# Algebra - problems - page 92

- Prime factors

Write 98 as product of prime factors - Rectangle diagonal

The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm^{2}. - Square

Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm^{2}? - Expressions 3

If k(x+6)= 4x^{2}+ 20, what is k(10)=? - Motorcyclist

From Trutnov, the motorcyclist started at an average speed of 60km/hour. At 12.30hrs the passenger car was started at a speed of 80km/hour. How many hours and at what distance from Trutnov will car catch a motorcycle? - Diagonals of pentagon

Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm. - Find two

Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum. - Square into three rectangles

Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible. - Two trains

From station A, the freight train traveled at a speed of 40 km/h in 9h. When he drove 15km, the fast train started from station A in the same direction at a speed of 70km/h. When will it the freight train catch up? - Beds

At the summer camp, there are 41 chalets. Some rooms are 3-beds, some 4-beds. How many campers from 140 are living in 3-bed? - Barrel with water

The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel. - Simple equations

Solve system of equations: 5x+3y=5 5x+7y=25 - Rectangle - area, perimeter

The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle. - Clothes

Danka and Janka collect clothes. Danka had 9 more than Janka, so she gave her 7. Which now has more cloth and how many? - Mixing water

The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix? - There

There are 32 trees of three species in the orchard. 25% cherries, three eighty pears, others plums. How many plums are in the orchard? - SSA and geometry

The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer. - Integer

Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6. - Clock's gears

In the clock machine, three gears fit together. The largest has 168 teeth, the middle 90 teeth, and the smallest 48 teeth. The middle wheel turns around its axis in 90 seconds. How many times during the day do all the gears meet in the starting position? - Simple equation 5

Solve equation with fractions: X × 3/8 = 1/2

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