# Examples for 9th grade

#### Number of problems found: 2595

- Rectangular trapezoid

In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v. - Quadrilateral 2

Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles. - Cable car

Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m. - Horizontal Cylindrical Segment

How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank? - Two numbers 7

The sum of two consecutive even numbers is 30. Find the numbers. - Map scale

Garden has on plan on a scale of 1: 150 width 22 cm and length 35 cm. What is the real area of the garden? - Angle of diagonal

Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - Scouts

Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type? - Volume of three cuboids

Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm. - Three friends

Three friends squirrels together went to collect hazelnuts. Zrzecka he found more than twice Pizizubka and Ouska even three times more than Pizizubka. On the way home they talked while eating and was cracking her nuts. Pizizubka eaten half of all nuts whi - Modulo

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

A pit is dug in the shape of a cuboid with dimensions 10mX8mX3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m X 30m. What is the increase in the level of the plot ? - Equilateral triangle

The equilateral triangle has a 23 cm long side. Calculate its content area. - Percentage reduction

Reducing the unknown number by 19% get number 700.7 Determine unknown number. - Word problem

348 students were on holiday in Hungary. 133 bought pizza, chips 28 pupils, 25 pupils bought soda, butter 26 pupils, 15 pupils fruits, vegetables 29 students. How much pay for all the food, if every meal cost 5.3 euros? - Savings

Paul has a by half greater savings than half Stanley, but the same savings as Radek. Staney save 120 CZK less than Radek. What savings have 3 boys together? - Mixture 2

How many liters of water must be added to 7 liters of a 20% solution to obtain a 10% solution? - Spruce height

How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree? - Numbers at ratio

The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers? - Three friends

Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much.

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