Examples for 9th grade - page 46
- Circle inscribed
Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
- Jane and Miro
Jane brother Miro is 42 years. And he is three times old as it was Jane when Miro was for so many years as there are now Jane. How old is Jane?
- 12 Moons
Good Marry came to ask twelve moons for help with collecting strawberries. All twelve moons 1200 strawberries picked in 20 minutes. But lazy months July and August cease tear after 5 minutes. How many minutes in total will take collect strawberries?
A trained athlete is able to exhale after a deep breath still 500 ml of air. At normal inhalation and exhalation is breathing 500 ml of air. Within one minute, one breath and exhaled 19 times. What part of breathing air per day is one exhalation?
The summer camp is 41 cottages. Rooms are for three and for four in them. How many of the 140 campers lives of three?
- Rectangle - sides 3
If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we incr
- Cube 7
Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
- Count of triangles
Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
- Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
In what quadrant is a 1501° angle?
- Three siblings
Three siblings have birthday in one day-today. Together they have 35 years today. The youngest is three years younger than middle and the oldest is 5 years older than middle. How old is each?
- Angles of a triangle
In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
- Freight train
The train carries 525 tons of limestone in 29 wagons. Wagons are 15 tonne and 20 tons. How many is 15 ton and how many is 20 ton wagons?
- The farmer
The farmer harvested 840 tons of grain in 2006, which was 44% less than in 2005, and one-fifth more than in 2004. How many tons of grain harvested in years 2005 and 2004?
How much of a mixed forest rangers want to cut down, if their head said: "We only cut down pine trees, which in our mixed forest 96%. After cut pine trees constitute 91% of all trees left."
- Smallest internal angle
Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
The product of two consecutive odd numbers is 899. What are this numbers?
- Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
- Hexa prism
Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
- Two numbers
The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number.