9th grade (14y) + system of equations - examples
- Largest angle of the triangle
What is the largest angle of the triangle if the second angle is 10° greater than twice the first and the third is 30° smaller than the second?
- Isosceles triangle
The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
- Book read
If Petra read 10 pages per day, she would read the book two days earlier than she read 6 pages a day. How many pages does a book have?
- Ratio of two unknown numbers
Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
- Cars speeds
Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes?
- Two numbers
The sum of the two numbers is 1. Find both numbers if you know that half of the first is equal to one seventh of the second number.
Students of high school have 10 points for each good solved task. The wrong answer is deducted by 5 points. After solving 20 tasks, student Michael had 80 points. How many tasks did he solve correctly and how many wrong?
There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag
If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately?
One meter of the textile were discounted by 2.4 USD. Now 6 m of textile cost as before 3 m. Calculate the old and new price of 1 m of the textile.
Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
- Right triangle Alef
The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.
- Circle arc
Circle segment has a circumference of 13.26 mm and 252.03 mm2 area. Calculate the radius of the circle and size of central angle.
- Triangle ABC
Calculate the sides of triangle ABC with area 883 cm2 and if a: b: c = 15:7:19
Cyclist started at 5:00 from point N to point O. After 20 minutes, followed him at the same speed the second cyclist. Walker, which went from O to N, started at 5:40. After 56 minutes he met the first cyclist and after next 16 minutes the second cyclist. D
- Right triangle
Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle.
Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears?
- R triangle
Calculate the area of a right triangle whose longer leg is 9 mm shorter than the hypotenuse and 4 mm longer than the shorter leg.
- Barrel of oil
Barrel of oil weighs 282 kg. When it mold 56% oil, weighed 138 kg. What is the mass of the empty barrel?
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 23 cm and tb=14 cm.