# Examples for 9th grade - page 87

- Triangles

Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle? - Exponential equation

Determine the value of having y in the expression (3^y): (4^-1)=36.Y is a natural number greater than zero. - Is right-angled

Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 a √8) be a right triangle? - The train

The train passed the observer in the 20s and passed through a 1500m tunnel in 2 minutes. Calculate the speed (km/h) and train length. - Water tank

A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water. - Inscribed circle

Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC. - CuSO4 mixture

How many grams of solid CuSO4 we have to add to 450g of 15% CuSO4 solution to produce a 25% solution? - Construct

Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long. - Functions f,g

Find g(1) if g(x) = 3x - x^{2}Find f(5) if f(x) = x + 1/2 - Average age

The company of five people has an average age of 46 years. The average age of the first four is 43 years. How many years has the fifth member of this company? - The pole

The telegraph pole is supported by a 4 m bullet at 3/4 of its height, the end of which is at a distance 2.5 m from the pole post. Calculate the height of the telegraph pole. - Repay, interest, loan

Ramchacha takes a loan amount of 240000 from a bank for constructing a house at the rate of simple interest of 12% per annum. After 1 yr. of taking the loan he rents the house at the rate of 5200 per month. Determine the number of years he would take to re - Four numbers

The first number is 50% second, the second number is 40% third, the third number is 20% of the fourth. The sum is 396. What are the numbers? - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees - Sum of squares

The sum of squares above the sides of the rectangular triangle is 900 cm^{2.}Calculate content of square over the triangle's hypotenuse. - Pendulum

Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm. - Tangent 3

In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm. - Shadow

A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house? - Klara

Klara and Jitka went on a hiking trip at 13 o'clock at speed 5km/h. At 14 o'clock, Tomas ride on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road Tomáš caught the two girls? - Body diagonal - cube

Calculate the surface and cube volume with body diagonal 15 cm long.

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