letter J? A A H A H O A H O J -------------------------- 4 3 2 1 - Church roof 2

The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m^{2}of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste? - Divisible by 5

How many three-digit odd numbers divisible by 5, which are in place ten's number 3? - Tailor

From the rest of the cloth tailor could cut off either 3 m in men's suits without vest or 3.6 m with vest. What shortest possible length could the rest of the cloth have? How many suits a) without a vest b) with vest could make the tailor from the re - Two numbers

We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers. - Equation

? - AP 6

Calculate the first five items of an arithmetic sequence if it is given: a_{2}– a_{3}+ a_{5}= 20 a_{1}+ a_{6}= 38 - Working together

One painter paint the nursery in 10 days, the second in 8 days. How many days will the nursery be painted if they work together? - Cuboid surface

Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm. - Diagonals of diamond

Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.

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