# Examples for 9th grade - page 91

- Construct

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

How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution? - Tetrahedron

What is the angle of the sides from the base of a three-sided pyramid where the sides are identical? - Sale discount

The product was discounted so that eight products at a new price cost just as five products at an old price. How many percents is the new price lower than the old price? - Butter

At the Orville redenbocher popcorn factory there is a tank of artificial butter substitute which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain? - Exponential equation

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

Our house would paint four painters in 14 days. How long could it paint five painters? How long will it take if two other painters will come to help after 5 days? - 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. - 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? - Bicycle gear

The pedal bicycle wheel has 56 teeth and a rear 20 gear tooth. How many times does the bicycle wheel turn when you make 20 turns of the pedal wheel? - Two diggers

Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers. - Body diagonal - cube

Calculate the surface and cube volume with body diagonal 15 cm long. - 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? - PIN code

PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second. - 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. - Functions f,g

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

Mother bought 21 desserts on the occasion of Mirka's birthday one tips was 9 CZK and the kremlin cost 12 CZK. For all desserts, she paid 213 CZK. How many kremlins and how many tips mums did buy? - Cross road

From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes?

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