Examples for 9th grade - page 20
- Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 48000 cm3. What is the area of surface of the prism?
Mother and Kate together weigh 27 kg more than the father. Father weighs 8.4 kg more than mother. Father weight 35 kg more than Kate. Determine weights of father mother and Kate.
- Count of triangles
Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
Perpendicular pole high 6 m tall broke and its toe fell 2.8 m from the bottom of the pole. At what height above the ground pole broke?
At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 24 L of 36-percent solution. What amount of solution from each container is needed to mix?
At the table sit 12 people, 6 on one side and 6 on the other side. Among them are 5 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
- Triangle SSS
Calculate perimeter and area of a triangle ABC, if a=58, b=83 and c=31.
- Cube volume
The cube has a surface of 384 cm2. Calculate its volume.
Shepherd tending the sheep. Tourists asked him how much they have. The shepherd said, "there are fewer than 500. If I them lined up in 4-row 3 remain. If in 5-row 4 remain. If in 6-row 5 remain. But I can form 7-row." How many sheep have herdsman?
Find the cuboid that has the same surface area as the volume.
Smiths paid a deposit for a vacation of two-sevenths of the total price of the vacation. Then paid also € 550. How much cost their vacation?
- Copy typist
Typist for 12 hours rewritten 15% of the manuscript. After how many hours he will done 35% of the manuscript?
Determine the number of items when the count of variations of fourth class without repeating is 50 times larger than the count of variations of third class without repetition.
- Midpoint of segment
Point A has coordinates [15; 1] and the midpoint of the segment AB is the point [-20; 13]. What are the coordinates of point B?
Man goes with a dog on a long walk 18 km from the house. Man is walking at speed 5.3 km/h and a dog that constantly running between house and man at 17.1 km/h. How many kilometers will run the dog when they reach their destination?
For vector w is true: w = 2u+2v. Determine coordinates of vector w if u=(-8, -5), v=(18, 19)
A cyclist is moving at 26 km/h and follow pedestrian who is walking at speed 7 km/h. Walker has an advantage 13 km. How long take cyclist to catch up with him?
Calculate distance between two points Z[7; -9] and U[-10; -8].
On the circle k with diameter |MN| = 41 J lies point J. Line |NJ|=12. Calculate the length of a segment JM.
- Combinations of sweaters
I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?