# Examples for 9th grade - page 62

- Inscribed circle

XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm. - Dollars

Mama split 760 dollars Jane, Dane and Eva as follows: Jane got three times more than Dane and Dane and got 40 more than Eva. How much does get each of them? - Reducing number

Reducing the an unknown number by 28.5% we get number 243.1. Determine unknown number. - Students

In the front row sitting three students and in every other row 11 students more than the previous row. Determine how many students are in the room when the room is 9 lines, and determine how many students are in the seventh row. - Painters

Five painters painting the fence for eight days. How many days over will take work if paint the fence only four decorators? - Dining room

The dining room has 11 tables (six and eight seats). In total there are 78 seats in the dining room. How many are six-and eight-seat tables? - The tent

The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m^{2}of cloth we need to make the tent if we have to add 7% of the seams? How many m^{3}of air will be in the tent? - Bath salts

Bath salt A weighs 900 grams and costs 36,40 CZK. Bath Salts B weighs 1000 grams, but costs 85 CZK. How much is a bath salt A cheaper than B one? - Sum 10

What is the probability that two dice throw twice in a row will result the sum of 10? - Forces

Determine the resultant of two perpendicular forces F_{1}= 560 N and second force of 25% smaller. - Cube diagonals

Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm. - Pears

Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears. - Locomotive

Locomotive pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done? - Salt

Sea water containing 5% salt. How many kg of fresh water necessary to pour into 40 kg of sea water so that the salinity fell to 2%? - Four swords

Obelix has three helmets, four swords and five shields. How many swords must make at the blacksmith forge Metallurgix to be able to walk another 90 days in unique armor? - Sides od triangle

Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm. - Two rooms

Woman cleans the room in 30 minutes a man in 90 minutes. How long will take they clean two rooms? - Copper wire

What is the weight of 1000 m copper wire with a diameter of 5 mm when rezistivity p = 8.8 g / cm^{3}? - Consecutive numbers

Sum of ten consecutive numbers is 105. Determine these numbers (write first and last). - Umbrella

Can umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm.

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